Evolutionary Computation

Robert S. RoosCMPSC 580

Junior SeminarSpring 2007

Recall…

Genetic algorithm(Holland, 1975)

[See CS 580 “Lecture Notes and Handouts” from 1/30/2007]

Initialize population P to random bit strings of length LRepeat: for each chromosome c in P compute fitness(c) repeat initialize new population P’ to emptyset, Ø select some fraction of P based on fitness, add to P’ fill in the rest of P’ by performing crossover randomly mutate elements of P’ P = P’ until stopping condition is met

Before Creating a GA……Is the problem well-suited to solution by a

genetic algorithm?“Find shortest paths in a given graph using a GA?” NO! Polynomial-time algorithm.

“Find minimum spanning tree in a given graph using a GA?” NO! Polynomial time algorithm.

“Can a given graph be colored using no more than k colors?” NO! This is a decision problem, not an optimization problem. (But if we ask “how many colors are needed?” it becomes an optimization problem.)

Many hard problems already have efficient approximation algorithms. For example, “pure” GAs are not as good as other methods for TSP.

To Create a GA, You Must…

• Select a representation (what do the chromosomes represent?)

• Select a fitness function for chromosomes

• (Maybe) design problem-specific mutation and crossover operators

• Select parameters (population size; crossover probability; mutation probability)

• Decide on stopping condition

Example

Zero-One Knapsack: Given n objects x0, x1, …, xn-1 with weights w0, w1, …, wn-1 and values v0, v1, …, vn-1

(respectively), and given a knapsack with capacity C, choose a set of objects of maximum total value whose total weight does not exceed C.

Chromosome: n-bit vector. The i-th bit is 1 if and only if xi is chosen.Fitness: ∑xivi – penalty, where penalty is zero if ∑xiwi ≤ C, some large value otherwise.Crossover, mutation: the usualParameters: Pop. Size=100, pc = .5, pm = .01Stopping condition: Halt when no change in best solution after 100 consecutive generations

VariationsReal-valued genes: Instead of using bits, use floating-point values.Crossover exchanges values rather than single bits; mutation adds or subtracts a small quantity from a real value.

Ordering Problems: chromosome is a permutation (TSP, scheduling, etc.) Needs specialized crossover and mutation operators. E.g., consider TSP, 5 cities, chromosomes ABDEC and ACDEB. Ordinary crossover could produce nonsense like “ABDEB” and “ACDEC”.

Hybrid GA: use non-genetic operators to improve solutions. E.g., for function maximization, use hill-climbing or other local search techniques in the neighborhood of a candidate solution to find a better solution

“Kick” operators: in the middle of computation, allow a portion of the population to be replaced with random chromosomes

Elitist GA: always keep current best-known solution in the population

Some TermsGenotype: The description of an individual at the gene level; the representation used for individuals in the genetic algorithm. Sometimes used in place of “chromosome”, but “genotype” is used more often in the context of broad discussions of GAs in general rather than particular GAs

Phenotype: The individual described by a given genotype; the result of expressing the genes in the genotype. (NOTE: there could be multiple genotypes that map to the same phenotype – e.g., “ABCDE” and “BCDEA” might both describe the same TSP tour)

Allele: One of the possible values that can be used in a particular position of the chromosome. In a bit string the alleles are just 0 and 1.

Codon: the smallest unit of a chromosome that represents a single “trait” of the individual. In simple bit string representations the codons are just 0 and 1, but if several positions in the bit string are always grouped together and given an interpretation as a single entity, each such group of bits is a codon.

Epistasis: Occurs when fitness is determined in a nonlinear way by a number of genes. E.g., f(001) = f(010) = f(100) = 1; f(011) = f(101) = f(110) = 2; f(111) = 2; and f(000) = 3. Also sometimes called Linkage.

Max-ones: a well-known “test” problem for GAs in which the goal is simply to maximize the number of 1’s in a bitstring. (Also “Onemax”)

Building Block: in the traditional GA, a collection of bits and their corresponding positions (i.e., a hyperplane) such that (1) individuals having those bits in those positions tend to have higher fitness; (2) the number of bits in the set is small (“low order”); (3) the bits are relatively close together (“small defining length”). The Building Block theorem shows that ordinary crossover and mutation tend to increase the number of representatives of building blocks in the population at an exponential rate.

Some Terms

Some TermsUniform Crossover: A type of crossover in which a child chromosome is formed from two parents by randomly selecting one of the two parents for each bit position. Roughly half of the bits in the child come from each parent. Ex: 01100 x 10101 -> 00101

“Exploration versus Exploitation”: the fundamental tension in a GA. We must balance work spent “exploring” the space of possible solutions versus the work spent “exploiting” promising areas of the solution space. Too much emphasis on either can result in convergence to local optima.

Deceptive problem: a problem that is hard for GAs to solve. For instance, define a four-bit subproblem in which the fitness of any string is the number of 1s EXCEPT for “1111”, which has fitness 3, and “0000”, which has fitness 4. Create a larger problem by stringing together a number of these smaller subproblems.Then f(0111 1011 1111) = 3+3+3=9, f(0010 0110 1001) = 1+2+2=5, etc., but f(0000 0000 0000) = 4+4+4 = 12.

Library Exercise

Find as many books as you can on the shelves of the Alden library about “genetic algorithms”, “genetic programming”, “evolutionary computation”, and related areas. DON’T remove them (unless you really intend to sign them out and use them), but jot down brief titles and authors. I’ll ask you to read this list out loud. I suggest you divide up into smaller groups.

Locate the areas on our shelves where books about genetic algorithms and evolutionary computation tend to be shelved. What call numbers seem to occur most often?

Make a list of titles and authors and bring this back to the classroom. I’ll ask you to read your list. Yes, there is a point to this exercise!

Past Student Research1998: Kim L. Bailey, ``Steady State Versus Generational Genetic Algorithms.''

1998: Ricardo D. Cortes. ``The Traveling Salesperson Problem.''

1999: Sarah Toohey.``Using Ant Colony Systems to Solve the Traveling Salesperson Problem.''

2000: Daniel Phifer.``Dynamic Genetic Operators and Local Optimum Escape.''

2001: Dmitri Zagidulin, ``Data Abstraction in Genetic Programming.''

2002: Charles DiVittorio. ``Numerical Sequence Recognition Using Genetic Programming.''

2002: Brian Hykes. ``Genetic Algorithms for Constraint Satisfaction: An Example Using the `Minesweeper' Problem.''

2002: Brian Zorman. ``The Creation and Analysis of a JavaSpace-Based Distributed Genetic Algorithm.''

GECCO 2002: Tiffany Bennett, Jennifer Hannon, Elizabeth Zehner, andRobert Roos. ``A genetic algorithm for improved shellsort sequences.''

2003. Chris McNamara. ``Experimenting with DistributedGenetic Grouping Algorithms.''

2004. Joe Zumpella. ``Genetic Algorithms for Texture Generation.''

2005. Kristen Walcott. ``Prioritizing Regression Test Suites for Time-Constrained Execution Using a Genetic Algorithm.''

2005. Jason Zeleznik. ``Optimizing Genetic Algorithms in the Presence of a Dynamic Fitness Function.''

Past Student Research

2006: Ian Volkwein. Optimizing Neural Network Topology Using Particle Swarms

2006: Jonathan Goytia. Investigating Cooperative Particle Swarm Optimization to Train Neural Networks for Learning Checkers

2006: Matthew McGettigan. Using Ant Colony Optimization with the Rural Postman Problem.

Past Student Research