An Introduction to
Artificial Life
Lecture 4b: Informed Search and Exploration
Ramin Halavati (halavati@ce.sharif.edu)
In which we see how information about the state space can
prevent algorithms from blundering about the dark.
Local search algorithms
• Some times the path to goal matters…
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Shortest route to a city.
The solution to 8-Puzzle.
Robot’s route in a building.
A Check-Mate
• And some times, not
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8 Queens.
Job-Shop Scheduling
Automatic program generation
Check-Mate in Barareh!
Local search algorithms
• When path doesn’t matter…
• State space = set of "complete" configurations
• Find configuration satisfying constraints
• Keep a single "current" state or a fixed number of
independent current states, try to improve it or
them.
Objective Landscape
Hill-Climbing Search
• "Like climbing Everest in thick fog with
amnesia"
•
• Greedy Local Search
Hill-Climbing Search: 8-Queens
• h = number of pairs of queens that are attacking each
other, either directly or indirectly
• h = 17 for the above state
•
Hill Climbing Problems
• Local Maxima/Minima
Hill Climbing Problems
• A local minimum with h = 1
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Hill Climbing Problems
• Ridges
Hill Climbing Problems
• Plateaux
– A state whose all neighbors have similar
fitness.
Hill Climbing, Now What?
• 8-Queens, random examples:
– 86% Failure, 14% Success.
– In average, 4 moves.
8
– State Space: 8 > 17,000,000
• Solution 1: Random Restart:
– Restart from a random point if failed.
• Almost 7 tries for 8-queens.
• 3,000,000 queens in less than 1 minute.
Hill Climbing, Now What?
• Solution 2:
– Sideway moves for plateaux. / Limited.
• Solution 3:
– Stochastic Hill Climbing, random selection
among up hills.
• Slower convergence, sometimes better solutions.
• Solution 4:
– First Choice Hill Climbing.
Practical State Spaces
Simulated Annealing Search
• Hill Climbing:
– Just move to a better state.
– Efficient, but can stuck in local maxima
• Random Walk:
– Move to a random neighbor.
– Complete, but extremely inefficient.
• Idea: Escape local maxima by allowing some
"bad" moves but gradually decrease their
frequency.
Simulated Annealing Search
Simulated Annealing Search
• One can prove: If T decreases slowly enough,
then simulated annealing search will find a global
optimum with probability approaching 1
•
• Widely used in VLSI layout, airline scheduling,
etc.
Local Beam Search
• Keep track of k states rather than just one
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• Start with k randomly generated states
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• At each iteration, all the successors of all k states
are generated
•
• If any one is a goal state, stop; else select the k
best successors from the complete list and
repeat.
Local Beam Search
• Looks similar to Parallel Random Start Hill
Climbers, but it’s not.
• Stochastic Beam Search
Genetic Algorithms
• Beagle Voyage
• Animals adopt to
environmental.
Genetic Algorithms
•
Natural Evolution:
– Given these requirements:
1. A creature whose features affects his reproduction
rate.
2. Offspring features are very much, but not exactly
similar to the parent(s).
3. There is a competition on resources.
– We will have
•
Gradual Progress
– The Blind Watchmaker - Dawkins
Genetic algorithms
• Start with k randomly generated states
(population)
•
• A successor state is generated by combining two
parent states
•
• Produce the next generation of states by
selection, crossover, and mutation.
• Evaluation function (fitness function). Higher
values for better states.
•
Genetic algorithms
• Cross Over:
– To select some part of the solution (state) from one person and
the rest from another.
• Mutation:
– To change a small part of one solution with a small probability.
Genetic algorithms
L.S. in Continues Spaces
• Infinite number of successor states.
– To select three best locations for airports.
• (x1,y1) , (x2,y2) , (x3,y3)
• Approach 1:
– To discretize
• Just change them by ±
• Approach 2:
– To compute gradient!
• xJ x    f  f  f  f  f  f 


 x1
y1
x2
y2
x3
y3 
Online Search / Unknown Env.
• Offline Search
– Generate as many nodes as you wish, in any
order.
• Online Search
– Interleave computation and action
• Dynamic Domains
• Stochastic Domains.
• Unknown Domains.
– Exploration
Online Search Problems
• You can see the successors just by applying an
action.
• You may have different results from repeating a
similar action at a certain state.
• You just see one step ahead.
G
S
Algorithms for Online Search
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•
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Nothing General Enough
Limitation to Local Search
Competitive Ratio
Safely Explorable
Hill Climbing, once more…
• Hill Climbing stores just one state, so it is
an online searcher
• But can not Randomly Restart.
– Random Walk
– Adding Memory:
• Learning Real Time A*
Learning Real Time A*
• To remember and update the costs of all
visited nodes.
Learning Real Time A*
Essay Proposals
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What is MA*? Compare it with SMA* and A*.
What is Tabu Search?
What is Viterbi Search?
What is Tree-Trellis?
What are variants of Genetic Algorithms?
What is Immunity System Search?
What is Simulated DNA Computing Search?
Compare Natural Evolution and Genetic
Algorithms.
Essay Proposals
• What is Game of Life?
• What other search method exist that are
inspired from nature?
Essay Proposals
• Bring a survey of any of the proposed
algorithms in real applications.
• Bring a detailed usage of one of the
algorithms in a real application.
• Choose 5 exercises and do them in details,
from any chapter, but tell me first.
Exercises
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Choose one of 4.15 – 4.18
Due: Esfand 30th
Email To: ghanbari@ce.sharif.edu
Subject: AIEX-415 .. AIEX-418
Project Proposals
• Make an improvement in one of the
algorithms, compare your results with
original one on different domains.
• …
Project Proposals
• Choose a real problem. Design and
implement a suitable algorithm for it.
Compare your results with required results
or other solutions.
Project Proposals
• Choose a one player game, find some
other people who agree on yours. Write a
common engine and perform a competition,
with or without time limit.
– Mahjongg, Solitaire, Open Tetris, …
That’s all.