Evolutionary Computation

Biologically inspired algorithms

BY:Andy GarrettYE Ziyu

What is Evolutionary Computation

• A subfield of artificial intelligence which mimics biology• Used in optimization of black box problems• Parallel processing

Types of Evolutionary Computation

• Evolutionary programing• Genetic algorithms• Evolutionary strategies• Genetic programing

• Genetic algorithms• Swarm intelligence

Genetic Algorithms

Genetic Algorithm——what is gene?

Biology:A certain DNA sequenceat a certain position of the chromosome.

Genetic Algorithm :A certain value of a certain element of the solution.

2 3 1 1 1

2 3 2 1 1

2 3 3 1 1

A certain element (an allele) of the solution (the chromosome)

Three alternative values (genes)

Genetic Algorithm——what is gene?

Biology Genetic Algorithm

Genes

Chromosome

Fitness of a individualIn the environment

Genes

Solution

Performance of a solutionin the problem. (Fitness)

constitute constitute

determines determines

Genetic Algorithm——what is gene?

In Genetic Algorithm, genes (values of elements of the solution) determine the fitness (performance) of a solution.

To solve a problem=

To find the combination of genes that provides the best fitness (performance)

Genetic Algorithm——Initiation

To conduct evolution,We need a set of solutions.(A population)

Initially, the population is generated randomly. This isthe first generation. A two-dimension search space

dotted by randomly generated solutions(each solution consists of two elements,

x and y)

X

Y

Genetic Algorithm——Reproduction: Crossover

Crossover is how we create new individuals from the existing ones.

2

3

1

4

4

1

2

2

1

3

Two solutions somehow be

selected as “parents”

2

3

1

4

4

1

2

2

1

3

Randomly selectone (or more)

point

2

3

2

1

3

1

2

1

4

4

Apply cross(Recombine the two solutions)

2

3

2

1

3

1

2

1

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4

Finish！These will be two

Individuals inthe next generation

Genetic Algorithm——Reproduction: Selection

• Individuals with higher fitness have a higher probability to be chosen as parents of the crossover operation.

• Survival of the fittest

Genetic Algorithm——Reproduction: SelectionWhat’s the effect?

Genes associated with high fitness are more likely to be passed to the new generation.

After some generations, the average fitness of the population gets improved!

Genetic Algorithm——Reproduction: Selection

In a graphic view: (use our two-dimension example)

The population gathers aroundthe optimal solution.

It’s like that the population is climbing the hill.

Problem solved?

X

Y

Genetic Algorithm——Mutation

Problem: What if we have multiple hills in the searching

space?

The individuals may climb onto a hill that is not the highest.

Thus, they may gather around a local optimum.

Y

X

Y

(Local optimum)

(Global optimum)

Genetic Algorithm——Mutation

According to the crossover operation, genes in the new generation only come from the previous generation.

Thus, once the solutions gather around a local optimum, they will be constrained in its vicinity!

They won’t find the global optimum.

X

Y

(Constraining region)

Genetic Algorithm——Mutation

Mutation: Make random changes to some genes in each generation.

NEW genes are created!Solutions can jump out of the region.After some generations, they may probably gather around theglobal optimum.

X

Y

Genetic Algorithm——Scenario

Step 1: Initiation (Randomly generate the first generation);Step 2: Mutation;Step 3: Fitness evaluation; Step 4: Reproduction:

Selection;Crossover;

Step 5: Go back to step 2, repeat this loop until a sufficiently good solution is found.

Swarm intelligence

Swarm Intelligence

Swarm intelligence=

cognition of individuals + communication

Application in optimization problems:Particle Swarm Optimization (PSO)

Swarm Intelligence——Initiation

Randomly generate a set of solutions (called a swarm of particles),their initial positions,and their initial speeds.

X

Y

V2oV3o

V1o

Swarm Intelligence——Travelling

Two forces are exertedon each particle:

X

Y

1. Force pointing to the bestsolution this particle has everpassed through (pbest)2. Force pointing to the bestsolution any particle has everpassed through (gbest) pbest gbest

pbest1

pbest2(gbest)

pbest3

Swarm Intelligence——Travelling

Forces pointing to pbests:Fp1, Fp2, Fp3

These forces result from the cognition of individual particles.

X

Y

Fp3

Fp2

Fp1

Swarm Intelligence——Travelling

Forces pointing to gbests:Fg1, Fg2, Fg3

These forces result from the communication among the particles.

X

Y

Fg3 Fg2Fg1

Swarm Intelligence——Travelling

After some time, the particles would probablyfind some solutions thatare sufficiently close theglobal optimum.

X

Y

Fg3 Fg2Fg1Fp3

Fp2

Fp1

https://www.youtube.com/watch?v=j028fsZZZI4

Evolutionary Computation

• Time complexity is not generally considered• Number of iterations required for convergence

Questions?