1. CSC 380: Design and Analysis of Algorithms
Dr. Curry Guinn

2. Quick Info Dr. Curry Guinn CIS 2015 guinnc@uncw.edu
Office Hours: MWF: 10:00am-11:00m and by appointment

3. Outline of today
Genetic Algorithms

4. Genetic Algorithms (GA)
A class of probabilistic optimization algorithms
Inspired by the biological evolution process
Uses concepts of “Natural Selection” and “Genetic Inheritance” (Darwin 1859)
Originally developed by John Holland (1975)
Genetic Programming: An Introduction
Bart Wyns

5. A genetic algorithm maintains a population of candidate solutions for the problem at hand, and makes it evolve by iteratively applying a set of stochastic operators
Genetic Programming: An Introduction
Bart Wyns

6. Stochastic operators
Selection replicates the most successful solutions found in a population at a rate proportional to their relative quality
Recombination decomposes two distinct solutions and then randomly mixes their parts to form novel solutions
Mutation randomly perturbs a candidate solution
Genetic Programming: An Introduction
Bart Wyns

7. The Metaphor Nature Genetic Algorithm
Individual’s degree of adaptation to its surrounding environment
Solutions quality (fitness function)
Individuals living in that environment
Feasible solutions
Environment
Optimization problem
Genetic Programming: An Introduction
Bart Wyns

8. Genetic Programming: An Introduction
The Metaphor (cont)
Evolution of populations to suit their environment
Iteratively applying a set of stochastic operators on a set of feasible solutions
A population of organisms (species)
A set of feasible solutions
Selection, recombination and mutation in nature’s evolutionary process
Stochastic operators
Nature
Genetic Algorithm
Genetic Programming: An Introduction
Bart Wyns

9. The Evolutionary Cycle
Parents
Selection
Genetic operators
Population
Example: Mutation
Replacement
Offspring
Genetic Programming: An Introduction
Bart Wyns

10. 2. Simple Genetic Algorithm
produce an initial population of individuals
evaluate the fitness of all individuals
while termination condition not met do
select fitter individuals for reproduction
recombine between individuals
mutate individuals
evaluate the fitness of the modified individuals
generate a new population
End while
Genetic Programming: An Introduction
Bart Wyns

11. Evaluating an Individual
This is by far the most costly step for real applications
=> do not re-evaluate unmodified individuals
It might be a subroutine, a black-box simulator, or any external process
Genetic Programming: An Introduction
Bart Wyns

12. Selection
Purpose: to focus the search in promising regions of the space
Inspiration: Darwin’s “survival of the fittest”
Trade-off between exploration and exploitation of the search space
Genetic Programming: An Introduction
Bart Wyns

13. Problems with FPS Premature convergence Stagnation
Assume an individual X with f_i >> f^ but f_i << max is produced in an early generation. As N_i >> 1, the genes of X quickly spread all over the population. At that point, crossover cannot generate any new solutions (only mutation can) and f^ << f_max forever.
Stagnation
Assume that at the end of a run (i.e. in one of the consecutive generations), all individuals have a relatively high and similar fitness, i.e. f_i is almost f_max for all i
Then, N_i is almost 1 for all i and there is virtually no selective pressure.
Genetic Programming: An Introduction
Bart Wyns

14. Local Tournament Selection
Extracts k individuals from the population with uniform probability (without re-insertion) and makes them play a “tournament”, where the probability for an individual to win is generally proportional to its fitness
Selection pressure is directly proportional to the number k of participants
Genetic Programming: An Introduction
Bart Wyns

15. Mutation Operators
We might have one or more mutation operators for our representation.
Some important points are:
At least one mutation operator should allow every part of the search space to be reached
The size of mutation is important and should be controllable.
Mutation should produce valid chromosomes
Genetic Programming: An Introduction
Bart Wyns

16. Example of Mutation mutated gene
before
after
mutated gene
Mutation usually happens with probability pm for each gene
Genetic Programming: An Introduction
Bart Wyns

17. Crossover Operators There are three basic types of crossover:
One-point crossover
Two-point crossover
Uniform crossover
Some important points are:
The child should inherit something from each parent. If this is not the case then the operator is a mutation operator.
The recombination operator should be designed in conjunction with the representation so that recombination is not always catastrophic
Recombination should produce valid chromosomes
Genetic Programming: An Introduction
Bart Wyns

18. One-point crossover . . . Whole Population:
Each chromosome is cut into n pieces which are recombined. (Example for n=1)
cut
cut
parents
offspring
Genetic Programming: An Introduction
Bart Wyns

19. Two-point crossover
The chromosomes are thought of as rings with the first and last gene connected (i.e., wrap-around structure).
The rings are cut in two sites and the resulting sub-rings are swapped.
For example, if P1 = and P2 = and the crossover points are between the 2nd and 3rd bits and between the 6th and 7th bits, then the offspring would be
O1 = and O2 =
Genetic Programming: An Introduction
Bart Wyns

20. Uniform crossover
Each gene of the offspring is selected randomly from the corresponding genes of the parents.
For example, if P1 = and P2 = then the offspring could be O =
N.B. One-point and two-point crossover produce two offspring, whilst uniform crossover produces only one
Genetic Programming: An Introduction
Bart Wyns

21. Stopping criterion The optimum is reached!
Limit on CPU resources: maximum number of fitness evaluations
Limit on the user’s patience: after some generations without improvement
Describe how you chose to represent the problem to your algorithm
How was the particular representation chosen e.g.. ordering of bits, gray coding, etc. etc. chosen, and what alternatives were evaluated.
What were the expected benefits of the proposed scheme?
e.g.. smaller search space
infeasible solutions avoided
etc.., etc..
The introductory slides show very basic forms of 1 point crossover and point mutation, so it may be necessary to have a slide for each of the operators you used, showing how they work.
Genetic Programming: An Introduction
Bart Wyns 6

22. Membrane Computing

23. For Next Class, Monday
Homework