Genetic Algorithms

1. Genetic Algorithms Dan Locker An Do

2. Underlying Concept • In his book The Origin of SpeciesCharles Darwin outlined the principle of natural selection. • Natural Selection is the process by which evolution occurs. • The fittest members of a species will survive and propagate more than those less fit.

3. Development of GAs • In 1975 John Holland developed the idea of Genetic Algorithms • These are algorithms that mimic the principles of natural selection to solve problems. • Often used for Optimization problems, and for biological simulations.

4. The Basic Idea • Possible solutions to a problem are labelled “Chromosomes” • An initial population of these chromosomes is created and mated via crossover and mutation algorithms to create 'offspring' • This process is repeated until the optimal solution is found.

5. Step-By-Step GAs • Step 1: Choose an initial population of chromosomes • Step 2: Create an offspring population from the parent population • Step 3:the offspring undergo a crossover • Step 4: mutations occur in the offspring population (this is based on a probability algorithm) • Step 5: evaluate the fitness of each offspring • Step 6: replace parents with offspring, and repeat 2-5 until the optimal solution is reached

6. Psuedocode! Choose an initial population of chromosomes while (termination condition not satisfied) do repeat if(crossover condition satisfied) then{ select parent chromosomes; choose crossover parameters; perform crossover; } if(mutation condition satisfied) then{ select chromosome for mutation; choose mutation point; perform mutation; } Evaluate fitness of offspring; until sufficient offspring created; select new population; end while Courtesy of Reves, Colin R. Genetic Algorithms – Principles and Perspectives : a Guide to GA Theory.

7. Step 1 – The Initial Population • These will be randomly generated strings in the problem set • The number of members in the initial population is determined on a case by case basis, but it is usually reliable in most cases to use lg(string length) initial chromosomes.

8. Step 2 & 3 – Create Offspring and Crossover • Two parents are chosen from the set, and an offspring is created. • The parent's chromosomes are then combined into the offspring through a process called “crossover”, in which certain genes from each parent are mixed together.

9. Crossover Schemes • Linear Crossovers: • single-point crossover • A 'crossover point' is randomly chosen • All of the genes (alleles) after the crossover point from one parent are copied into their corresponding location on the other. • (a,b,c,d,e,f,g) and (1,2,3,4,5,6,7) • Crossover point is 3 • (a,b,3,4,5,6,7) and (1,2,c,d,e,f,g) are created • These are the offspring of the 2 parents • There are many other crossover techniques, most involving the same concept, but multiple crossover points

10. N-Point Crossover Algorithm Choose a random integer n; choose n cross points; generate random permutation ð of (1...,n+1) for segment order; designate one parent for copying; k <-- 1; repeat copy all compatible alleles of segment ðk from designated parent; swap parent designations; k++; until k = n+1; if child incomplete then insert legal alleles at required position, using random tie breaking if necessary.

11. Step 4 - Mutations? • An important event for the evolution of any species is mutation. A new trait is developed, and if it is beneficial, often it will be propagated. • The same must be true for GAs • Mutation is not always required in all matings. So a probability of mutation equation should be set up (this will vary depending on the problem). • Each time a new child is created a random number is generated and checked by this mutation equation to see if a mutation should occur.

12. Step 5: Evaluate the Fitness • In order to decide which traits are beneficial and should be passed on, a fitness algorithm must be performed on the children. • These fitness algorithms are completely problem specific • There are 2 basic types of algorithm • Probability dependent • Rank Dependent

13. Probability Dependent Selection • Each one of the offspring is analysed using some problem specific algorithm to determine the probability that it will lead to a successful solution • Roulette wheel type: • Each offspring is assigned a segment of the roulette wheel based on its probability. • A random number is then generated, and whichever section of the wheel it fall into is the offspring that is chosen for reproduction

14. Rank Dependent Selection • Each offspring is analysed by a ranking algorithm and its fitness is returned as some number. • The greater the number the greater the fitness • All of these ranks are ordered, and the best fit offspring are chosen for reproduction.

15. Other Selection Methods • Scaling • Generational • Hierarchical

16. Step 6 • The chosen offspring are then made the parents for the next iteration of the process • The algorithm repeats until some specified condition (Problem Specific) is met.

17. Analysis of GAs • Strengths • GAs are ‘parallel’ • Can examine multiple solutions at once • Limitations • Deceptive fitness functions • Can be time consuming • Only deal with one trait at a time