Intro to Artificial Intelligence: CS203 Lecture

CS203 Artificial intelligence Dr. Doaa El-Shahat Lecturer at Computer Science Department Zagazig University, Egypt Lecture 1 An Introduction to Artificial Intelligence Dr. Doaa El-Shahat Lecturer at Computer Science Department Zagazig University, Egypt Content ▪ What is intelligence? ▪ Artificial intelligence in daily life ▪ What is artificial intelligence? ▪ History of Artificial intelligence. ▪ Foundation of Artificial intelligence. Artificial intelligence in daily life Digital assistants •Cortana (Microsoft) Siri (Apple) Alexa (Amazon) https://www.youtube.com/watch?v=whMS3QbYAP0 Artificial intelligence in daily life Search engines ▪ ▪ ▪ ▪ ▪ Google Opera Firefox Safari Internet explorer Artificial intelligence in daily life Social media ▪ Facebook ▪ Instagram ▪ YouTube ▪ TikTok Artificial intelligence in daily life ▪ Google translate ▪ QuillBot ▪ Grammarly ▪ ChatGPT ▪ Deepseek Artificial intelligence in daily life What is intelligence? ▪ Intelligence is the ability to learn, solve problems, and use knowledge to adapt to new situations. What is Artificial intelligence? ▪ Some definitions of AI, organized into four categories (Rusell and Norvig): Thinking humanly Thinking rationally “Cognitive modeling approach” “Laws of thought approach using logic” Acting humanly Acting rationally “Turing test ” “The rational agent approach” • Rationally= doing the right thing • Acting= behavior What is Artificial intelligence? ▪ Some definitions of AI, organized into four categories: Systems that act like humans Systems that act rationally Turing test approach The rational agent approach Systems that think like humans Systems that think rationally Cognitive modeling approach Laws of Thought approach using logic What is Artificial intelligence? ▪ Some definitions of AI, organized into four categories: Systems that act like humans Systems that act rationally The art of creating machines that perform functions that require human intelligence. (Kurzweil, 1990) Systems that think like humans Systems that think rationally Approach 1: Acting Humanly •Turing test (Imitation game): ▪It is an ultimate test for acting humanly. ▪ It is a test for machine intelligence. ▪Computer and human both interrogated by a judge. ▪ The computer passes the test if the judge can’t tell the difference. Alan Turing, 1950: was an English mathematician, wartime code-breaker and pioneer of computer science. Systems that act like humans (Turing test) The system (machine) would need to possess the following capabilities: ▪ Natural language processing to enable it to communicate successfully in English. ▪ Knowledge representation to store what it knows or hears. ▪ Automated reasoning to use the stored information to answer questions and draw new conclusions. ▪ Machine learning to adapt to new circumstances and to detect and extrapolate patterns. Notable AI machines and Their Attempts at the Turing Test • ELIZA (1966) • PARRY (1972) • ALICE • Eugene Goostman Interviewing Sophia: https://www.youtube.com/watch?v=0HoSwHNUOHg BabyX virtual https://www.youtube.com/watch?v=fNWjKtVWToc Why do we want an intelligent system to act like human? •Because for many tasks, humans are still the gold standard. •Humans are needed in high-skilled innovation and critical decision-making jobs, as well as in fields that require emotional intelligence. Total Turing test • Turing test is extended to include physical aspects of human behavior, and hence the computer capabilities will be extended to include: ▪ Computer vision to perceive objects. ▪ Robotics to manipulate objects and move. Computer vision • It is a field of computer science that allows computers to see and understand the contents of digital images, such as photographs or videos. Uses of computer vision Is this a cat? What is there in the image and where? Which pixels belong to which object? Uses of computer vision •Object detection: find where the objects are in the image. and draw a bounding box around it. •Semantic Segmentation: what pixels belong to the object in the image? each pixel is assigned to an object •Classification/Recognition: Given an image with an object, find out what that object is. In other words, classify it in a class from a set of predefined categories. Robotics ▪ Robotics is a branch of engineering and computer science that involves the conception, design, manufacture, and operation of robots. Natural language processing (NLP) NLP is a machine-learning technology that gives computers the ability to interpret, manipulate, and comprehend human language. Uses of Natural Language Processing ▪ Summarization: NLP can also be used to summarize text ▪ Speech to Text Conversion ▪ Sentiment Analysis: NLP is used to analyze the positive and negative nature of the sentence. ▪ Text classification ▪ Spell checking ▪ Grammar checking: ex. Grammarly, Quillbot ▪ Question answer: ex. ChatGPT, Gemini, DeepSeek ▪ Voice Assistants: ex. Siri in iPhone, Amazon Alexa Approach 2 : thinking humanly “The cognitive modeling approach” • To say that a given program thinks like a human, we need to get inside the workings of the human mind: 1. Introspection—trying to catch our own thoughts 2. psychological experiments—observing a person in action 3. brain imaging—observing the brain in action. • Once we have a sufficiently precise theory of the mind, it becomes possible to express the theory as a computer program What is Artificial intelligence? ▪ Some definitions of AI, organized into four categories: Systems that act like humans Systems that act rationally The art of creating machines that perform functions that require human intelligence. Systems that think like humans The effort to make computers think . . . Machines with mind. Systems that think rationally Cognitive science ▪ Cognitive Science is the study of the human mind and brain, focusing on how the mind represents and manipulates knowledge. Approach 3: Thinking rationally “laws of thought” approach Systems that act like humans Systems that act rationally The art of creating machines that perform functions that require human intelligence. Systems that think like humans Systems that think rationally The effort to make computers The study of the computations that make think . . . Machines with mind. it possible to perceive, reason, and act. Approach 3: thinking rationally “laws of thought” approach •Systems yielded correct conclusions when given correct premises—for example, “Socrates is a man; all men are mortal; therefore, Socrates is mortal.” •Obstacles • It is not easy to express informal knowledge by logical notation, particularly when the knowledge is less than 100% certain. • Second, there is a big difference between solving a problem “in principle” and solving it in practice. Even problems with just a few hundred facts can exhaust the computational resources of any computer unless it has some guidance. Approach 4: Thinking rationally “The rational agent approach” Systems that act like humans Systems that act rationally The art of creating machines that It is the study of intelligent agent perform functions that require design. human intelligence. Systems that think like humans Systems that think rationally The effort to make computers think The study of the computations . . . Machines with mind. that make it possible to perceive, reason, and act. Intelligence 11:00 PM · Mar 5, 2024 · 422 Views Settings . #HistoryofAI #TechEvolution Foundations of Artificial Intelligence ▪ Philosophy ✓ Can the formal rules be used to draw conclusions? ✓ How does knowledge lead to an action? ▪ Mathematics ✓ What are the formal rules to draw conclusions? ▪ Neuroscience ✓ how does the brain process information? ▪ Psychology ✓ How do humans and animals think and act? ▪ Economics ✓ How should we maximize profit? do to ▪ Computer engineering ✓ How can we build an efficient computer? ▪ Linguistics ✓ how does thought? language relate to Assignment 1 ▪ What is intelligence? ▪ What is artificial intelligence using four different categories? ▪ Define the following concepts: Turing test- total Turing test- computer vision- robotics- natural processing language (NLP)- cognitive scienceclassification – object segmentation – object detection ▪ State some uses of the computer vision field. ▪ State some uses of natural processing language. ▪ What can AI do today? ▪ Describe the foundation of Artificial intelligence. ▪ Why do we want an intelligent system to act like a human? ▪ Describe the capabilities that need to be found in the computers for the Turing test. Reference resources • Russell, S. J., & Norvig, P. (2016). Artificial intelligence: a modern approach. Pearson. • Ertel, W. (2024). Introduction to artificial intelligence. Springer Nature. CS203 Artificial intelligence Dr. Doaa El-Shahat Lecturer at Computer Science Department Zagazig University, Egypt Lecture 2 Intelligent agents Dr. Doaa El-Shahat Lecturer at Computer Science Department Zagazig University, Egypt Lecture Content  Recap  What is an intelligent agent? Ex. Vacuum cleaner agent  Agents and environments  Rationality  Specifying task environment: PEAS (Performance measure, Environment, Actuators, Sensors)  Environment properties  Agent classification (types) Recap  Some definitions of AI, organized into four categories (Rusell and Norvig): Thinking humanly Thinking rationally “Cognitive modeling approach” “Laws of thought approach using logic” Acting humanly “Turing test ” • Rationally= doing the right thing • Acting= behavior Acting rationally “The rational agent approach” What is an intelligent agent?  An intelligent agent is an entity that perceives its environment through sensors and acts on that environment through actuators. (Rusell and Norvig) Intelligent agent  Agents can be biological (people or animals, for example), robotic, or computational (software).  Human agent :  Sensors = eyes, ears  Actuators (effectors) = hands, legs, mouth.  Robotic agent:  Sensors = cameras, sonar, lasers.  Effectors = grippers, manipulators, motors. Gripper Intelligent agent properties 1. Autonomy 2. Adaption 3. Cooperation 1. Autonomy  It is the ability of an agent to act and make decisions independently of the user. Example  An intelligent buying agent that buys goods on behalf of a user’s needs and makes decisions about what items to purchase without checking back with the user. Adaption  It is the ability of an agent to learn and adapt when presented with new situations. Example:  Agents can learn from a user by observing actions or by being given instructions.  Agents can also learn from other agents in multiagent systems. Cooperation  In multiagent systems, the gent can cooperate with each other.  It is a form of social interaction between agents.  Example:  A buying agent may negotiate with a selling agent to make purchases. Agent function  Agent function describes the agent behavior that maps any given percept sequence to an action.  It is an abstract mathematical description.  Example: Vacuum cleaner. A vacuum-cleaner world with just two locations The agent function of Vacuum cleaner agent Tabulation of a simple agent function for the vacuum cleaner world Percept sequence [A, clean] Action Right [A, dirty] [B, clean] [B, dirty] Suck Left Suck [A, clean], [B, clean] Right [A, clean], [B, dirty] Suck [A, Clean], [A, Clean], [A, Clean] Right … … Vacuum cleaner world with just two locations Agent program  Agent program is an internal implementation of the agent function.  Example: The agent program for a simple reflex agent in the two-state vacuum environment. function REFLEX-VACUUM-AGENT( [location, status] ) returns an action if status = Dirty then return Suck else if location = A then return Right else if location = B then return Left Agent architecture  Agent architecture is the physical components of agent (sensors and actuators) in which the agent program will run. Agent = Architecture + Program  The program has to be appropriate for the architecture.  Ex: If the program will recommend actions like Walk, the architecture had better to have legs. Rational agent  Rationality means doing the right thing  A rational agent is an agent that does the right thing.  A performance measure evaluates how successful the agent is.  There is no fixed performance measure for all tasks and agents  a designer will devise one appropriate to the circumstances.  Ex: Performance measure for a vacuum cleaner agent:  Awarding one point for each clean square  Penalty for electricity consumed and noise generated. Rational agent What is rational at any given time depends on four things:  The performance measures that define the success criteria (goals).  The agent’s prior knowledge of the environment.  percept sequence up to date.  The possible actions of the agent. Rational agent  Performance measure awards one point for each clean square.  The environment is known a priori  Two locations A, B  The dirt distribution and agent’s initial location are not known.  Actions: Suck, Left, Right.  The agent perceives its location and whether that location contains dirt. Omniscient agent  An omniscient agent knows the actual outcome of its actions and can act accordingly, but omniscience is impossible in reality.  In comparison, a rational agent behaves according to its percepts and knowledge and attempts to maximize the expected performance.  Example: if I look both ways before crossing the street and then as I cross, I am hit by a car. I can hardly be accused of lacking rationality. Omniscient = have all knowledge Omniscient ≠ rational Task environment  Before we design an intelligent agent, we must specify its task environment.  PEAS:  Performance measure  Environment  Actuators  Sensors Task environment Describe the task environment (PEAS) for the following:  Pacman  Autonomous taxi driver  Chess game  Medical diagnosis system  Part-picking robot  Interactive English tutor  Backgammon Pacman game  Performance measure: -1 per step, +10 food, +500 win, -500 die, +200 hit scared ghost  Environment: Pacman dynamics barriers, ghosts, Pacman, white dots  Actuators: down.  