Genetic (Evolutionary) Algorithms CEE 6410 David Rosenberg “Natural Selection or the Survival of the Fittest.” -- Charles Darwin

Learning Objectives Map concepts from evolutionary biology to genetic algorithms (GAs) Identify parameters for running a GA Use a GA to solve an optimization problem List limitations CEE 6410David Rosenberg 2

Biology - A Brief Review CEE 6410David Rosenberg 3

Darwin’s Theory of Evolution Genetic makeup determines an individual’s physical characteristics The environment acts on individuals to determine an individual’s –Suitability to survive –Likelihood to reproduce Individuals more fit to survive in a particular environment: –Pass more genetic material to their offspring –Their offspring are better fit to survive CEE 6410David Rosenberg 4

CEE 6410David Rosenberg 5 Which of the following statements comes closest to your views on the origin and development of human beings?

Map Concepts CEE 6410David Rosenberg 6 BiologyGenetic Algorithms Systems Analysis Gene – sequence of nucleotides on a DNA strand GeneDecision variable value Chromosome – group of genes on a single strand of DNA ChromosomeArray of decision variables Individual – collection of chromosomes Chromosome / Individual Alternative – array of decision variables Population – collection of individuals PopulationA set of alternatives FitnessFitness functionObjective function value

GA Solution Process 1.Generate the initial population (e.g., random) 2.Evaluate fitness of each individual 3.Test for completion –Are our stop criteria met? 4.Generate new population (use genetic operators) 5.Return to Step #2 CEE 6410David Rosenberg 7

1. Generate the Population CEE 6410David Rosenberg 8

2. Evaluate Fitness CEE 6410David Rosenberg 9

3. Test for Completion Maximum number of iterations (generations) reached? Maximum execution time reached (e.g., Excel)? Convergence criteria reach (e.g., in Excel, difference in fitness between the 1 st and 99 th percentile individuals) CEE 6410David Rosenberg 10

3. Genetic operators to generate a new population Selection –Select 2 parent individuals from current population –Randomly select parents by their fitness Crossover –Use genes from one or the other of the parents Mutation –Make a random (small) change in a gene value Elitism –Retain the fittest parent individuals (alternatives) in the next generation CEE 6410David Rosenberg 11

The Crossover Operator CEE 6410David Rosenberg 12

The Mutation Operator CEE 6410David Rosenberg 13

The Elitism Operator CEE 6410David Rosenberg 14 Parent Population Fitness Rank Next Generation 1 Retain New 7 : : : n Selection, crossover, & mutation

Key GA Simulation Parameters CEE 6410David Rosenberg 15 SymbolDescription nPopulation size (#) pcpc Probability of crossover (0 ≤ p c ≤ 1) pmpm Probability of mutation (0 ≤ p m ≤ 1) G max Maximum number of generations ENumber of elite individuals

Ex 1. Solve the nonlinear optimization problem with a GA Max Z = f(x,y) = 1000 – [(x-1) 2 + (y-1) 2 ] s.t.-10 ≤ x ≤ ≤ y ≤ 10 With n = 100 p m = 0.05 G max = 100 p c, E = as appropriate Hint: Use the Evolutionary Solve method in Excel CEE 6410David Rosenberg 16

Ex 2. Which GA Simulation Parameters are missing in Excel? CEE 6410David Rosenberg 17

GA Solution Convergence (McKee) CEE 6410David Rosenberg 18

GA Limitations Optimal solution not guaranteed Larger population increases –Likelihood to find optimal solution –Computation effort Higher mutation probability –Avoids getting stuck in a local optimum –Increases the tendency for solutions to wander Parameter settings are specific to the problem structure CEE 6410David Rosenberg 19

Conclusions Genetic algorithms provide a flexible tool to solve complex optimization problems Can embed simulation models Parameter settings are specific to the problem structure Lots of public-domain and commercial software available CEE 6410David Rosenberg 20