smile.gap

Class GeneticAlgorithm<T extends Chromosome>

java.lang.Object

smile.gap.GeneticAlgorithm<T>

public class GeneticAlgorithm<T extends Chromosome>
extends Object

A genetic algorithm (GA) is a search heuristic that mimics the process of natural evolution. This heuristic is routinely used to generate useful solutions to optimization and search problems. Genetic algorithms belong to the larger class of evolutionary algorithms (EA), which generate solutions to optimization problems using techniques inspired by natural evolution, such as inheritance, mutation, selection, and crossover.

In a genetic algorithm, a population of strings (called chromosomes), which encode candidate solutions (called individuals) to an optimization problem, evolves toward better solutions. Traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodings are also possible. The evolution usually starts from a population of randomly generated individuals and happens in generations. In each generation, the fitness of every individual in the population is evaluated, multiple individuals are stochastically selected from the current population (based on their fitness), and modified (recombined and possibly randomly mutated) to form a new population. The new population is then used in the next iteration of the algorithm. Commonly, the algorithm terminates when either a maximum number of generations has been produced, or a satisfactory fitness level has been reached for the population. If the algorithm has terminated due to a maximum number of generations, a satisfactory solution may or may not have been reached.

A typical genetic algorithm requires:

• a genetic representation of the solution domain,
• a fitness function to evaluate the solution domain.

A standard representation of the solution is as an array of bits. Arrays of other types and structures can be used in essentially the same way. The main property that makes these genetic representations convenient is that their parts are easily aligned due to their fixed size, which facilitates simple crossover operations. Variable length representations may also be used, but crossover implementation is more complex in this case. Tree-like representations are explored in genetic programming and graph-form representations are explored in evolutionary programming.

The fitness function is defined over the genetic representation and measures the quality of the represented solution. The fitness function is always problem dependent.

Once we have the genetic representation and the fitness function defined, GA proceeds to initialize a population of solutions randomly, then improve it through repetitive application of selection, crossover and mutation operators.

Here are some basic recommendations of typical parameter values on binary encoding based on empiric studies.

Crossover Rate

Crossover rate determines how often will be crossover performed. If there is no crossover, offspring is exact copy of parents. If there is a crossover, offspring is made from parts of parents' chromosome. If crossover rate is 100%, then all offspring is made by crossover. If it is 0%, whole new generation is made from exact copies of chromosomes from old population. However, it this does not mean that the new generation is the same because of mutation. Crossover is made in hope that new chromosomes will have good parts of old chromosomes and maybe the new chromosomes will be better. However it is good to leave some part of population survive to next generation. Crossover rate generally should be high, about 80% - 95%. However some results show that for some problems crossover rate about 60% is the best.

Mutation Rate

Mutation rate determines how often will be parts of chromosome mutated. If there is no mutation, offspring is taken after crossover (or copy) without any change. If mutation is performed, part of chromosome is changed. Mutation is made to prevent falling GA into local extreme, but it should not occur very often, because then GA will in fact change to random search. Best rates reported are about 0.5% - 1%.

Population Size

Population size is the number of chromosomes in population (in one generation). If there are too few chromosomes, GA have a few possibilities to perform crossover and only a small part of search space is explored. On the other hand, if there are too many chromosomes, GA slows down. Good population size is about 20-30, however sometimes sizes 50-100 are reported as best. Some research also shows, that best population size depends on encoding, on size of encoded string.

Selection

Tournament selection has become the primary selection technique used for the Genetic Algorithm. Basic roulette wheel selection can be used, but sometimes rank selection can be better. In general, elitism should be used unless other method is used to save the best found solution.

This implementation also supports Lamarckian algorithm that is a hybrid of of evolutionary computation and a local improver such as hill-climbing. Lamarckian algorithm augments an EA with some hill-climbing during the fitness assessment phase to revise each individual as it is being assessed. The revised individual replaces the original one in the population.