Sensors: Entire state is visible  full observable board. Left, right, up Task environment for autonomous taxi driver  Performance measure: safe, fast, comfortable, profit, fines  Environment: roads, traffic, pedestrians, customers, other vehicles, traffic officers  Actuators: steering, accelerator, brake, signal, horn  Sensors: cameras, Infrared or sonar sensors to detect distances and obstacles, speedometer, GPS, odometer, accelerometer, engine sensors, Keyboard or Microphone for passengers to request destination. Task environment for chess game Agent type Performance measure Chess game 1 point Win -1 point lose 0 point draw Environment Sensor Actuator Chessboard, See board opponent position as 8×8 matrix Move piece to target position Game idea: https://www.youtube.com/watch?v=ctDQCpSSzow Task environment for medical diagnosis system Agent type Medical diagnosis system Performance measure Healthy patient, reduced costs Environmen Sensor t Patient, Keyboard entry hospital, of symptoms, Staff, findings, patient’s answers Actuator Display of questions, tests, diagnoses, treatments, referrals Task environment for Part-picking robot Agent type Performance Environment measure Part-picking Percentage of Conveyor belt robot parts in correct bins with parts, bins Sensor Actuator Camera, joint Jointed arm and angle hand sensors Task environment for Interactive English tutor Agent type Performanc Environment e measure Interactive Student’s Set of English tutor score students on test Sensor Actuator Keyboard entry, camera, microphone, speaker Display of exercises, suggestions, corrections Backgammon Performance measure: The first player to bear off all 15 pieces wins the game Environment: Game board, opponent Actuator: roll dice, move pieces Sensors: the full board Game idea: https://www.youtube.com/watch?v=AlkR73-U_00 Properties of task environment  Single agent vs. multiagent  Fully observable vs. partially observable  Competitive vs. Cooperative  Deterministic vs. Stochastic  Episodic vs. Sequential  Static vs. dynamic  Discrete vs. Continuous Single-agent vs Multi-agent  Single-agent environment contains only one agent.  Ex: Crossword is a single agent,  Ex: a single person in a maze is a single-agent system.  A multi-agent environment contains more than one agent.  Ex: chess and football are multi-agent environments. Fully Observable vs Partially Observable  The environment is fully observable when an agent sensor can access the complete state of the environment.  No need to keep track of the surroundings’ history.  An environment might be partially observable due to noisy and inaccurate sensors or since parts of the environment are inaccessible.  An environment is called unobservable when the agent has no sensors in its environment. •Examples: • Chess – the board is fully observable and opponent’s moves. • Taxi driver – the environment is partially observable as what’s around the corner is not known. Example Crossword Fully Poker Backgammon Taxi driver Partially Partially Partially Part-picking robot Partially Image analysis Fully Deterministic vs Stochastic  Deterministic environment: if the next state of the environment is completely determined by the current state and the action executed by the agent.  The stochastic environment is random in nature which is not unique and cannot be completely determined by the agent.  Examples:  Chess – there would be only a few possible moves for a chess piece at the current state and these moves can be determined.  Vacuum environment is deterministic  Taxi driver: the actions of a taxi driver are not unique, it varies time to time (stochastic).  Stochastic is connected to randomness events Competitive vs Collaborative  An agent is in competitive environment when it competes against another agent to optimize the output.  The game of chess is competitive as the agents compete with each other to win the game which is the output.  An agent is in a collaborative environment when multiple agents cooperate to produce the desired output.  multiple self-driving cars cooperate with each other to avoid collisions and reach their destination which is the output desired.  Players of a single football team. Dynamic vs Static  A dynamic environment is constantly changing while the agent is deliberating.  Ex: taxi driving is dynamic  An idle environment with no change in its state is called a static environment.  EX: An empty house is static as there’s no change in the surroundings when an agent enters.  EX: Crossword puzzles are static  Semidynamic: If the environment itself does not change with the passage of time but the agent's performance score does. Discrete vs Continuous  If an environment consists of a finite number of actions that can be deliberated in the environment to obtain the output, it is a discrete environment.  Chess is discrete as it has only a finite number of moves. The number of moves might vary with every game, but still, it’s finite.  The environment in which the actions are performed cannot be numbered i.e. is said to be continuous.  Self-driving cars are continuous environments as their actions are driving, parking, etc. cannot be numbered. Episodic vs Sequential  In an episodic environment, the agent’s actions are divided into atomic episodes. There is no dependency between current and previous episodes. In each episode, an agent receives input from the environment and performs the corresponding action.  Ex: Pick and Place robot, which is used to detect defective parts from the conveyor belts. Every time, the robot (agent) will decide on the current part i.e. there is no dependency between current and previous decisions.  In a sequential environment, the previous decisions can affect all future decisions. The agent’s next action depends on what action he has taken previously and what action he is supposed to take in the future.  Ex: Chess- the previous move can affect all the following moves.  Taxi driver Known vs Unknown  In a known environment, the output for all probable actions is given.  In the case of an unknown environment, for an agent to make a decision, it has to gain knowledge about how the environment works.  It isn’t a property of the environment, but it is the property of agent’s state of the knowledge. Environment types  The simplest environment is fully observable, deterministic, episodic, static, discrete, and singleagent.  Most real situations are Partially observable, stochastic, sequential, dynamic, continuous, and multi-agent. Environment properties Environment Observable Deterministic Episodic Static Discrete Agents Crossword puzzle Fully deterministic Sequential static Discrete single Chess with a clock Fully deterministic Sequential semi Discrete Multi Poker Partial Stochastic Sequential Static Discrete Multi Backgammon Fully Stochastic Sequential Static Discrete Multi Taxi driving Partial Stochastic Sequential Dynamic Continuous Multi Medical diagnosis Partial Stochastic Sequential Dynamic Continuous Single Image analysis Fully Deterministic Episodic Semi Discrete Robot part picking Fully Deterministic Episodic Semi Continuous Single Refinery controller Partial stochastic sequential dynamic continuous Interactive English tutor Partial Stochastic Sequential Dynamic Discrete Single single Multi Basic agent types  Simple reflex agents.  Model-based reflex agents.  Goal-based agents.  Utility-based agents. Basic agent types  Simple reflex agents.  Model-based reflex agents.  Goal-based agents.  Utility-based agents. Simple reflex agent  It select actions based on the current percept, ignoring the rest of the percept history.  Ex: vacuum cleaner is a simple reflex agent, why? Since its decision is based only on the current location and whether it contains dirt. function REFLEX-VACUUM-AGENT( [location, status] ) returns an action if status = Dirty then return Suck else if location = A then return Right Condition-action rule else if location = B then return Left  When the current square is dirty, the action does not depend on the location. Simple reflex agents Ex: The driver of the automated taxi if car-in-front-is-braking then initiate-braking. Simple reflex agents Drawback:  Work only if the environment is fully observable  A little bit of unobservability can cause serious trouble. Drawback of simple reflex agent  For example, the braking rule given earlier assumes that the condition car-in-front-is-braking can be determined from the current percept—a single frame of video. This works if the car in front has a centrally mounted brake light.  Unfortunately, older models have different configurations of taillights, brake lights, turn-signal lights, and it is not always possible to tell from a single image whether the car is braking. A simple reflex agent driving behind such a car would either brake continuously and unnecessarily, or, worse, never brake at all. Basic agent types  Simple reflex agents.  Model-based reflex agents.  Goal-based agents.  Utility-based agents. Model-based reflex agent  It can handle partial observable environments.  The agent has a memory to maintain the percept history.  For the braking problem, the internal state is not too extensive— just the previous frame from the camera, allowing the agent to detect when two red lights at the edge of the vehicle go on or off. Model-based reflex agent  It requires two kinds of knowledge to be encoded in the agent program (Model of the world). 1. How the world evolves independently of the agent. For example, that an overtaking car generally will be closer behind than it was a moment ago. 2. How the agent’s own actions affect the world. For example, that when the agent turns the steering wheel clockwise, the car turns to the right Model-based reflex agents Model-based reflex agents Drawback of model-based agent  Percepts alone are insufficient to decide what to do.  For example, at a road junction, the taxi can turn left, turn right, or go straight on. The correct decision depends on where the taxi is trying to get to. Basic agent types  Simple reflex agents.  Model-based reflex agents.  Goal-based agents.  Utility-based agents. Goal-based agents  It keeps track of the world state in addition to a set of goals it is trying to achieve, and chooses an action that will lead to the achievement of its goals.  It works towards goals.  Example:  Taxi driver destination. Goal-based agents Drawback of goal-based agent  Goals alone are not enough to generate high-quality behavior in most environments.  For example, many action sequences will get the taxi to its destination, but some are quicker, safer, more reliable, or cheaper than others. Utility-based agents  several possible actions can be taken in a given situation.  Utility–based agent selects the action that maximizes their reward.  Utility function maps a state (or sequence of states into a real number). The agent uses this number to weigh the importance of the competing goals.  Ex: taxi driver may have many paths leading to the goal, but some are safer, quicker, and cheaper. Utility-based agents Learning agent  Learning agents improve their behavior over time.  They can become more competent over time.  It tries to maximize their own expected ―happiness.‖  They can start with an initially empty knowledge base.  They can operate in initially unknown environments. Learning agent Determines the agent performance Suggests exploratory actions that will lead to new informative experiences Responsible for making improvements Take percept and decide an action Assignment 2  Define intelligent agent, omniscient agent, rational agent, and agent function.  Describe intelligent agent properties.  Describe the (PEAS) task environment for the following: Autonomous taxi driver. Chess Medical diagnosis systems Satellite imagery Part-picking robot Refinery controller Interactive English tutor Backgammon Assignment 2  Differentiate between the following: Human agent and robotic agent. Fully observable and partially observable environments Deterministic vs. Stochastic environments Competitive vs collaborative environments  Single-agent vs multi-agent environments Dynamic and static environments Sequential and episodic environments Known and unknown  Goal-based agent and utility-based agent  Describe the environment properties of the following: crossword puzzle- chess-poker-taxi driver- robot part picking- interactive English tutor- refinery controller. Reference resources  Coppin, B. (2004). Artificial intelligence illuminated. Jones & Bartlett Learning.  Russell, S. J., & Norvig, P. (2016). Artificial intelligence: a modern approach. Pearson.  https://tutorialforbeginner.com/types-of-ai-agents  https://slideplayer.com/slide/14293658/ CS203 Artificial intelligence Dr. Doaa El-Shahat Lecturer at Computer Science Department Zagazig University, Egypt 2/22/2025 Lecture 3 Solving problems by searching Dr. Doaa El-Shahat Lecturer at Computer Science Department Zagazig University, Egypt 2/22/2025 Lecture Content  Recap  Agent types: model-based agent, goal-based agent, utilitybased agent.  Problem-Solving Agents  Example Problems  Searching for Solutions  Uninformed Search Strategies  Informed (Heuristic) Search Strategies  Heuristic Functions 2/22/2025 Recap  Some definitions of AI, organized into four categories (Rusell and Norvig): Thinking humanly “Cognitive modeling approach” Thinking rationally Laws of thought approach using logic” Acting humanly Acting rationally “Turing test ” “The rational agent approach” • Rationally= doing the right thing • Acting= behavior 2/22/2025 Recap Autonomy Adaption Cooperation 2/22/2025 Agent Sensors ? Actuators Environment  Fully observable vs. partially observable  Single agent vs. multiagent  Competitive vs. Cooperative  Deterministic vs. Stochastic  Episodic vs. Sequential  Static vs. dynamic  Discrete vs. Continuous Agent types  Simple reflex agents.  Model-based reflex agents.  Goal-based agents.  Utility-based agents. 2/22/2025 Simple reflex agent Agent Sensors What the world is like now Condition-action rules What action I should do now Effectors Environment  It select actions based on the current percept, ignoring the rest of the percept history.  