Evolution Programs: Genetic Algorithms for Problem Solving

1. Evolution Programs (insert catchy subtitle here)

2. Evolution Programs • Basic idea: use principles of evolution and heredity to “evolve” solutions to a problem

3. Rabbits • At any given time, there is a population of rabbits. Some are smarter/faster than the others. • Foxes eat most of the slower, dumber rabbits (but not all). • More of the fast, smart rabbits reproduce. • “Wild hare” mutations possible (think Monty Python here). • The next generation will be, on average, faster and smarter than the original population.

4. How do we apply this? • This is NOT DNA-based computing as practiced in this department. • Ideas? • Battlebots? (but how do robots breed?) • Blade Runner?

5. Outline of evolution program • Maintain a population of individuals P(t) • Each individual represents a potential solution to the problem at hand • Evaluate each solution for fitness. • Form a new population P(t+1) • Select the most fit individuals • Some members undergo transformations by means of “genetic operators” to form new solutions

6. Basic evolution program t <- 0 Initialize P(t) Evaluate P(t) while not (termination condition) do t <- t+1 select P(t) from P(t-1) recombine P(t) evaluate P(t) end

7. Genetic Algorithms • Subset of evolution programs • Solutions represented as bit strings • Each solution is a chromosome • Each bit is a gene

8. Genetic Algorithms • Components: • Genetic representation for potential solutions to the problem • Method for creating initial population • Evaluation function to rate relative “fitness” • Genetic operators that alter composition of solutions during reproduction • Values for parameters that algorithm uses (population size, probability of applying operators)

9. Genetic Operators • Mutation • Arbitrary alteration of one or more genes of a selected chromosome by random change with probability equal to the mutation rate • Intuition: introduce some extra variability into the population

10. Genetic Operators • Crossover • Combine the features of two parent chromosomes to form two similar offspring by swapping corresponding segments of the parents • Intuition: information exchange between different potential solutions

11. Example: Function optimization • Problem: Maximize the function • f(x) = x sin (10 x) + 1.0 over the domain [-1..2]. • Desired accuracy is six decimal places

12. Example: Function optimization • Representation • Use a binary vector as a chromosome to represent real values of x. • Domain of length 3, so we need 3x106 values. • Can be represented as a 22-bit vector

13. Example: Function optimization • Initial population • For a population of size n, create n 22-bit chromosomes with randomly initialized bit values. • Evaluation function • eval(v) = f(x)

14. Example: Function optimization • Genetic operators • Use classical operators: mutation and crossover. • Mutation • flip a bit with probability equal to mutation rate • Crossover • randomly select crossover point • A crossover after the 5th bit of 00101|100 and 11010|011 yields two children • 00101|011 and 11010|100

15. Example: Function optimization • Parameters • population size = 50 • probability of crossover = 0.25 • probability of mutation = 0.01

16. Function optimization: Results

17. Example: Prisoner’s dilemma • Problem: • Two prisoners are held in separate cells, unable to communicate with each other. • Each can choose either to defect and betray the other prisoner, or cooperate with the other prisoner by maintaining silence. • Rewards • If both cooperate, moderate rewards for both • If only one defects, defector is rewarded, cooperator is punished • If both defect, both are tortured

18. Reward structure for PD

19. Representation for PD • Population of “players”, each of whom has a particular strategy • Initial strategy chosen at random • Players play games against each other, scores are recorded

20. Representing the strategy for PD • Deterministic strategy • Use outcomes from 3 previous moves to determine next move • 4 outcomes /move, 3 moves -> 64 possible histories • 64-bit string to represent choice for each possible history • Plus 6 bits to encode the three moves preceding the start of the game

21. Outline of algorithm • Randomly initialize population • Test each player by playing games. Score is average over all games played. • Select players to breed. • Mate players to produce offspring.

22. Results for PD • Random start -- produced populations whose median member is as successful as best known heuristic • Patterns evolved: • Don’t rock the boat: (CC)(CC)(CC) -> C • Be provokable: (CC)(CC)(CD) -> D • Accept apology: (CD)(DC)(CC) -> C • Forget: (DC)(CC)(CC) -> C • Accept a rut: (DD)(DD)(DD) -> D

23. A shot at TSP • Traveling Salesman Problem • The salesperson must visit every city on route exactly once and return to start. Minimize the cost of travel over entire tour • Problem: how do we represent the problem? As a bit string? as an integer vector? • If bit string, genetic operators may produce non-legal children • Choose integer vector

24. Traveling Salesperson Problem • Representation: • Integer vector • Example: (3 6 4 8 2 1 5 7) • Initialization: • random • output from greedy TSP • Evaluation: • calculate cost of tour

25. Traveling Salesperson Problem • Genetic operator • Must preserve legality • Want to exploit similarities • Choose subsequence of one parent and preserve relative order of cities from other parent • Parents • (1 2 3 4 5 6 7 8 9 10 11 12) • (7 3 1 11 4 12 5 2 10 9 6 8) • Subsequence (4 5 6 7) • Offspring: (1 11 12 4 5 6 7 2 10 9 8 3)

26. TSP: Results • Results averaged over 20 random runs • Applied to 100 randomly generated cities • After 20k generations, value of whole tour is 9.4% above optimal

27. Characterization • Genetic algorithms/evolution programs can be viewed as a form of search • Like hill-climbing • But hill-climbing search get stuck in local maxima • Results depend on starting point • GAs are probabilistic algorithms • But not random algorithms -- directed search • Parallel search

28. One wag’s comment • “Neural networks are the second best way of doing just about anything. . .” • “. . . and genetic algorithms are the third.” • Genetic algorithms/evolution programs can be used on a wide variety of problems

29. Cool looking stuff • (see web pages)