The number of iterations t during each fitness assessment is a knob that adjusts the degree of exploitation in the algorithm. If t is very large, then we're doing more hill-climbing and thus more exploiting; whereas if t is very small, then we're spending more time in the outer algorithm and thus doing more exploring.

Author:

Haifeng Li

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	GeneticAlgorithm.Selection The way to select chromosomes from the population as parents to crossover.

Constructor Summary

Constructors

Constructor and Description
GeneticAlgorithm(T[] seeds) Constructor.
GeneticAlgorithm(T[] seeds, GeneticAlgorithm.Selection selection) Constructor.

Method Summary

Modifier and Type	Method and Description
T	evolve(int generation) Performs genetic algorithm for a given number of generations.
T	evolve(int generation, double threshold) Performs genetic algorithm until the given number of generations is reached or the best fitness is larger than the given threshold.
int	getElitism() Returns the number of best chromosomes to copy to new population.
int	getLocalSearchSteps() Gets the number of iterations of local search for Lamarckian algorithm.
double	getTournamentProbability() Returns the best-player-wins probability in tournament selection.
int	getTournamentSize() Returns the tournament size in tournament selection.
T[]	population() Returns the population of current generation.
GeneticAlgorithm	setElitism(int elitism) Sets the number of best chromosomes to copy to new population.
GeneticAlgorithm	setLocalSearchSteps(int t) Sets the number of iterations of local search for Lamarckian algorithm.
GeneticAlgorithm	setTournament(int size, double p) Set the tournament size and the best-player-wins probability in tournament selection.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

GeneticAlgorithm

public GeneticAlgorithm(T[] seeds)

Constructor. The default selection strategy is tournament selection of size 2. Elitism is also used (the best chromosome is copied to next generation).

Parameters:

seeds - the initial population, which is usually randomly generated.

GeneticAlgorithm

public GeneticAlgorithm(T[] seeds,
                        GeneticAlgorithm.Selection selection)

Constructor. By default, elitism is used (the best chromosome is copied to next generation).

Parameters:

selection - the selection strategy.

seeds - the initial population, which is usually randomly generated.

Method Detail

population

public T[] population()

Returns the population of current generation.

setElitism

public GeneticAlgorithm setElitism(int elitism)

Sets the number of best chromosomes to copy to new population. Sets the value to zero to disable elitism selection. When creating new population by crossover and mutation, we have a big chance, that we will loose the best chromosome. Elitism first copies the best chromosome (or a few best chromosomes) to new population. The rest is done in classical way. Elitism can very rapidly increase performance of GA, because it prevents losing the best found solution.

getElitism

public int getElitism()

Returns the number of best chromosomes to copy to new population.

setTournament

public GeneticAlgorithm setTournament(int size,
                                      double p)

Set the tournament size and the best-player-wins probability in tournament selection.

Parameters:

size - the size of tournament pool.

p - the best-player-wins probability.

getTournamentSize

public int getTournamentSize()

Returns the tournament size in tournament selection.

getTournamentProbability

public double getTournamentProbability()

Returns the best-player-wins probability in tournament selection.

setLocalSearchSteps

public GeneticAlgorithm setLocalSearchSteps(int t)

Sets the number of iterations of local search for Lamarckian algorithm. Sets it be zero to disable local search.

Parameters:

t - the number of iterations of local search.

getLocalSearchSteps

public int getLocalSearchSteps()

Gets the number of iterations of local search for Lamarckian algorithm.

Returns:

t the number of iterations of local search.

evolve

public T evolve(int generation)

Performs genetic algorithm for a given number of generations.

Parameters:

generation - the number of iterations.

Returns:

the best chromosome of last generation in terms of fitness.

evolve

public T evolve(int generation,
                double threshold)

Performs genetic algorithm until the given number of generations is reached or the best fitness is larger than the given threshold.

Parameters:

generation - the maximum number of iterations.

threshold - the fitness threshold. The algorithm stops when a solution is found that satisfies minimum criteria.

Returns:

the best chromosome of last generation in terms of fitness.