Ex: Vacuum cleaner  It works well in fully observable environment.  Basic components: 1. Sensors: gathers information about what the world is like now (status). 2. Condition-action rules: the agent matches the status with its. 3. Actuators: executes the selected action. Simple reflex agent  Automatic Doors: Open when sensing movement nearby. The door react to immediate presence detection, requiring no memory or context.  Smoke Detectors: Trigger an alarm upon detecting smoke particles in the air. Their responses are immediate and based solely on current air quality. Agent types  Simple reflex agents.  Model-based reflex agents.  Goal-based agents.  Utility-based agents. 2/22/2025 Model-based reflex agent  It can handle environments. dynamic and partial observable  The agent keeps track of the part of the world it can’t see now.  The agent has a memory to maintain the percept history.  For the braking problem,— from the previous frame of the camera, the agent can detect when two red lights at the edge of the vehicle go on or off. 2/22/2025 Model-based reflex agent Internal state State How the world evolves What my actions do Condition-action rules Agent 2/22/2025 Sensors What the world is like now What action I should do now Effectors Environment  The agent interprets the current state with reference to previous percepts, leading to more informed decisions, and even predicting the impact of its actions. Model-based reflex agent  It requires two kinds of knowledge to be encoded in the agent program (Model of the world). 1. How the world evolves independently of the agent. For example, an overtaking car generally will be closer behind than it was a moment ago. 2. How the agent’s own actions affect the world. For example, when the agent turns the steering wheel clockwise, the car turns to the right. 2/22/2025 Model-based reflex agent  Autonomous vehicles: use an internal model of the environment to navigate, considering past data like road conditions, nearby vehicles, and traffic signals to make real-time driving decisions.  Robotic Vacuum Cleaners: Advanced models map the area to remember cleaned spots and avoid obstacles, adjusting paths based on past data for more efficient cleaning. 2/22/2025 Model-based reflex agents 2/22/2025 Simple reflex agent vs. model-based agent 2/22/2025 Simple reflex agent vs. model-based reflex agent Aspect Simple Reflex Agent Decision Basis Current percept Memory Environment Example response Complexity 2/22/2025 Model-Based Reflex Agent Current percept+ internal state None Retains past states to inform decisions Effective in fully observable, Better for dynamic or partially observable static environments environments A robot vacuum updating its map to avoid Smoke detector obstacles Faster response Slower response Low computational resources It requires resources to build, update, and utilize the internal model, leading to increased computational complexity. Drawback of model-based agent  Percepts alone are insufficient to decide what to do.  For example, at a road junction, the taxi can turn left, turn right, or go straight on. The correct decision depends on where the taxi is trying to get to. (goal) 2/22/2025 Basic agent types  Simple reflex agents.  Model-based reflex agents.  Goal-based agents.  Utility-based agents. 2/22/2025 Goal-based agents  It keeps track of the world state in addition to a set of goals it is trying to achieve, and chooses an action that will lead to the achievement of its goals.  It works towards goals.  Example: - Taxi driver destination (airport). 2/22/2025 Goal-based agents Internal state State What the world is like now What my actions do What it will be like if I do action A Goals Agent 2/22/2025 What action I should do now Effectors Environment How the world evolves Sensors Drawback of goal-based agent  Goals alone are not enough to generate high-quality behavior in most environments.  For example, many action sequences will get the taxi to its destination, but some are quicker, safer, more reliable, or cheaper than others. 2/22/2025 Model-based agent vs. goal-based agent 2/22/2025 Aspect Decision Basis Model-Based Agents Goal-Based Agents React to changes using Act to achieve defined condition-action rules goals Requires planning and Memory Simple rule-based reactions evaluating future actions Suitable for environments Best for tasks needing Environmental requiring context-aware long-term goal Suitability reactions achievement A smart sprinkler system A GPS system planning Example adjusting watering schedules the optimal route to a based on soil moisture destination 2/22/2025 Basic agent types  Simple reflex agents.  Model-based reflex agents.  Goal-based agents.  Utility-based agents. 2/22/2025 Utility-based agents  Several possible actions can be taken in a given situation.  Utility–based agent selects the action that maximizes their reward.  Utility function maps a state (or sequence of states) into a real number. The agent uses this number to weigh the importance of the competing goals.  Ex: taxi driver may have many paths leading to the goal, but some are safer, quicker, and cheaper. 2/22/2025 Utility-based agents 2/22/2025 Problem-solving agent  It is a kind of goal-based agent.  The agent adopts a goal and aims at achieving it. 2/22/2025 Problem formulation  Problem formulation is the process of deciding what actions and states to consider, given a goal.  The process of looking for action/action sequence that reaches the goal is called search. 2/22/2025 Problem formulation  A problem can be defined by five components: 1 2 3 4 5 Initial state Actions Transition model Goal test Path cost possible determines function that actions that defines the new whether a assigns a agent starts in an agent can state resulting given state is a numeric cost goal state from doing an to each path take for a action in the given state current state 2/22/2025 Example problems 2/22/2025 Example 1: Romania Vacation  On vacation in Romania; currently in Arad.  Flight leaves tomorrow from Bucharest. 2/22/2025 State Space/Transition model defined as graph 2/22/2025 Example 1: Romania Vacation  Initial state: Arad  Actions: Drive from one city to another.  Transition model and states: If you go from city A to city B, you end up in city B.  Goal state: Bucharest  Path cost: Sum of edge costs. 2/22/2025 Example: Romania map 2/22/2025 Example 1: Romania map On holiday in Romania; currently in Arad.  Flight leaves tomorrow from Bucharest.  Formulate goal:  be in Bucharest  Formulate problem:  States: various cities  Actions: drive between cities  Find solution:  Sequence of cities, e.g., Arad Sibiu Fagaras Bucharest  Optimal solution is a set of sequence actions/states that has the best cost among all solutions. 2/22/2025 Example 2: vacuum cleaner  States: determined by both the agent location and the dirt locations.  Initial state: Any state can be designed as the initial state.  Actions: Left, Right, Suck.  Transition model: (A, dirty) Suck  Goal test: checks if all squares are clean.  Path cost: Each step costs 1. The agent is in one of two locations, each of which might or might not contain dirt. 2 × 𝟐𝟐 = 8 states 2/22/2025 Example 2: vacuum cleaner State space graph of vacuum cleaner Goal state 2/22/2025 Example 3: 8 puzzle  States: each state denotes the location of eight tiles and the blank in one of the nine squares.  Number of states approximately is n! permutation of the 9 tiles. 7 5 8 2 3 4 6 1 Start state  Initial State: Any state can an initial state.  Actions: Move blank left, right, up, down  Transition model: Given a state and action, this returns the resulting new state  Goal state: arrange tiles as empty and 1:8 in order.  Path cost: 1 per tile move. 2/22/2025 1 2 3 4 5 6 7 8 Goal state Example 3: 8 puzzle 2/22/2025 Example 3: 8 puzzle State space graph 2/22/2025 Solving Search Problem Given a search problem definition  Initial state  Actions  Transition model  Goal state  Path cost Optimal solution is a set of actions/states sequence that has the best cost among all solutions. 2/22/2025 How do the optimal solution is found (sequence of actions/states)? Construct a search tree for the state space graph! Issue: Transition Model is Not a Tree! It can have Redundant Paths. Cycles Return to the same state Goal states 2/22/2025 Issue: Transition Model is Not a Tree! It can have Redundant Paths. Non-cycle redundant paths Path 1 Goal states 2/22/2025 Path 2 Graph  A graph is a set of nodes and links (edges) that connect them.  A path cost function that assigns a numeric cost to each path. cost Undirected graph 2/22/2025 Undirected graph Directed graph (digraph) Search tree  Search tree is a tree representation of a search problem. The root node corresponds to the initial state found at the top of the search tree. Root node (initial state) • The children of node B are D, E • The parent of node F is C A B D 2/22/2025 C E F G Search tree If the node has at least one child Siblings: 5,9 Tree height Parent of 5, 9 is 7 2/22/2025 Search space  A search space is a collection of probable solutions that a system could have.  A solution is an action sequence that goes from the initial state to a goal state.  State space: set all states in the space (A, B, C, D, E, F, G). Root node (initial state) A B D 2/22/2025 C E F G Goal node Redundant path  They exist whenever there is more than one way to get from one state to another. ACG ABEG A B D C E G 2/22/2025 F G Tree search approaches  There are two main approaches to searching a search tree: data-driven search and goal-driven search. Tree search algorithms Data-driven search 2/22/2025 Goal-driven search Tree search approaches  Data-driven search starts from an initial state and uses actions that move forward until a goal is reached. 2/22/2025 Tree search approaches  Goal-driven search starts at the goal and works back toward the initial state, by seeing what moves could have led to the goal state. 2/22/2025 State graph of Romania 2/22/2025 Search tree for Romania  The root node of the tree corresponds to the initial state, (Arad).  The first step is to test whether this is a goal state. Arad 2/22/2025 State graph of Romania 2/22/2025 Search tree for Romania (a) After expanding Arad Arad Sibiu 2/22/2025 Timisoara Zerind State graph of Romania 2/22/2025 Search tree for Romania (c) After expanding Sibiu Arad Sibiu Arad Fagaras Timisoara Oradea Zerind Rimnicu Vilcea Loopy path: in which the path contains a repeated state in the search tree. Ex: Arad Sibiu Arad 2/22/2025 3  What are the different types of Agent?  Compare between simple reflex agent and model-based reflex agent.  Differentiate between goal based agent and utility-based agent.  Describe the problem formulation of the puzzle game.  Describe the problem formulation of the vacuum cleaner.  Assume you are in a vacation to Egypt, describe the problem formulation if you are in Cairo and you want to go Luxor. 2/23/2025 2/22/2025 Reference resources • Ertel, W. (2024). Introduction to artificial intelligence. Springer Nature. • Russell, S. J., & Norvig, P. (2016). Artificial intelligence: a modern approach. Pearson. 2/22/2025 CS203 Artificial intelligence Dr. Doaa El-Shahat Lecturer at Computer Science Department Zagazig University, Egypt 3/15/2025 Lecture 4 Solving problems by searching Uninformed search strategies Dr. Doaa El-Shahat Lecturer at Computer Science Department Zagazig University, Egypt 3/15/2025 Lecture Content  Searching for Solutions  Uninformed Search Strategies  Informed (Heuristic) Search Strategies  Heuristic Functions 3/15/2025 Recap Autonomy Adaption Cooperation 3/15/2025 Agent Sensors ? Actuators Environment  Fully observable vs. partially observable  Single agent vs. multiagent  Competitive vs. Cooperative  Deterministic vs. Stochastic  Episodic vs. Sequential  Static vs. dynamic  Discrete vs. Continuous Recap  Simple reflex agents.  Model-based reflex agents.  Goal-based agents.  Utility-based agents. 3/15/2025 Goal-based agent environment properties Static or dynamic? Fully or partially observable? Discrete or continuous? Deterministic or stochastic? Episodic or sequential? Single agent or multiple agent? 3/15/2025 Example: Romania map 3/15/2025 General Search tree Frontier means unexpanded node 3/15/2025 Search tree for Romania  The root node of the tree corresponds to the initial state, (Arad).  The first step is to test whether this is a goal state. Initial state frontier 3/15/2025 Arad State graph of Romania 3/15/2025 Search tree for Romania (a) After expanding Arad Arad Sibiu 3/15/2025 Timisoara Zerind State graph of Romania 3/15/2025 Tree search for Romania (c) After expanding Sibiu Arad Sibiu Arad Fagaras Timisoara Oradea Zerind Rimnicu Vilcea Loopy path: in which the path contains a repeated state in the search tree. Ex: Arad Sibiu Arad 3/15/2025 Graph search Traversing node means visiting this node Explored node means visiting their children Frontier means unexpanded node 3/15/2025 Graph search for Romania  The root node of the tree corresponds to the initial state, (Arad).  The first step is to test whether this is a goal state. Initial state frontier Arad Frontier: Arad 1 Explored set: - Traversing node means visiting this node Explored node means visiting their children Frontier means unexpanded node 3/15/2025 State graph of Romania 3/15/2025 Graph search for Romania Frontier: Arad 1 Explored set: - (a) After expanding Arad 2 Frontier: Sibiu, Timisora, Zerined Explored set: Arad Arad Sibiu 3/15/2025 Timisoara Zerind frontier State graph of Romania 3/15/2025 Tree for Romania using graph search Frontier: Sibiu, Timisora, Zerined 2 Explored set: Arad (c) After expanding Sibiu Arad Sibiu Fagaras Arad 3/15/2025 Timisoara Oradea Frontier: Arad 1 Explored set: - 3 Frontier: Timisora, Zerined, Fagaras, Oradea, Rimnci vilcea Explored set: Arad, Sibiu Zerind Rimnicu Vilcea Don’t put Arad as it exists in the explored set  Every time you expand a node, add it to the explored set; don’t put the explored set on the frontiers again.  