Population-based metaheuristics
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Nature-inspired
Initialize a population
A new population of solutions is generated
Integrate the new population into the current one using one these
methods – by replacement which is a selection process from the new and
current solutions
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Evolutionary Algorithms – genetic algorithm
Estimation of distribution algorithm (EDA)
Scatter search
Evolutionary programming- genetic programming
Swarm Intelligence
• Ant colony
• Particle swarm optimization (PSO)
• Bee colony
– Artificial Immune system AIS
• Continue until a stopping criteria is reached
• The generation and replacement process could be memoryless or some
search memory is used
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Common concepts of Evolutionary Algorithm
• Main search components are
– Representation For Ex: in Genetic Algorithm GA, the encoded solution
is called a chromosome. The decision variables within a solution are
genes. The possible values of the genes are alleles and the position of
the element (gene) within a chromosome is named locus.
– Population Initialization
– Objective function, also called fitness in EA terminology.
– Selection strategy – which parents are chosen for the next generation
with the objective of better fitness
– Reproduction strategy – mutation, crossover, merge, or from a shared
memory
– Replacement strategy – using the best of the old and new population –
survival of the fittest
– Stopping criteria
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Genetic Programming
• More recent approach than GA (1992, Koza from MIT)
• Instead of fixed length strings as in GA, the individuals in GP
are programs- nonlinear representation based on trees.
• Crossover is based on subtree exchange and mutation is
based on random changes in the tree
• Parent selection is fitness proportional and replacement is
generational.
• One of the issue is the uncontrolled growth of trees – known
as bloat
• Used in machine learning and data mining tasks such as
prediction and classification.
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Genetic Programming
• GP uses terminal (leaves of a tree) and function (interior nodes) sets
• The objective is to generate programs that perform a task
• The programs grow or shrink in size at each iteration as the search
progresses
• 1) Generate an initial population of random compositions of the functions
and terminals of the problem (computer programs).
2) Execute each program in the population and assign it a fitness value
according to how well it solves the problem.
3) Create a new population of computer programs.
i) Copy the best existing programs
ii) Create new computer programs by mutation.
iii) Create new computer programs by crossover(sexual reproduction).
4) The best computer program that appeared in any generation, the bestso-far solution, is designated as the result of genetic programming
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Genetic Programming Examples
Symbolic regression problem (in statistics)
– Obj is to find a program that fits a given data set
– Discovers both the form of the model and its parameters.
- Functions (interior nodes) are math operators +,-, *,/
- Terminals (leaves) are variables and constants
- Evaluate the program and check deviation from
the known value of the function Z for several set s of parameter
x,y,z values. Minimize mean square error
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Z= (x*5)+(z+(x*y))+y
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Genetic Programming Examples
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Artificial ant on the Santa Fe trail
32X32 grid
Food pellets are mapped on some cells.
Find a shortest path to maximize food intake (number of
squares or dots)
• The if constraints are sensing functions for locating food. If
food then do x or y. If no food then do m or n
• Terminal set would be forward left or right movements
• Autonomous Navigation Control of UAVs
Using Genetic Programming
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Genetic Programming Examples
• A program to control flow of water through a network of water
sprinklers
• There are several sprinklers on a golf course and several valves that
can turn on/off to let water flow through them.
• The objective (fitness function) is to achieve correct amount of
water output from each sprinkler and achieve uniform distribution
(pressure). Measure fitness by placing measuring devices (e.g rain
gauge) that record the amount of water collected then minimize
the standard deviation among these devices.
• Opening too many valves at a time will drop the pressure in the
system (some areas may not get water), and too few will result in
excess flow due to high pressure.
• The terminal sets are sprinklers (leaves) and function sets interior
nodes) are valves
• The solution is to generate programs that open and close valves to
achieve the above objective.
• There are many solutions to evaluate
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Swarm Intelligence
• Algorithms inspired by collective behavior of species
– Ants, bees, termites etc.
• Inspired from the social behavior of the species as they
compete for food
• Particles are
– Simple, non-sophisticated agents
– Agents cooperate by indirect communication
– Agents move around in the decision space.
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Ant Colony Optimization
• Ants transport food and find shortest paths
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Use simple communicating methods
Leave a chemical trail – that is both olfactive and volatile
The trail is also called a pheromone trail
The trail guides the other ants toward the food
The larger the amount of pheromone then larger the probability that
a trail will be chosen
– The pheromone evaporates over time
• In optimization
– Initialize pheromone trails
– Construct solutions using the pheromone trails
– Pheromone update using generated solutions
• Evaporation
• reinforcement
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Ant Colony Optimization
• The pheromone trails memorize the characteristics of good
generated solutions, which guides the construction of new
solutions
• The trails change dynamically to reflect acquired knowledge
• Evaporation phase: The trail decreases automatically. Each
pheromone value is reduced by a fixed proportion
– The goal is to avoid a premature convergence to the good solution for
all the ants
– Also helps in diversification
• Reinforcement Phase: the pheromone trail is updated
according to the generated solution
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ACO for TSP
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n cities
G = (V,E) input graph
dij is the distance between i and j
For each ant randomly select an initial city i
Set up the pheromone matrix tij for edge i,j
– tij represents the desirability of an edge (i,j) in a tour
– Initialize tij =1
• Each ant will construct a tour in a stochastic way starting from city i
• An ant will select the next city j using the probability
pij =
𝑡𝛼𝑖𝑗 𝑋 𝛾𝛽𝑖𝑗
𝛼
𝑘∈𝑆 𝑡 𝑖𝑘 𝑋 𝛾𝛽𝑖𝑘
∀𝑗 ∈𝑆
𝛾𝑖𝑗 = 1/dij
S is the set of not yet visited cities of the Graph G
𝛼, 𝛽 are parameters representing the influence of the pheromone and
problem specific values such as the distance in TSP
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ACO for TSP
• Continue until S is a null set
• Update the pheromone using the quality –obj fnc f(𝜋) of
solution 𝜋 from each ant or a set of k best ants where k<n
– tij = tij + ∆ where ∆ is 1/ f(𝜋) and (i, j ) are edges in solution 𝜋
• Good tours emerge as tij is updated by the ants
• The pheromone is evaporated by tij = (1-𝜌)tij where 0 < 𝜌< 1
is the reduction rate of the pheromone
• Repeat the process several times with a set of new ants
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