Every time you add a node to the frontier, check whether it already exists with a higher path cost, and if yes, replace that node with the new one. Tree for Romania using graph search Frontier: Arad 1 Explored set: - (c) After expanding Sibiu 2 Frontier: Sibiu, Timisora, Zerined Arad Explored set: Arad Sibiu Fagaras Timisoara Oradea Zerind 3 Rimnicu Vilcea 4 3/15/2025 Frontier: Timisora, Zerined, Fagaras, Oradea, Rimnci vilcea Explored set: Arad, Sibiu Frontier: Timisora, Zerined, Fagaras, Oradea, Rimnci vilcea Explored set: Arad, Sibiu Search algorithms  A search algorithm takes a problem as input and returns a solution in the form of an action sequence. Problem 3/15/2025 Input Search algorithm Action sequence solution Search algorithms  Uninformed search algorithms (blind)—algorithms that are given no information about the problem other than its definition.  Informed search algorithms (heuristic) can do quite well given some guidance on where to look for solutions. Search algorithms Informed search algorithms 3/15/2025 Uniformed search algorithms Informed Search algorithms  Informed search algorithms (heuristic) can do quite well given some guidance on where to look for solutions.  It contains an array of knowledge, such as how far we are from the goal, path cost, how to reach to goal node, etc. .  This knowledge help agents to explore less to the search space and find more efficiently the goal node. 3/15/2025 Search algorithms  Uninformed( Blind) search:  Breadth-first search  Depth-first search  Depth limited search  Iterative deepening search  Uniform cost search  Informed (Heuristic) search: search is guided by an evaluation function:  Greedy best-first search  A* search  IDA* search  beam search 3/15/2025 Brute force search (Exhaustive search)  It assumes no additional knowledge other than how to traverse the search tree and identify leaf nodes and goal nodes.  It examines every node in the tree until it finds a goal. 3/15/2025 Measuring problem-solving performance “Properties of Search Methods”  Completeness: Is the algorithm guaranteed to find a solution when there is one?.  Optimality: Does the strategy find the optimal solution?.  Time complexity: How long does it take to find the goal state?  Space complexity: How much memory is needed to perform the search? 3/15/2025 Time and Space Complexity ? Time and space complexity are measured in terms of:  Branching factor (b): maximum number of successors of any node. The length of a path to a goal is the depth d. m: Maximum length of any path in the state space. Start node A B m=3 D H Depth=0 C E F Depth=1 G Depth=2 Max children of any node is b=2 27 Uniformed search algorithms 1. Breadth first search 2. Depth first search 3. Depth limited search 4. Iterative deepening search 5. Uniform cost search 3/15/2025 1. Breadth first search 1. Breadth- first search (BFS)  Breadth-first algorithm starts by examining all nodes one level after another starting from the root node.  Implementation:  Use of a First-In-First-Out (FIFO) queue.  Nodes visited first are expanded first. Start node A B D 3/15/2025 C E F G Goal node Breadth first search A A B D 3/15/2025 C E F G Breadth first search A AB B D 3/15/2025 C E F G Breadth first search A ABC B D 3/15/2025 C E F G Breadth first search A ABCD B D 3/15/2025 C E F G Breadth first search A ABCDE B D 3/15/2025 C E F G Breadth first search A ABCDEF B D 3/15/2025 C E F G Breadth first search A ABCDEFG B D C E F G Goal is found  This search continues examining nodes in each level, reporting success when a goal node is found, and reporting failure if all nodes have been examined and no goal node has been found. 3/15/2025 Breadth first search In the worst case all the nodes will be traversed in the tree and the time complexity 𝑑 will be O(𝑏 ).      3/15/2025 Stop traversing the tree if the goal is found Branching factor (b)=2 Number of nodes in level 0: 𝑏 0 =1 Number of nodes in level 1: 𝑏1 =2 Number of nodes in level 2: 𝑏 2 =4 Number of nodes in level 3: 𝑏 3 =8  Then the number of traversed nodes at depth (d) will be = 𝑏 0 + 𝑏1 + 𝑏 2 + …. + 𝑏 𝑑 = 𝑂(𝑏 𝑑 ) Evaluation of tree-search strategies  Once a goal node is generated, it is the shallowest goal node as all the shallower nodes must have been generated.  The shallowest goal node is not necessarily the optimal one.  BFS is optimal if the path cost is a nondecreasing function of the depth of the node. 3/15/2025 Time and memory requirements for breadth-first search 3/15/2025 Breadth first search  The problem is to get from Sibiu to Bucharest. Sibiu Fagaras Bucharest Ignore loopy path Rimnicu vilcea Pitesti Bucharest Sibiu  3/15/2025 Fagaras Rimnivu vilcea Bucharest Breadth first search  The problem is to get from Sibiu to Bucharest. Sibiu Is it goal? No Sibiu  3/15/2025 Breadth first search  The problem is to get from Sibiu to Bucharest. Sibiu Is it goal? No Fagaras Rimnicu vilcea Sibiu  3/15/2025 Fagaras Breadth first search  The problem is to get from Sibiu to Bucharest. Sibiu Fagaras Rimnicu vilcea Is it goal? NO Sibiu  3/15/2025 Fagaras Rimnicu vilcea  Breadth first search  The problem is to get from Sibiu to Bucharest. Sibiu Rimnicu vilcea Fagaras Bucharest Is it goal? Yes, then stop expanding. Ignore loopy path Sibiu  3/15/2025 Fagaras Rimnivu vilcea Bucharest Breadth first search B D A F A H C E G B B C F E G D B 3/15/2025 H E 2. Uniform cost search Uniform cost search  When all step costs are equal, breadth-first search is optimal because it always expands the shallowest unexpanded node.  Instead of expanding the shallowest node, uniform-cost search expands the node n with the lowest path cost g(n).  It is guided by path costs rather than depths. Nodes are ordered according to their path cost.  Expand least-cost unexpanded node  Equivalent to breadth-first if step costs all equal  Implementation:  3/15/2025 fringe = queue ordered by path cost Uniform cost search using graph search  The problem is to get from Sibiu to Bucharest. Sibiu Fagaras Bucharest Rimnicu vilcea Pitesti Bucharest Ignore loopy path 3/15/2025 Uniform cost search Sibiu 99 Fagaras 0 80 Rimnicu vilcea  The successors of Sibiu are Rimnicu Vilcea and Fagaras with costs 80 and 99, respectively. 3/15/2025 Uniform cost search 0 Sibiu 80 99 Rimnicu vilcea Fagaras 97 Pitesti Sibiu Now, we will Ignore loopy path and in the next iterations 3/15/2025 Uniform cost search Sibiu 99 99 Fagaras 0 80 Rimnicu vilcea 80 97 Pitesti 3/15/2025 177  Adding Pitesti with cost 80 + 97 = 177. Uniform cost search Sibiu 99 99 Fagaras 0 80 Rimnicu vilcea 80 97 310 Bucharest 3/15/2025 Pitesti 177  The least-cost node is now Fagaras, so it is expanded, adding Bucharest with cost 99 + 211 = 310.  Don’t stop explore all other paths. Uniform cost search Sibiu 99 99 Fagaras 211 310 Bucharest 0 80 Rimnicu vilcea 80 97 Pitesti 177 101 Bucharest 3/15/2025 278  Now, a goal node is generated, but uniform-cost search keeps going, by expanding Pitesti and adding a second path to Bucharest with cost 80+97+101 = 278. Uniform Cost Search (UCS) Sibiu 99 99 Fagaras 211 310 Bucharest 0 80 Rimnicu vilcea 80 97 Pitesti 177 101 Bucharest 278 Sibiu Rimnicu vilceaPitesti Bucharest 3/15/2025  Now UCS checks if this new path is better than the old one; it is, so the old one is discarded.  Bucharest, now with g-cost 278, is selected for expansion and the solution is returned. Uniform Cost Search (UCS) Sibiu 99 99 Fagaras 211 310 Bucharest 0 80 Rimnicu vilcea 80 97 Pitesti 177 101 Bucharest 278 Sibiu Rimnicu vilceaPitesti Bucharest 3/15/2025 Drawbacks  Uniform-cost search is guided by path costs rather than depths, so its complexity is not easily characterized in terms of b and d.  let C∗ be the cost of the optimal solution and assume that every action costs at least ∈ . Then the algorithm’s worstcase time and space complexity is O(𝑏1+𝐶∗/∈ ) which can be much greater than 𝑏 𝑑 .  When all step costs are the same, UCS is similar to BFS, except that the BFS stops as soon as it generates a goal, whereas UCS examines all the nodes at the goal’s depth to see if one has a lower cost; thus uniform-cost search does strictly more work by expanding nodes at depth d unnecessarily. Evaluation of tree-search strategies 3/15/2025 3. Depth first search Depth-first search (DFS)  Follows each path to its deepest node, before backtracking to try the next path.  Start from the left side and work toward the right, depth-first search involves working all the way down the left-most path in the tree until a leaf node is reached. If this is a goal state, the search is complete.  If the leaf node does not represent a goal state, search backtracks up to the next highest node that has an unexplored path. 3/15/2025 Depth-first search 3/15/2025 Depth-first search A B D H 3/15/2025 I C E J F k L G M N O Depth-first search A B D H 3/15/2025 I C E J F k L G M N O Depth-first search A B D H 3/15/2025 I C E J F k L G M N O Depth-first search A B D H 3/15/2025 I C E J F k L G M N O Depth-first search A B D H 3/15/2025 I C E J F k L G M N O Depth-first search A B D H 3/15/2025 I C E J F k L G M N O Depth-first search A B D H 3/15/2025 I C E J F k L G M N O Depth-first search A B D H 3/15/2025 I C E J F k L G M N O Depth-first search A B D H 3/15/2025 I C E J F k L G M N O Depth-first search A B D H 3/15/2025 I C E J F k L G M N O Depth-first search A B D H 3/15/2025 I C E J F k L G M N O Depth-first search A B D H 3/15/2025 I C E J F k L G M N O Depth-first search A B D H 3/15/2025 I C E J F k L G M N O Depth-first search A B D H I C E J F k L G M N Goal node 3/15/2025 O Depth first search  Given the following state space (tree search), give the sequence of visited nodes when using DFS (assume that the node O is the goal state): A B F A,B,F,  G,K,  L, O: Goal State  C G K D H L I M E J N O 75 Depth first search  The problem is to get from Sibiu to Bucharest. Sibiu Fagaras Bucharest Ignore loopy path 3/15/2025 Rimnicu vilcea Pitesti Bucharest Sibiu  Depth first search  The problem is to get from Sibiu to Bucharest. Sibiu Fagaras Bucharest Ignore loopy path Rimnicu vilcea Pitesti Bucharest Sibiu  3/15/2025 Fagaras Depth first search  The problem is to get from Sibiu to Bucharest. Sibiu Fagaras Bucharest Ignore loopy path Rimnicu vilcea Pitesti Bucharest Sibiu  Fagaras Bucharest 3/15/2025 Breadth first search vs. depth first search  Breadth-first search is a poor idea in trees where all paths lead to a goal node with similar length paths.  In situations such as this, depth-first search would perform far better because it would identify a goal node when it reached the bottom of the first path it examined. Breadth first search vs. depth first search Scenario Some paths are extremely long or even infinite All paths are of similar length All paths are of similar length, and all paths lead to a goal state High branching factor Depth first Performs bad Breadth first Performs well Performs well Performs well Performs well Wasteful of time and memory Performance depends on other factors Performs poorly Evaluation of tree-search strategies  DFS needs to store only a single path from the root to a leaf node along with the remaining unexpanded sibling nodes for each node on the path.  For a state space with branching factor b and maximum depth m, DFS requires storage of only O(bm) nodes. 3/15/2025 4. Depth limited search Depth-Limited Search (DLS)  Given the following state space (tree search), give the sequence of visited nodes when using DLS (Limit = 2): A Limit = 0 B Limit = 1 Limit = 2 F C G K D H L I M E J N O 83 Depth-Limited Search (DLS)  A, A B C D E Limit = 2 84 Depth-Limited Search (DLS)  A,B, A B Limit = 2 F C D E G 85 Depth-Limited Search (DLS)  A,B,F, A B Limit = 2 F C D E G 86 Depth-Limited Search (DLS)   A,B,F, G, A B Limit = 2 F C D E G 87 Depth-Limited Search (DLS)    A,B,F, G, C, A B Limit = 2 F C G D E H 88 Depth-Limited Search (DLS)    A,B,F, G, C,H, A B Limit = 2 F C G D E H 89 Depth-Limited Search (DLS)     A,B,F, G, C,H, D, A B Limit = 2 F C G D H I E J 90 Depth-Limited Search (DLS)     A,B,F, G, C,H, D,I A B Limit = 2 F C G D H I E J 91 Depth-Limited Search (DLS)      A,B,F, G, C,H, D,I J, Limit = 2 A B F C G D H I E J 92 Depth-Limited Search (DLS)       A,B,F, G, C,H, D,I J, E Limit = 2 A B F C G D H I E J 93 Depth-Limited Search (DLS)       A,B,F, G, C,H, D,I J, E, Failure Limit = 2 A B F C G D H I E J 94 Depth-Limited Search (DLS) DLS algorithm returns Failure (no solution)  The reason is that the goal is beyond the limit (Limit =2): the goal depth is (d=4)  A B Limit = 2 F C G K D H L I M E J N O 95 Evaluation of tree-search strategies  DFS needs to store only a single path from the root to a node in limit (l) along with the remaining unexpanded sibling nodes for each node on the path.  For a state space with branching factor b and maximum limit l, DFS requires storage of only O(bl) nodes. 3/15/2025 5. Iterative Deepening Search IDE Iterative Deepening Search  Strategy: • Based on depth-limited (depth-first) search. • Repeat search with gradually increasing depth limit until a goal state is found.  Implementation: for depth  0 to ∞ do result  depthLimitedSearch(problem, depth) if result ≠ cutoff then return result Iterative Deepening Search (IDS) DLS with bound = 0 Iterative Deepening Search (IDS)  A, Limit = 0 A 100 Iterative Deepening Search (IDS)  A, Failure Limit = 0 A 101 Iterative Deepening Search (IDS) DLS with bound = 1 Iterative Deepening Search (IDS)  A, A Limit = 1 B C D E 103 Iterative Deepening Search (IDS)  A,B, A Limit = 1 B C D E 104 Iterative Deepening Search (IDS)   A,B, C, A Limit = 1 B C D E 105 Iterative Deepening Search (IDS)    A,B, C, D, Limit = 1 A B C D E 106 Iterative Deepening Search (IDS)     A,B C, D, E, Limit = 1 A B C D E 107 Iterative Deepening Search (IDS)     A,B, C, D, E, Failure Limit = 1 A B C D E 108 Iterative Deepening Search (IDS)  A, A B C D E Limit = 2 109 Iterative Deepening Search (IDS)  A,B, A B Limit = 2 F C D E G 110 Iterative Deepening Search (IDS)  A,B,F, A B Limit = 2 F C D E G 111 Iterative Deepening Search (IDS)   A,B,F, G, A B Limit = 2 F C D E G 112 Iterative Deepening Search (IDS)    A,B,F, G, C, A B Limit = 2 F C G D E H 113 Iterative Deepening Search (IDS)    A,B,F, G, C,H, A B Limit = 2 F C G D E H 114 Iterative Deepening Search (IDS)     A,B,F, G, C,H, D, A B Limit = 2 F C G D H I E J 115 Iterative Deepening Search (IDS)     A,B,F, G, C,H, D,I A B Limit = 2 F C G D H I E J 116 Iterative Deepening Search (IDS)      A,B,F, G, C,H, D,I J, Limit = 2 A B F C G D H I E J 117 Iterative Deepening Search (IDS)       A,B,F, G, C,H, D,I J, E Limit = 2 A B F C G D H I E J 118 Iterative Deepening Search (IDS)       A,B,F, G, C,H, D,I J, E, Failure Limit = 2 A B F C G K D H L I M E J N O 119 Iterative Deepening Search (IDS) DLS with bound = 3 Iterative Deepening Search (IDS)  A, A B C D E Limit = 3 121 Iterative Deepening Search (IDS)  A,B, A B F C D E G Limit = 3 122 Iterative Deepening Search (IDS)  A,B,F, A B F C D E G Limit = 3 123 Iterative Deepening Search (IDS)   A,B,F, G, A B F Limit = 3 C D E G K L 124 Iterative Deepening Search (IDS)   A,B,F, G,K, A B F Limit = 3 C D E G K L 125 Iterative Deepening Search (IDS)    A,B,F, G,K, L, A B F Limit = 3 C D E G K L 126 Iterative Deepening Search (IDS)     A,B,F, G,K, L, C, A B F Limit = 3 C G K D E H L 127 Iterative Deepening Search (IDS)     A,B,F, G,K, L, C,H, A B F Limit = 3 C G K D E H L 128 Iterative Deepening Search (IDS)      A,B,F, G,K, L, C,H, D, A B F Limit = 3 C G K D H I E J L 129 Iterative Deepening Search (IDS)      A,B,F, G,K, L, C,H, D,I, A B F Limit = 3 C G K D H L I E J M 130 Iterative Deepening Search (IDS)      A,B,F, G,K, L, C,H, D,I,M, A B F Limit = 3 C G K D H L I E J M 131 Iterative Deepening Search (IDS)       A,B,F, G,K, L, C,H, D,I,M, J, Limit = 3 A B F C G K D H L I M E J N 132 Iterative Deepening Search (IDS)       A,B,F, G,K, L, C,H, D,I,M, J,N, Limit = 3 A B F C G K D H L I M E J N 133 Iterative Deepening Search (IDS)        A,B,F, G,K, L, C,H, D,I,M, J,N, E, Limit = 3 A B F C G K D H L I M E J N 134 Iterative Deepening Search (IDS)        A,B,F, G,K, L, C,H, D,I,M, J,N, E,Failure Limit = 3 A B F C G K D H L I M E J N O 135 Iterative Deepening Search (IDS) DLS with bound = 4 Iterative Deepening Search (IDS)  A, A B C D E Limit = 4 137 Iterative Deepening Search (IDS)  A,B, A B F C D E G Limit = 4 138 Iterative Deepening Search (IDS)  A,B,F, A B F C D E G Limit = 4 139 Iterative Deepening Search (IDS)   A,B,F, G, A B F C D E G K L Limit = 4 140 Iterative Deepening Search (IDS)   A,B,F, G,K, A B F C D E G K L Limit = 4 141 Iterative Deepening Search (IDS)    A,B,F, G,K, L, A B F D E G K Limit = 4 C L O 142 Iterative Deepening Search (IDS)    A,B,F, G,K, L, O: Goal State A B F D E G K Limit = 4 C L O 143 Iterative Deepening Search (IDS)  It does this by gradually increasing the limit—first 0, then 1, then 2, and so on—until a goal is found.  Like DFS, its memory requirements are modest: O(bd).  Like BFS, it is complete when the branching factor is finite and optimal when the path cost is a nondecreasing function of the depth of the node. (optimal if step costs are all identical or increasing)  Iterative deepening search may seem wasteful because states are generated multiple times. It turns out this is not too costly. The reason is that in a search tree with the same (or nearly the same) branching factor at each level, most of the nodes are in the bottom level, so it does not matter much that the upper levels are generated multiple times.  It gives a time complexity of O(b)—asymptotically the same as breadth-first search. Assignment 4 • Depth first search is implemented using …………….. data structure. • Breadth first search is implemented using …………….. data structure. Iterative Deepening Search (IDS) • In general, IDS is the preferred uninformed search method when the search space is large and the depth of the solution is not known. Evaluation of tree-search strategies The total number of nodes generated in the worst case is Assignment 4  Given the following state space (tree search), give the sequence of visited nodes when using BFS, DFS, IDS, DLS (assume that the node O is the goal state): A B F C G K D H L I M E J N O 148 Reference resources • Coppin, B. (2004). Artificial intelligence illuminated. Jones & Bartlett Learning. • Ertel, W. (2024). Introduction to artificial intelligence. Springer Nature. • Russell, S. J., & Norvig, P. (2016). Artificial intelligence: a modern approach. Pearson. 3/15/2025 3/15/2025 CS203 Artificial intelligence Dr. Doaa El-Shahat Lecturer at Computer Science Department Zagazig University, Egypt 3/15/2025 Lecture 5 Solving problems by searching Informed search strategies Dr. Doaa El-Shahat Lecturer at Computer Science Department Zagazig University, Egypt 3/15/2025 Lecture Content  Informed (Heuristic) Search Strategies  Greedy best first search  A* search  Heuristic Functions 3/15/2025 Solve using uniform cost search 5 B c 2 10 8 3 A D F 11 6 4 2 7 E G 5 Initial state: A Goal state: F 3/15/2025 3 Uniform cost search  Uniform cost search is optimal, complete, but inefficient in time and space.  Greedy best first search is not optimal, not complete, but efficient and directed based on selecting good heuristic. 3/15/2025 3/15/2025 Goal-based agent environment properties Static or dynamic? Fully or partially observable? Discrete or continuous? Deterministic or stochastic? Episodic or sequential? Single agent or multiple agent? 3/15/2025 Example: Romania map “Distance in kilometer” 3/15/2025 Search algorithms  uninformed( Blind) search:  breadth-first search  depth-first search  depth limited search  iterative deepening search  bidirectional search  Informed (heuristic) search: search is guided by an evaluation function:  Greedy best-first search  A* search  Recursive best-first search 3/15/2025 Using problem specific knowledge to aid searching  With knowledge, one can search the state space as if he was given “hints” when exploring a maze.  Heuristic information in search = Hints  Leads to dramatic speed up in efficiency. A Search only in this subtree !! C B F G K D H L O I M E J N Greedy best-first search  The algorithm is called “greedy” as it expands the node that is closest to the goal.  It evaluates nodes using the heuristic function: f(n)=h(n). h(n): the straight line distance from node n to goal state.  Note: hSLD values cannot be computed from the problem description. Moreover, it is a useful heuristic to know that hSLD is correlated with actual road distances.  The implementation of best-first search is identical to that for uniform-cost search, except for the use of h(n) instead of g(n) to order the priority queue. Greedy best-first search: Example 1 Evaluation-function: f(n) = h(n) h(n) If n is goal then h(n)=0 Arad Bucharest Craiova Drobeta Eforie Fagaras Giurgiu Hirsova Lasi Lugoj Mehadia Neamt Oradea Pitesti Rimnicu Vilcea Sibiu Timisora Urziceni Vaslui Zerind 366 0 160 242 161 176 77 151 226 244 241 234 380 100 193 253 329 80 199 374 State graph of Romania h(n) 366 3/15/2025 Greedy best-first search (tree search version) Initial state frontier Arad 366 Arad Bucharest Craiova Drobeta Eforie Fagaras Giurgiu Hirsova Lasi Lugoj Mehadia Neamt Oradea Pitesti Rimnicu Vilcea Sibiu Timisora Urziceni Vaslui Zerind 366 0 160 242 161 176 77 151 226 244 241 234 380 100 193 253 329 80 199 374 Greedy best-first search (tree search version) Initial state frontier Arad 366 Arad Bucharest Craiova Drobeta Eforie Fagaras Giurgiu Hirsova Lasi Lugoj Mehadia Neamt Oradea Pitesti Rimnicu Vilcea Sibiu Timisora Urziceni Vaslui Zerind 366 0 160 242 161 176 77 151 226 244 241 234 380 100 193 253 329 80 199 374 State graph of Romania 374 3/15/2025 State graph of Romania 253 3/15/2025 State graph of Romania 329 3/15/2025 Greedy best-first search Sibiu 253 Arad 366 Timisoara 329 Zerind 374 Arad Bucharest Craiova Drobeta Eforie Fagaras Giurgiu Hirsova Lasi Lugoj Mehadia Neamt Oradea Pitesti Rimnicu Vilcea Sibiu Timisora Urziceni Vaslui Zerind 366 0 160 242 161 176 77 151 226 244 241 234 380 100 193 253 329 80 199 374 State graph of Romania 176 3/15/2025 State graph of Romania 193 3/15/2025 State graph of Romania 380 3/15/2025 State graph of Romania 366 3/15/2025 Greedy best-first search Arad 366 Timisoara 329 253 Sibiu Zerind Arad Fagaras Oradea Rimnicu Vilcea 366 176 380 193 374 Arad Bucharest Craiova Drobeta Eforie Fagaras Giurgiu Hirsova Iasi Lugoj Mehadia Neamt Oradea Pitesti Rimnicu Vilcea Sibiu Timisora Urziceni Vaslui Zerind 366 0 160 242 161 176 77 151 226 244 241 234 380 100 193 253 329 80 199 374 Greedy best-first search Arad 366 Timisoara 329 Arad  Sibiu  Fagaras  Bucharest h(n) = 366 from Arad to Buchrest dist(n) = 140 + 99 + 211 = 450 253 Sibiu Arad 366 Fagaras 176 Oradea Rimnicu Vilcea 380 193 Sibiu Bucharest 253 0 Goal state Zerind 374 Arad Bucharest Craiova Drobeta Eforie Fagaras Giurgiu Hirsova Iasi Lugoj Mehadia Neamt Oradea Pitesti Rimnicu Vilcea Sibiu Timisora Urziceni Vaslui Zerind 366 0 160 242 161 176 77 151 226 244 241 234 380 100 193 253 329 80 199 374 Greedy best-first search “tree search version”  Complete? No, is incomplete even in finite state space, much like depthfirst search.(graph search) Consider the problem of getting from Iasi to Fagaras. Iasi Vaslui Neamt Dead end  The heuristic suggests that Neamt be expanded first because it is closest to Fagaras, but it is a dead end. Iasi Vaslui Neamt Vaslui Iasi Neamt Greedy best-first search “tree search version” Arad  Sibiu  Fagaras  Bucharest h(n) = 366 from Arad to Buchrest dist(n) = 140 + 99 + 211 = 450  Optimal? No, since the algorithm only considers the heuristic value and ignores edge weights, it may find a solution that isn’t the shortest or least costly.  There are another path with lower cost value: Arad  Sibiu  Rimnicu Vilcea  PitestiBucharest = 144 + 80 + 97 + 101 = 422 km  Time? O(bm) -- but a good heuristic can give dramatic improvement.  Space? O(bm) -- keeps all nodes in memory. Greedy best-first search We stop when the node with the lowest f-value is a goal state.  Is this guaranteed to find the shortest path? No. Because it always selects the node with the smallest heuristic value, Greedy Best-First Search may quickly find a path, but it does not guarantee finding the shortest path unless the heuristic satisfies certain conditions (complete and optimal) A* search  Greedy search minimizes a heuristic h(n) which is an estimated cost from a node n to the goal state. However, although greedy search can considerably cut the search time (efficient), it is neither optimal nor complete.  Uniform-Cost Search minimizes the cost g(n) from the initial state to n. It is optimal and complete but not efficient.  New Strategy (A* search): Combine greedy search and uniform-cost search to get an efficient algorithm which is complete and optimal. Heuristic Functions  g(n) = The path cost from the initial state to node n.  h(n) = The straight line distance from node n to the goal state.  Three approaches to define f(n): 1. f (n) = g(n)  Uniform cost search “not heuristic function alone” 2. f(n) = h(n)  Greedy best-first search 3. f(n) = g(n) + h(n)  A* search hSLD(n) = straight-line distance from n to Bucharest 30 A* search  It is the best-known form of best-first search.  It is identical to uniform-cost search except that A* uses g + h instead of g. If h(n) =0 for all nodes.  It avoids expanding paths that are already expensive.  Evaluation function: f(n)=g(n) + h(n)  g(n) = The path cost from the initial state to node n.  h(n) = The straight line distance from node n to the goal state.  f(n): The estimated cost of the cheapest solution through n.  It finds the cheapest solution, a reasonable thing to try first is the node with the lowest value of g(n)+h(n). A* search Arad 366=0+366 Arad has the cheapest cost of 366 among frontiers Arad Bucharest Craiova Drobeta Eforie Fagaras Giurgiu Hirsova Lasi Lugoj Mehadia Neamt Oradea Pitesti Rimnicu Vilcea Sibiu Timisora Urziceni Vaslui Zerind 366 0 160 242 161 176 77 151 226 244 241 234 380 100 193 253 329 80 199 374 State graph of Romania 3/15/2025 A* search using tree search Arad 393=140+253 Sibiu 366=0+366 447=118+329 449=75+374 Timisoara Zerind Sibiu has the cheapest cost of 393 among frontiers Note: frontiers are colored with pink color. Arad Bucharest Craiova Drobeta Eforie Fagaras Giurgiu Hirsova Lasi Lugoj Mehadia Neamt Oradea Pitesti Rimnicu Vilcea Sibiu Timisora Urziceni Vaslui Zerind 366 0 160 242 161 176 77 151 226 244 241 234 380 100 193 253 329 80 199 374 A* search using tree search Arad 393=140+253 Sibiu 366=0+366 447=118+329 449=75+374 Timisoara Zerind 646=280+366 415=239+176 671=291+380 Arad Fagaras Oradea 413=220+193 Rimnicu Vilcea Rimnicu Vilcea has the cheapest cost of 413 among frontiers Arad Bucharest Craiova Drobeta Eforie Fagaras Giurgiu Hirsova Lasi Lugoj Mehadia Neamt Oradea Pitesti Rimnicu Vilcea Sibiu Timisora Urziceni Vaslui Zerind 366 0 160 242 161 176 77 151 226 244 241 234 380 100 193 253 329 80 199 374 A* search Arad 393=140+253 Sibiu 366=0+366 447=118+329 449=75+374 Timisoara Zerind 646=280+366 415=239+176 671=291+380 Arad Fagaras Oradea Rimnicu Vilcea 526=366+160 417=317+100 Craiova 413=220+193 Pitesti 553=300+253 Sibiu Fagaras has the cheapest cost of 415 among frontiers Arad Bucharest Craiova Drobeta Eforie Fagaras Giurgiu Hirsova Lasi Lugoj Mehadia Neamt Oradea Pitesti Rimnicu Vilcea Sibiu Timisora Urziceni Vaslui Zerind 366 0 160 242 161 176 77 151 226 244 241 234 380 100 193 253 329 80 199 374 A* search Arad 393=140+253 Sibiu 366=0+366 447=118+329 449=75+374 Timisoara Zerind 646=280+366 415=239+176 671=291+380 Arad Fagaras Oradea Rimnicu Vilcea 526=366+160 417=317+100 Craiova Pitesti 591=338+253 Sibiu 450=450+0 Bucharest 413=220+193 553=300+253 Sibiu Pitesti has the cheapest cost of 417 among frontiers Arad Bucharest Craiova Drobeta Eforie Fagaras Giurgiu Hirsova Lasi Lugoj Mehadia Neamt Oradea Pitesti Rimnicu Vilcea Sibiu Timisora Urziceni Vaslui Zerind 366 0 160 242 161 176 77 151 226 244 241 234 380 100 193 253 329 80 199 374 A* search Arad 393=140+253 Sibiu 366=0+366 447=118+329 449=75+374 Timisoara Zerind 646=280+366 415=239+176 671=291+380 Arad Fagaras Oradea 413=220+193 Rimnicu Vilcea 591=338+253 450=450+0 526=366+160 417=317+100 Sibiu Bucharest Craiova Pitesti Goal 553=300+253 Sibiu Bucharest Craiova Rimnicu Vilcea 418=418+0 615=455+160 607=414+193 Arad Bucharest Craiova Drobeta Eforie Fagaras Giurgiu Hirsova Lasi Lugoj Mehadia Neamt Oradea Pitesti Rimnicu Vilcea Sibiu Timisora Urziceni Vaslui Zerind 366 0 160 242 161 176 77 151 226 244 241 234 380 100 193 253 329 80 199 374 Properties of A* search Complete? Yes (unless there are infinitely many nodes) Time? Exponential Space? Keeps all nodes in memory Optimal? Yes A* search  A∗ search is both complete and optimal.  It has the following properties:  The tree-search version of A* is optimal if h(n) is admissible.  The graph-search version A* is optimal if h(n) is consistent.  A heuristic h(n) is admissible if for every node n h(n) ≤ h*(n), where h*(n) is the true cost to reach the goal state from n.  An admissible heuristic never overestimates the true cost from node n to reach the goal. h*(n) = c(n, goal) Consistency (monotonic) Theorem: If h(n) is consistent, A* using GRAPH-SEARCH is optimal. A heuristic is consistent if for every node n, every successor n' of n generated by any action a h(n) ≤ c(n,a,n') + h(n') Any consistent heuristic is admissible. 3 Admissible? 3 4 3 A 2 S 1 C 7 G 2 B 3 10 3 3 A 2 S C 7 G 2 B 3 5 S h(S)=4 4<= 2+3+7 ✔ 4<=2+2+4 ✔ 4<=1+5+4 ✔ 4<=1+10 ✔ C 7 2 1 G 2 B 5 3 C h(C)=1 1<=7 ✔ D 0 4 10 D h(D)=2 2<=4 ✔ 1 2 1 0 4 D 5 2 4 3 A S 2 1 4 Start state: S Goal state: G 1 D 10 4 0 A h(A)=3 3<= 3+7 ✔ 3<=2+4 ✔ B h(B)=3 3<=5+4 ✔ 3<=10 ✔ Yes, Since for every node n h(n) ≤ h*(n) where h*(n) is the true cost to reach the goal state from n. Consistent? Start state: S Goal state: G 3 4 3 A 2 S 1 C 7 2 1 G 2 B 3 5 D S 4<=3+2 ✔ 4<=3+1 ✔ 0 4 10 Yes, As for every node n: h(n) ≤ c(n, a, n') + h(n'), where n' is a successor of n. A 3<=1+3 ✔ 3<=2+2 ✔ B 3<=2+5 ✔ 3<=0+10 ✔ C 1<=0+7 ✔ D 2<=0+4 ✔ Uninformed search algorithms Informed search algorithms Assignment 5 Solve using BFS, DFS, DLS, IDS, greedy search and A* search using both tree search and graph search A 118 111 Start 75 B 140 C D E 80 99 G F 97 H 101 211 I Goal State A B C D E F G H I Heuristic: h(n) 366 374 329 244 253 178 193 98 0 46 Example 2 • Initial state: Linz • Goal state: Ulm Straight-line distance to Ulm Example 3 Straight-line distance h(n) 5 B 11 6 4 A c 2 3 8 7 2 D E F 10 G 5 3 A B C 28 30 56 D E F G 60 44 10 36 48 Determine if the following graph is admissible and consistent for using the following heuristics h1, h2: State S A B C D G h1 5 3 6 2 3 0 h2 4 2 6 1 3 0 Reference resources • Coppin, B. (2004). Artificial intelligence illuminated. Jones & Bartlett Learning. 3/15/2025 3/15/2025 CS203 Artificial intelligence Dr. Doaa El-Shahat Lecturer at Computer Science Department Zagazig University, Egypt 3/17/2025 Lecture 6 Game theory (Adversarial search) Dr. Doaa El-Shahat Lecturer at Computer Science Department Zagazig University, Egypt 3/17/2025 Lecture Content  What is adversarial search?  Typical assumptions  Different types of games.  Adversarial search formulation  Adversarial search algorithms  Min-max algorithms  Alpha beta pruning 3/17/2025 Adversarial search  Adversarial search is a technique in AI that deals with decision-making problems where multiple agents compete against each other.  These agents often have conflicting goals, making zero-sum game—one agent’s gain is another’s loss.  It is a cornerstone of game theory and forms the foundation for AI systems in competitive environments.  Adversarial search problems are called games. 3/17/2025 Typical assumptions  Two agents whose actions alternate in a competitive environment.  Environment is fully observable, deterministic, turn-taking and zero-sum games.  A zero-sum game is one where the total utility of all players is the same for every instance of the game.  Ex: Chess is zero-sum because every game has utility of either 0+1, 1+0 or 1/2+1/2. 3/17/2025 Turn-taking Different types of games • • • • • • Tic-Tac-Toe Checkers Chess Go Nim Othello  These games are all observable because every player always knows the complete game state.  Games for two players, such as chess, checkers, Othello, and Go are deterministic because each move results in the same child state given the same parent state.  In contrast, backgammon is stochastic because its child state depends on the result of a dice roll. 3/17/2025 Adversarial search formulation  Initial state: specifies how the game is set up at the start.  Players: Defines which player has the move in a state.  Actions: the set of legal moves in a state.  Transition model: defines the result of a move.  Terminal-test: which is true when the game is over and false otherwise. States where the game has ended are called terminal states.  Utility or objective function: defines the final numeric value for a game that ends in terminal state for a player. 3/17/2025 Partial Tic-Toc-Toe tree 3/17/2025  Initial state is the root node.  MAX moves first, placing an X in an empty square.  The tree shows alternating moves between MIN (O) and MAX (X), until reaching terminal states, which can be assigned utilities according to game rules. -1: X lose 0: X draw +1: X win Adversarial search algorithms  They are designed to help agents evaluate and select the optimal moves in competitive environments.  They simulate potential future actions and counteractions to identify the best strategy.  Two of the most widely used algorithms are the Minimax algorithm and Alpha-Beta pruning. 3/17/2025 Minimax Algorithm  The goal of each player is to make optimal moves that result in victory.  Opponents are referred to by MIN and MAX.  MAX player is trying to Maximize his opportunity to win (choose moves with the highest value).  MIN player is trying to Minimize MAX’s opportunity to win (reduce the maximizer’s score). 3/17/2025 Example: Two-ply game tree MAX  The▲ nodes are “MAX nodes” in which it is MAX’s turn to move and the▼ nodes are “MIN nodes.”  The terminal nodes show the utility values for MAX  MAX’s best move at the root is a1, because it leads to the state with the highest minimax value MIN’s best reply is b1, because it leads to the state with the lowest minimax value 3/17/2025 Minimax tree Example 3/17/2025 Time complexity O(𝑏 𝑑 ) Space complexity is O(𝑏 𝑑 ) 𝒃𝟎 +𝒃𝟏 +𝒃𝟐 +…+𝒃𝒅 = O(𝒃𝒅 ) d: is the depth of the tree b: is the branching factor Minimax tree Example 3/17/2025 Alpha-beta pruning  Alpha–beta pruning is a search algorithm that seeks to decrease the number of nodes that are evaluated by the minimax algorithm in its search tree.  Alpha-beta pruning can be applied at any depth of a tree, and sometimes it not only prune the tree leaves but also entire sub-tree.  Condition for Alpha-beta pruning: if α>=β then prune 3/17/2025 Alpha-beta pruning α: MAX’s best option on path to root β: MIN’s best option on path to root  A search space is explored in depth-first down to the full ply depth.  Apply heuristic evaluation to a state and all its siblings.  For MIN nodes, the maximum is backed up to their parent (a MAX node).  For MAX nodes, the minimum is backed up to their parent (a MIN node).  This value is offered to the grandparent as Beta value for MIN nodes, or Alpha value for MAX nodes.  Alpha is a value associated with MAX nodes, that can never decrease.  Beta is a value associated with MIN nodes, that can never increase. 3/17/2025 Example 1 3 3/17/2025 4 7 2 8 1 Example 1 Max (∝) Min (𝜷) Max (∝) 3/17/2025 3 4 7 2 8 1 Example 1 Max (∝) <=3 Min (𝜷) Max (∝) 3/17/2025 3 4 7 2 8 1 Example 1 Max (∝) <=3 Min (𝜷) Max (∝) 3 4 7 2 8 1 Compare 3 with second child 4, Beta will remain 3 3/17/2025 Example 1 Max (∝) <=3 3 Min (𝜷) Max (∝) 3 4 7 2 8 1 Compare Beta value 3 with third child 7, Beta will remain 3 3/17/2025 Example 1 Max (∝) >=3 Min (𝜷) 3 Max (∝) 3 4 7 2 8 1 Alpha=3 is a value associated with player max 3/17/2025 Example 1 Max (∝) >=3 Min (𝜷) 3 Max (∝) 3/17/2025 3 4 7 2 8 1 Example 1 Max (∝) >=3 Min (𝜷) 3 Max (∝) 3 4 <=2 7 Beta value will be <= 2 3/17/2025 2 8 1 Example 1 Max (∝) >=3 Min (𝜷) 3 Max (∝) 3 4 2 7 2 <=2 8 1 Compare beta value with alpha value, if the alpha>=beta value, prune the rest of the tree 3>=2 yes 3/17/2025 Example 1 3 Max (∝) 3 Min (𝜷) Max (∝) 3 4 2 7 2 <=2 8 1 Compare beta value with alpha value, if the alpha>=beta value, prune the rest of the tree 3>=2 yes 3/17/2025 Alpha-beta pruning 3/17/2025 Alpha-beta pruning 3/17/2025 Alpha-beta pruning 3/17/2025 Alpha-beta pruning 3/17/2025 Alpha-beta pruning 3/17/2025 Alpha-beta pruning 3/17/2025 Alpha-beta pruning 3/17/2025 Alpha-beta pruning 3/17/2025 Complexity of alpha beta algorithm  Alpha-beta algorithm performs a complete depth-first exploration of the game tree. m: maximum depth of the tree b: legal moves at each point  Time complexity: O(𝑏 𝑚 ).  Space complexity: O(bm) if algorithm generates all actions at once or O(m) if algorithm generates actions one at a time. 3/17/2025 Assignment 6 Max (∝) Min (𝜷) Max (∝) 3/17/2025 Assignment 6 3/17/2025 Assignment 6 3/17/2025 3/17/2025 CS203 Artificial intelligence Dr. Doaa El-Shahat Lecturer at Computer Science Department Zagazig University, Egypt 4/19/2025 Lecture 7 Fuzzy sets and fuzzy logic Dr. Doaa El-Shahat Lecturer at Computer Science Department Zagazig University, Egypt 4/19/2025 Lecture Content 4/19/2025 4 Set • Set is a collection of elements. – Crisp set. – Fuzzy set. 5 The crisp set The crisp set is also called classical = traditional =conventional =ordinary sets. Crisp means clean, clear and sharp. The set is a collection of elements. Each element either belongs to the set or it does not (member or not member),(true or false), (zero or one). 6 The crisp set Examples:  A={x|x is even natural number}  A={x|x=2n,n is natural number}  A={apple, orange, mango}  A={a, b , c, d, e, i, y} 1 𝑖𝑓 𝑥 ∈ 𝐴 Membership or characteristic function: 𝜇𝐴 𝑥 = 0 𝑖𝑓 𝑥 ∉ 𝐴  A={x|x is even natural number}. 𝝁𝑨 𝟓 =0, 𝝁𝑨 𝟒 = 𝟏  A={apple, orange, mango}. 𝝁𝑨 𝒂𝒑𝒑𝒍𝒆 = 𝟏 7 Operations on crisp sets • Union: A  B = {x | x  A or x  B} • Intersection: A  B = {x | x  A and x  B} • Complement: A’ = {x | x  A, x  X} • Difference: A | B = {x | x  A and x  B} It is also denoted by A - B 8 Properties of the crisp sets • • • • AB=BA AB=BA A  (B  C) = (A  B)  C A  (B  C) = (A  B)  C • A  (B  C) = (A  B)  (A  C) • A  (B  C) = (A  B)  (A  C) • • • • • • AA=A AA=A AU=U AU=A A=A A= 9 Crisp set • A crisp set is defined by sharp boundaries and contain the precise location of the set boundaries. • It is clear that an element either belongs to a set or does not belong to that set in the classical set and its operation. • The temperature can be divided into three categories: LOW (0~30°F), MEDIUM (30°F~70°F) and HIGH (70~120°F) and the boundary is crystal clear. 10 Origins of fuzzy logic Lotfi Asker Zadeh ( 1965 )  First to publish ideas of fuzzy logic.  Professor Toshire Terano ( 1972 )  Organized the world's first working group on fuzzy systems.  F.L. Smidth & Co. ( 1980 )  First to market fuzzy expert systems. Crisp/classical vs. fuzzy sets 12  The temperature 40°F belongs to LOW with 0.5 degree, but at the same time it belongs to MEDIUM to about 0.7 degree.  The temperature 50°F, can be considered to belong to LOW and HIGH to around degree and belong to MEDIUM to almost 1 degree Fuzzy set Fuzzy – “not clear, vague, not distinct, or not precise”. • A set defined by membership functions is a fuzzy set. • Given a fuzzy set A and an element x, “x is a member of A” is not necessarily either true or false(0 or 1). • In fuzzy set, each possible element has its degree of membership ∈ [𝟎, 𝟏]. • 𝜇𝐴 𝑥 → [0, 1] 14 Example (Discrete Universe) Given a universe U={1,2,3,4,5,6,7,8}. The fuzzy set A can be represented as: First representation: A={(1,0.1),(2,0.3),(3,0.8),(4,1),(5,0.9),(6,0.5),(7,0.2),(8,0.1)} Second representation: A    A ( xi ) / xi xi U A  0.1/ 1  0.3/ 2  0.8/ 3  1.0 / 4  0.9 / 5  0.5/ 6  0.2 / 7  0.1/ 8 15 Example (Continuous Universe) possible ages U : the set of positive real numbers B  ( x,  B ( x )) x  U   B ( x)  1  x  50  1   5   4 1.2 1  B ( x) Alternative Representation: B about 50 years old 0.8 0.6 0.4 0.2 1 R  1  x 550  4 x 0 0 20 40 x : age 60 80 100 16 Alternative Notation A  ( x,  A ( x )) x  U  U : discrete universe A    A ( xi ) / xi U : continuous universe A    A ( x) / x xi U U Note that  and integral signs stand for the union of membership grades; “ / ” stands for a marker and does not imply division. 17 Fuzzy set • A fuzzy set is determined by its indeterminate boundaries, there exists an uncertainty about the set boundaries. • For example, the temperature 40°F can be considered to belong to LOW to a certain degree, say 0.5 degree, but at the same time it can belong to MEDIUM to about 0.7 degree. 18 Linguistic variable • Fuzzy terms are reffered as linguistic variables. • Linguistic variable is a term used in our natural language to describe some concept that usually has vague or fuzzy values. • Each linguistic variable has name, fuzzy sets. • Example Name Temprature Height Speed Price Fuzzy sets hot, cold, warm, cool. short, medium, tall. slow, fast, creepting. cheap, expensive. 19 Hedges • Hedges are qualifiers of a linguistic variable. All purpose: very, quite, extermely. Probability: likely, unlikely. Quantifiers: most several, few. Possability: almost, impossible, quite possible. 20 Linguistic variable • Example: Jhon is very tall. • Name: height. • Fuzzy set: tall. • Hedge: very. 21 Natural Language  Consider:  Joe is tall -- what is tall?  Joe is very tall -- what does this differ from tall?  Natural language (like most other activities in life and indeed the universe) is not easily translated into the absolute terms of 0 and 1. “false” “true” 22 Example: “Young”  Example:  Ann is 28,  Bob is 35,  Charlie is 23, 0.8 in set “Young” 0.1 in set “Young” 1.0 in set “Young”  Unlike statistics and probabilities, the degree is not describing probabilities that the item is in the set, but instead describes to what extent the item is the set. 23 Membership function of fuzzy logic Fuzzy values Degree of Membership 1 Young Middle Old 25 40 55 0.5 0 Age Fuzzy values have associated degrees of membership in the set. 24 Example II Linguistic Variable : temperature Linguistics Terms (Fuzzy Sets) : {cold, warm, hot} (x) 1 cold warm 20 hot 60 x 25 Crisp vs fuzzy Basis for comparison Fuzzy Set Crisp Set Basic Prescribed by vague or ambiguous properties. Defined by precise and certain characteristics. Property Elements are allowed to be partially included in the set. Element is either the member of a set or not. Applications Used in fuzzy controllers Digital design Logic multi-valued logic bi-valued logic 26 Fuzzy sets: basic concepts • Consider three fuzzy sets that represent the concepts of a young, middle-aged, and old person. The membership functions are defined on the interval [0,80] as follows: Find line passing through (x,y) and (20,1): 1/[35-20] = y/[35-x] 27 Fuzzy sets: basic concepts 28 Operations of fuzzy sets • The complement of fuzzy set A with respect to the universal set X is x X defined for all by the equation A ( x )  1  A( x ) A ( x)  A( x) • Elements of X for which are called equilibrium points of A. For example, the equilibrium points of A2 in Fig. 1.7 are 27.5 and 52.5. 29 Operations on fuzzy sets • Equality of fuzzy sets • Containment of fuzzy sets • Complement of a fuzzy set • Intersetion of fuzzy sets (AND) • Union of fuzzy sets (OR) 30 Equality of two fuzzy sets • For crisp sets, sets are equal if the two sets have exactly the same elements. • For fuzzy sets, however, equality cannot be concluded if the two sets have the same elements. The degree of membership of elements to the sets must also be equal. That is, the membership functions of the two sets must be the same. • Therefore, two fuzzy sets A and B are equal if and only if the sets have the same domain, and μA(x) = μB(x) for all x ∈ X. That is, A=B. • Example: domain X={1,2,3}, A={(1,0.1),(2,0.5),(3,0.4)}, B={(1,0.1),(2,0.5),(3,0.4)} 31 Containment of fuzzy sets • For crisp sets, A ⊂ B if all the elements of A are also elements of B. • For fuzzy sets, this definition is not complete, and the degrees of membership of elements to the sets have to be considered. • Fuzzy set A is a subset of fuzzy set B if and only if μA(x) ≤ μB(x) for all x ∈ X. That is, A ⊂ B. 32 Complement of a fuzzy set (NOT) • The complement of a crisp set is simply the set containing the entire domain without the elements of that set. • For fuzzy sets, the complement of the set A consists of all the elements of set A, but the membership degrees differ. Let A denote the complement of set A. Then, for all x∈X, μA(x)=1−μA(x). It also follows that A∩ 𝐴 =∅ and A∪𝐴=X. (T or F) 33 Fuzzy sets 34 Complement of A 35 Intersection of fuzzy sets (AND) • The intersection of crisp sets is the set of elements occurring in both sets. • Operators that implement intersection are referred to as tnorms. The result of a t-norm is a set that contain all the elements of the two fuzzy sets, but with degree of membership that depends on the specific t-norm. A number of t-norms have been used, of which the min-operator and the product operator are the most popular. If A and B are two fuzzy sets, then – Min-operator: μA∩B(x) = min{μA(x),μB(x)}, ∀x ∈ X. 36 Intersection of fuzzy sets (AND) 37 Intersection 38 Union of fuzzy sets (OR) • The union of crisp sets contains the elements of all of the sets. • The same is true for fuzzy sets, but with membership degrees that depend on the specific union operator used. These operators are referred to as s-norms, of which the max-operator and summation operator are most frequently used: – Max-operator: μA∪B(x) = max{μA(x),μB(x)}, ∀x ∈ X 39 Union of fuzzy sets (OR) 40 Fuzzy set characteristics • Normality • Height • Cardinality • Support • Core • ∝ −𝑐𝑢𝑡 41 Normality • A fuzzy set A is normal if that set has an element that belongs to the set with degree 1. That is, ∃x ∈ A • μA(x) = 1 • then A is normal, otherwise, A is subnormal. 42 Fuzzy set characteristics • The height of a fuzzy set is defined as the supremum of the membership function, i.e. height(A) = sup μA(x) • The support of fuzzy set A is the set of all elements in the universe of discourse, X, that belongs to A with non-zero membership. That is, support(A) = {x ∈ X|μA(x) > 0} • The core of fuzzy set A is the set of all elements in the domain that belongs to A with membership degree 1. core(A) = {x ∈ X|μA(x) = 1} 43 Fuzzy set characteristics • α-cut: The set of elements of A with membership degree greater than α is referred to as the α-cut of A: Aα = {x ∈ X|μA(x) ≥ α} 44 Fuzzy set characteristics • The cardinality of crisp sets is simply the number of elements within the sets. • The cardinality of fuzzy set A, for a finite domain, X, is defined as card(A) = 𝑥∈𝑋 μA(x) • • • • • For example, X = {a, b, c, d}, and A = 0.3/a + 0.9/b + 0.1/c + 0.7/d, Cardinality (A) or |A| = 0.3 + 0.9 + 0.1 + 0.7 = 2.0. Height(A)=0.9. Support of (A)={a, b, c, d} Core(A)=∅ no elements with membership=1. 45 Fuzzy Sets Example Consider the following two fuzzy sets: Universe={1,2,3,4,5} A = { 1/2 + 0.5/3 + 0.3/4 + 0.2/5} B = {0.5/2 + 0.7/3 + 0.2/4 + 0.4/5} 𝐴= { 1/1 + 0/2 + 0.5/3 + 0.7/4 +0.8/5} 𝐵 = { 1/1 + 0.5/2 + 0.3/3 + 0.8/4 +0.6/5} Union: A U B = {1/2 + 0.7/3 + 0.3/4 +0.4/5} Intersection: A ∩B = {0.5/2 + 0.5/3 + 0.2/4 +0.2/5} 46 47 48 Boolean logic  In Boolean logic, only two possibilities (0 and 1) exist, where 1 denotes the absolute truth value and 0 denotes the absolute false value. 49 Fuzzy logic  In fuzzy logic, there are multiple possibilities present between the 0 and 1, which are partially false and partially true.  Fuzzy logic can be implemented in systems, such as:  micro-controllers  workstation-based or large network-based systems for achieving the definite output.  Fuzzy logic can also be implemented in both hardware or software 50 4/19/2025 Lec. 5 Artificial neural network Faculty of Computers and Informatics, Computer Science Department, Zagazig University, Egypt Artificial neural network  Artificial neural network (ANN) can be defined as an information-processing model inspired by the biologcal nervous systems (biological neural network), such as the brain.  This model tries to replicate the most basic functions of the brain.  ANN is an architecture consisting of a large number of neurons organized in different layers and the neurons of one layer are connected to those of another layer by means of weights. By Doaa El-Shahat 3 Biological neural network  The human brain consists of nearly 1011 of neurons and 60 trillion connections (synapses) among them.  Each neuron has a very simple structure, but a huge number of such neurons constitute a tremendous processing power.  By using multiple neurons simultaneously, the brain can perform its functions in parallel and much faster than the fastest computers.  The information is stored and processed simultaneously throughout the whole network rather than specific locations. In other words, processing is global rather than local. By Doaa El-Shahat 4 Biological neural network Dendrites  The biological neuron consists of three main parts:  Soma or cell body: where the cell nucleous is located.  Dendrites: where the nerve is connected to the cell body  Axon: which carries the impulses of the neuron  Synapse is that part of a neuron, where its axon contacts the dendrites of its neighboring neuron. Soma Axon Synapse 5 Biological neural network  The neurons are communicating with each other with the help of electrical impulses. 6 Biological neural network  A neuron collects information from its neighbors with the help of its dendrites.  The collected information is then summed up in the cell body, before it passes through the axon. This information is then transferred to the next neuron through the synapse.  Learning is a fundamental and essential characteristic of biological neural network. 7 Brain vs. computer ANN BNN Speed Faster in processing information.Response time is nanosecond. Slower in processing information. Response time in milliseconds processing Serial processing Massively parallel processing Size and complexity Less size complexity Storage Replaceable Information storage: replacing new data with old data. & Highly complex Information storage is adaptable means such that new information is added by adjusting the interconnection strengths without destroying old information By Doaa El-Shahat 8 Brain vs. computer ANN Fault tolerance BNN Information once It possesses fault corrupted cannot be tolerance as it can store retrieved in case of and retrieve information. failure of the system By Doaa El-Shahat 9 Artificial neural network  ANN consists of a number of very simple processors, also called neurons, which are analogous to the biological neurons in the brain. By Doaa El-Shahat 10 Artificial neuron Biological NN Artificial NN Cell Neuron Dendrite Input Soma Net input Synapse weight Axon Output By Doaa El-Shahat 11 Basic concept of ANN  Dendrites are represented as input signal where data, such as features or variables for problem solving will be provided here.  Cell body or soma is where linear combination computation ( ) and activation function f ( ) is applied.  Axon is represented as output signal where the result of computation process in cell body will be delivered to another neuron. By Doaa El-Shahat 12 Artificial neuron model By Doaa El-Shahat 13 Artificial neuron model  Suppose that there are n input signals (I1,I2,I3,…, In) to a neuron. Each input signal has a weight (w1,w2,w3,…,wn).  Weights determines strength of connections between neurons. It can amplify or deamplify the input signal. if wj>1 amplify input signal if wj<1 deamplify input signal neuron 14 Artificial neuron model  The summing junction of artificial neuron computes the weighted sum of input signals (net input). (similar to the function of dendrites and soma). Net input= uj = 𝐧 𝐣=𝟏 𝐈𝐣 × 𝑾𝒋+ b  To obtain the output signal of a neuron, the net input is passed as input to the activation function: Output=Oj=f(uj) neuron 15 Activation function  To better understand the role of the activation function, let us assume a person is performing some work. To make the work more efficient and to obtain exact output, some force or activation may be given.  The activation function (transfer function) is used to transfer the net input into output signal.  It decides whether the neuron can be activated or not based on a threshold value.  There are various types of activation function that can be used. By Doaa El-Shahat 16 Activation function (cont.) Identity function (linear) It is a linear function and can be defined as: 𝒇(𝒙) = 𝒙 𝒇𝒐𝒓 𝒂𝒍𝒍 𝒙 The output remains as the same as input. Binary step function converts the net input into binary ouput 1 or 0. 𝜽 is a threshold value 𝒇 𝒙 = 𝟏 𝒊𝒇 𝒙 ≥ 𝜽 𝟎 𝒊𝒇 𝒙 < 𝜽 Bipolar step function converts the net input into bipolar ouput 1 or -1. 𝜽 is a threshold value 𝒇 𝒙 = 𝟏 𝒊𝒇 𝒙 ≥ 𝜽 −𝟏 𝒊𝒇 𝒙 < 𝜽 17 Activation function (cont.) Binary sigmoid function converts the net input into ouput in [0,1]. 𝝀 is a steepness (slope) parameter to obtain sigmoid functions of different slopes. 𝟏 𝑓 𝒙 = 𝟏 + 𝒆−𝝀𝒙 Bipolar sigmoid function converts the net input into ouput in [-1,1]. 𝝀 is a slope parameter −𝝀𝒙 𝒇 𝒙 = 𝟐 𝟏−𝒆 − 𝟏 = 𝟏 + 𝒆−𝝀𝒙 𝟏 + 𝒆−𝝀𝒙 Ramp function maps the net input to output over a range (0,1). 𝟏 𝒊𝒇 𝒙 > 𝟏 𝒇 𝒙 = 𝒙 𝒊𝒇 𝟎 ≤ 𝒙 ≤ 𝟏 𝟎 𝒊𝒇 𝒙 < 𝟎 18 Sigmoid function with varying slope 𝜆 = 0.5 𝜆=1 𝜆=2 By Doaa El-Shahat 19 Example 1 By Doaa El-Shahat 20 Solution to Example 1 By Doaa El-Shahat 21 Example 2 By Doaa El-Shahat 22 Solution to Example 2 By Doaa El-Shahat 23 Example 3 By Doaa El-Shahat 24 Solution to Example 3 By Doaa El-Shahat 25 Solution to Example 3 By Doaa El-Shahat 26 Example 4 By Doaa El-Shahat 27 Example 5 By Doaa El-Shahat 28 Bias  Bias allows you to shift the net input by adding a constant (i.e., the given bias) to the input.  It is somehow similar to the constant b of a linear function y = ax + b y=I1 W1+b  With b, we can shift the line to fit the prediction with the data better. Without b, the line always goes through the origin (0, 0) and you may get a poorer fit which is not in accordance with real-world scenario. Y=ax Y=ax+b 29 Bias  Bias plays a major role in determining the output of the network.  The bias can be of two types: positive bias and negative bias.  The positive bias helps in increasing the net input of the network.  The negative bias helps in decreasing the net input of the network.  Thus, as a result of the bias effect, the output of the network can be varied. By Doaa El-Shahat 30 Bias  Given I1=1, w1=2, I2=2, w2=2. Compute net input. Net input=I1×W1+I2×W2=1×2+2×2=6  Suppose after applying activation function the output becomes 1.To control the output, we can add the bias, suppose b=-6. Net input=I1×W1+I2×W2+b=1×2+2×2+(-6)=0 Suppose after applying activation function the output becomes 0. By Doaa El-Shahat 31 Layer of neurons Layer of neurons contains n input signals(I1, I2, . . . , In) connected to this layer of neurons through the weights [W ]. By Doaa El-Shahat 32 Types of layers in ANN • An Input Layer that takes as input the raw data and passes them to the rest of the network. • One or more Hidden Layers that are intermediate layers between the input and output layer and process the data by applying complex non-linear functions to them. • An Output Layer that takes as input the processed data and produces the final results. By Doaa El-Shahat 33 Multiple layers of neurons By Doaa El-Shahat 34 ANN usages By Doaa El-Shahat 35 Regressoin  Regression: is a statistical method that determines relationship between independent variable to dependent variable to obtain fitted function according to data.  The purpose of using ANN for Regression over Linear Regression is that the linear regression can only learn the linear relationship between the features and target and therefore cannot learn the complex non-linear relationship. 36 • Regression estimates the relationship between a target outcome label and one or more feature variables to predict a continuous numeric value. In the simple example below linear regression is variables to predict a continuous numeric value. • In the simple example below linear regression is used to estimate the house price (the label) based on the house size (the feature). By Doaa El-Shahat 37 By Doaa El-Shahat 38 Regressoin (cont.)  ANNs can learn the complex relationship between the features and target due to the presence of non-linear activation function in each layer. Best fitting, linear regression Poor fitting, non-linear regression By Doaa El-Shahat Good fitting, non-linear regression 39 Classification  Classification predict class of input data according to target or data label. By Doaa El-Shahat 40 Clustering  Clustering is the task of grouping set of objects that are similar in the same cluster or group without data label or target. By Doaa El-Shahat 41 Forecasting  Forecasting: predict future condition using present and past data or known as time series data. By Doaa El-Shahat 42 Artificial neuron Learning  Is there an approach for determining the values of the weights 𝑾𝒊 and threshold 𝜽?  It is easy to calculate the values of 𝑊𝑖 and 𝜃 for simple problems.  But suppose that no prior knowledge exists except for data. How can 𝑊𝑖 and 𝜃 values be computed? Through learning.  The AN learns the best values for the 𝑊𝑖 and 𝜃 from the given data. By Doaa El-Shahat 43 Learning  Learning consists of adjusting weight and threshold values until a certain criterion (or several criteria) is (are) satisfied.  There are three main types of learning: 1. Supervised learning. 2. Unsupervised learning. 3. Reinforcement learning. 44 Supervised learning  The neuron (or NN) is provided with a data set consisting of input and desired output. This data set is referred to as the training set.  The aim of supervised training is then to adjust the weight values such that the error between the output o = f(net−θ), of the neuron and the desired output is minimized.  Develop predictive model based on input and output data. By Doaa El-Shahat 45 Supervised learning • Supervised machine learning, also called predictive analytics, uses algorithms to train a model to find patterns in a dataset with labels and features. • It then uses the trained model to predict the labels on a new dataset’s features. • Supervised learning can be further categorized into classification and regression. By Doaa El-Shahat 46 Supervised learning By Doaa El-Shahat 47 By Doaa El-Shahat 48 Unsupervised learning  Unsupervised learning, where the aim is to discover patterns or features in the input data with no assistance from an external source.  No idea which types of results are expected, such as clustering and dimensionality reduction.  Unsupervised learning doesn’t have labeled data provided in advance, and can aid data scientists in finding previously unknown patterns in data. These algorithms attempt to ‘learn’ the inherent structure in the input data, discovering similarities, or regularities. Common unsupervised tasks include clustering andEl-Shahat association. By Doaa 49 Unsupervised learning In clustering, an algorithm classifies inputs into categories by analyzing similarities between input examples. An example of clustering is a company that wants to segment its customers in order to better tailor products and offerings. Customers could be grouped on features such as demographics and purchase histories. By Doaa El-Shahat 50 By Doaa El-Shahat 51 Reinforcement learning  There are no training data sets.  An example of reinforcemnent learning problem is playing game.  where the aim is to reward the neuron (or parts of a NN) for good performance, and to penalize the neuron for bad performance.  Several learning rules have been developed for the different learning types. Before continuing with these learning rules, we simplify our AN model by introducing augmented vectors. By Doaa El-Shahat 52 Learning By Doaa El-Shahat 53 Drawbacks of neural networks By Doaa El-Shahat 54 1. High Computational Cost • Explanation: Training ANNs requires massive computational power, especially for large datasets or deep architectures (e.g., CNNs, transformers). • Example: Training GPT-3 (a large language model) costs millions of dollars in computing resources. • Impact: Limits accessibility for individuals/small organizations without access to GPUs/TPUs. • By Doaa El-Shahat 55 2. Need for Large Datasets • Explanation: ANNs often require vast amounts of labeled data to generalize well. • Example: Image recognition models like ResNet need millions of labeled images (e.g., ImageNet). • Impact: Collecting and annotating data is time-consuming and expensive. By Doaa El-Shahat 56 3-Overfitting • Explanation: ANNs may memorize noise/patterns in training data instead of learning generalizable features. • Example: A model trained to classify cats/dogs fails on new images because it overfits to background colors. • Solution: Regularization (e.g., dropout, weight decay) or cross-validation. By Doaa El-Shahat 57 When to Avoid ANNs? • Small datasets. • Real-time applications with limited computational resources By Doaa El-Shahat 58 Optimization 1  Optimization is the process of finding the best solution out of all feasible solutions. Optimization  The aim of optimization is to find an algorithm which solves a given class of problems.  There exists no specific method which solves effectively all optimization problems (No free launch theorems). 2 Classification of optimization problems 1. Depending on the nature of equations involved in the objective function and constraints:  Linear optimization problem  Non-linear optimization problem 3 Linear optimization problem  An optimization problem is called linear, if both the objective function as well as all the constraints are found to be linear functions of design variables. Maximize: y = f(x1, x2) = 2x1 + x2 subject to: x1 + x2 ≤ 3, 5x1 + 2x2 ≤ 10. and x1, x2 ≥ 0. 4 -> objetive function -> constraint ->bounds of a variable Non-linear optimization problem  An optimization problem is called non-linear, if any one or both of the objective function and the constraints are found to be non-linear functions of design variables. Maximize: y = f(x1, x2) =x12 + x23 subject to: x14 + x22 ≤ 629, x13 + x23 ≤ 133, and x1, x2 ≥ 0. 5 Classification of optimization problems (cont.) 2. Based on the existence of any functional constraint:  Un constrained optimization problem.  Constrained optimization problem. 6 Un constrained vs constrained optimization problem  The unconstrained optimization problem does not contain any functional constraints, such as: Minimize: y = f(x1, x2) = (x1 − 5)2 + (x2 − 1)2 and x1, x2 ≥ 0.  The constrained optimization problem contains at least one functional constraint, such as: Minimize: y = f(x1, x2) = (x1 − 5)2 + (x2 − 1)2 Subject to: x1 − 5 x2 < 50. and x1, x2 ≥ 0. 7 Classification of optimization problems (cont.) 3. Depending on the type of design variables:  Integer programming optimization problem.  Real-valued programming optimization problem.  Mixed integer programming optimization problem. 8 Integer programming problem  An optimization problem is said to be an integer programming problem, if all the design variables take only integer values. Maximize y = f(x1, x2) = 2x1 + x2 subject to x1 + x2 ≤ 3, 5x1 + 2x2 ≤ 9. and x1, x2 ≥ 0, x1, x2 are integers. 9 Real-valued programming problem  An optimization problem is said to be real-valued programming problem, if all the design variables take only real values. Maximize y = f(x1, x2) = 2x1 + x2 subject to x1 + x2 ≤ 3.2, 5x1 + 2x2 ≤ 9.5. and x1, x2 ≥ 0.0, x1, x2 are real values. 10 Mixed programming problem  An optimization problem is said to be an mixed programming problem, if some of the design variables take integer values and the remaining design variables take real values. Maximize y = f(x1, x2) = 2x1 + x2 subject to x1 + x2 ≤ 3.2, 5x1 + 2x2 ≤ 9.5. and X1>3, x2 ≥ 0.0, x1 is integer and x2 real values. 11 Single objective vs multi-objective optimization problem 4. Depending on the number of objective functions:  Single optimization problem.  Multi-objective optimization problem.  Single optimization problem is a problem that contains only one objective function to be optimized (maximized or minimized).  Multi-objective optimization problem is a problem that has a set or vector of conflicting objective functions to be optimized. 12 Combinatorial vs continuous optimization problem 13 ▪ Combinatorial or discrete optimization problem is an optimization problem in which its design variables takes discrete values. ▪ Continuous optimization problem is an optimization problem in which its design variables takes continuous values. Optimization methods 1. Exact method  Advantage: it can guarantee to find the accurate and optimal solution, such as dynamic programming, branchand-bound, and integer linear programming.  Disadvantage: in the worst case, if the problem size is increased, the time complexity would be increased exponentially.  It is suitable for small- scale optimization problems. 2. Approximate method  It can not guarantee to find the accurate solution.  It obtains approximate solutions in an acceptable and reasonable time.  It is suitable for large-scale optimization problems. 14 Heuristic method  It is an approximate method designed to solve quickly the problem, while scarifying the exact solution.  They are often problem-dependent, that is, you define a heuristic for a given problem.  The quality of solution depends on the initial starting points. 15 Knapsack problem  Knapsack problem is difficult to solve in large scale.  Exact methods may take thousands of years (NP-hard ). 0-1 Knapscak problem (cont.)  0-1 KP contains a set of 𝑛 items. Each item 𝑖 has a weight 𝑤𝑖 and a profit 𝑝𝑖 .  Objective function: maximize profit of the selected items in the knapsack.  Constraint: The sum of weights of packed items must not exceed the knapsack capacity 𝑐. Each item can be selected once or not (𝑥𝑖 = 1 𝑜𝑟 𝑥𝑖 = 0). 𝑛 𝑀𝑎𝑥 𝑖=1 𝑝𝑖 𝑥𝑖 0−1 𝐾𝑃 𝑆. 𝑡. 𝑛𝑖=1 𝑤𝑖 𝑥𝑖 ≤ c 𝑥𝑖 ∈ 0,1 Fractional knapsack problems(cont.)  In 0-1 knapsack problems, each item is selected or not to be in put in the knapsack with nor fractions.  In fractional knapsack problem, we can take fraction of an item such that the total weights of all items can’t exceed the capacity of the knapsack. Solved example using greedy algorithm • • Knapsack Capacity: 15 kg Items (Weight, Value): • Item 1: 2 kg, $10 • Item 2: 5 kg, $20 • Item 3: 10 kg, $30 • Item 4: 5 kg, $16 • Item 5: 3 kg, $18 1. Calculate Value-to-Weight Ratios: ▪ 1 10/2=5$ ▪ 2 20/5=4$ ▪ 3 30/10=3$ ▪ 4 16/5=3.2$ ▪ 5 18/3=6$ 2. Sort Items by Value/kg (Descending): Item 5 → Item 1 → Item 2 → Item 4 → Item 3. 19 Greedy algorithm for 0-1 KP • • 1. Calculate Value-to-Weight Ratios: Knapsack Capacity: 16 kg ▪ 1 10/2=5$ Items (Weight, Value): ▪ 2 20/5=4$ • Item 1: 2 kg, $10 ▪ 3 30/10=3$ • Item 2: 5 kg, $20 ▪ 4 16/5=3.2$ • Item 3: 10 kg, $30 ▪ 5 18/3=6$ • Item 4: 5 kg, $16 • Item 5: 3 kg, $18 2. Sort Items by Value/kg (Descending): Item 5 → Item 1 → Item 2 → Item 4 → Item 3. 20 • Total weight=3 + 2 + 5 + 5=15Kg • Total value=18+ 10+20+16=64$ • Items: 5, 1, 2, 4, stop as fractions can’t be allowed Greedy algorithm for fractional KP • • 1. Calculate Value-to-Weight Ratios: Knapsack Capacity: 16 kg ▪ 1 10/2=5$ Items (Weight, Value): ▪ 2 20/5=4$ • Item 1: 2 kg, $10 ▪ 3 30/10=3$ • Item 2: 5 kg, $20 ▪ 4 16/5=3.2$ • Item 3: 10 kg, $30 ▪ 5 18/3=6$ • Item 4: 5 kg, $16 • Item 5: 3 kg, $18 2. Sort Items by Value/kg (Descending): Item 5 → Item 1 → Item 2 → Item 4 → Item 3. 21 • Total weight=3 + 2 + 5 + 5+1=16 Kg • Total value=18+ 10+20+16+6=70$ optimal • Items: 5, 1, 2, 4, 1/10 of item 3 Knapsack problem (cont.) Example of knapsack problem Example of knapsack problem Item no. Weight Profit 1 2 3 4 5 12 1 4 1 2 4 2 10 1 2 Problem Statement ▪ ▪ ▪ 25 Knapsack Capacity: 15 kg Items Available: ▫ Item 1: Weight = 10 kg, Value = $60 ▫ Item 2: Weight = 20 kg, Value = $100 ▫ Item 3: Weight = 30 kg, Value = $120 Goal: Maximize the total value without exceeding the knapsack capacity (fractions allowed). Solution Using Greedy Algorithm ▪ Step 1: Calculate Value-to-Weight Ratio Sort items by value per kilogram (descending order): ▪ ▪ ▪ ▪ Item 1: 60/10 = 6$ Item 2: 100/20 = 5$ Item 3: 120/30 = 4$ Sorted Order: Item 1 → Item 2 → Item 3 ▪ Step 2: Fill the Knapsack Greedily ▪ Take Item 1 (10 kg): ▫ Remaining Capacity: 15−10=5 kg15−10=5kg ▫ Value Added: $60 ▪ Take Fraction of Item 2 (5 kg): ▫ Item 2’s total weight = 20 kg, but only 5 kg needed. ▫ Fraction Taken: 520=0.25205=0.25 ▫ Value Added: 0.25×100=$250.25×100=$25 ▫ Remaining Capacity: 5−5=0 kg5−5=0kg ▪ Item 3 is skipped (no remaining capacity). Final Result ▪ Total Value: $60+$25=$85 ▪ Total Weight: 10 kg+5 kg=15 kg10kg+5kg=15kg ▪ Explanation The greedy algorithm prioritizes items with the highest value per unit weight. By taking all of Item 1 and a fraction of Item 2, we maximize the total value without exceeding the knapsack’s capacity. This approach guarantees an optimal solution for the fractional knapsack problem. 28 29 Example for 0-1 Knapsack (Greedy Fails ❌ ) Problem: ▪ ▪ 30 Capacity: 50 kg Items: ▫ Item A: Weight = 10 kg, Value = $60 ▫ Item B: Weight = 20 kg, Value = $100 ▫ Item C: Weight = 30 kg, Value = $120   31 Fill the knapsack greedily:  Take Item A (10 kg → $60).  Take Item B (20 kg → $100).  Total weight = 10+20=30 kg10+20=30kg, remaining capacity = 20 kg.  Item C (30 kg) cannot fit. Total Value: $60+$100=$160$60+$100=$160. Example of asymmetric TSP (permutation problem) Distance matrix Dij 1 2 3 4 5 6 7 1 0 10 15 20 2 8 7 2 8 0 5 21 22 11 9 3 5 19 0 13 19 5 3 4 23 25 17 0 16 3 13 5 26 9 10 17 0 14 18 6 2 12 18 15 4 0 24 7 13 10 3 11 19 26 0 2. Fitness function No. 1 2 3 4 5 6 7 8 9 10 position X Fitness= 𝑫𝒊𝒋 1523476 1352764 7341526 6425137 5143762 3241576 4315267 2153746 5273461 4156723 2+9+5+13+13+26+2=70 15+19+9+9+26+15+23=116 3+13+23+2+9+11+24=85 15+25+22+26+15+3+26=132 26+20+17+3+26+12+22=126 19+21+23+2+18+26+18=127 17+5+2+9+11+24+11=79 8+2+10+3+11+3+12=49 9+9+3+13+3+2+2=41 23+2+14+24+10+5+13=91 Dij 1 2 3 4 5 6 7 1 0 10 15 20 2 8 7 2 8 0 5 21 22 11 9 3 5 19 0 13 19 5 3 4 23 25 17 0 16 3 13 5 26 9 10 17 0 14 18 6 2 12 18 15 4 0 24 7 13 10 3 11 19 26 0 TSP example 34 Metaheuristic algorithm  Metaheuristics are approximate methods that can not guarantee the exact and optimal solutions.  They are problem-independent techniques that can be applied to a broad range of problems.  For example, genetic algorithm and particle swarm algorithms are metaheuristic algorithms. 35

Intro to Artificial Intelligence: CS203 Lecture

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