xegaPermGene {xegaPermGene}

Package xegaPermGene.

Description

Genetic operations for permutation genes.

Details

Permutation genes are a representation of a tour of a Traveling Salesman Problem (TSP).

For permutation genes, the xegaPermGene package provides

• Gene initiatilization.

• Decoding of parameters.

• Mutation functions as well as a function factory for configuration.

• Crossover functions as well as a function factory for configuration.

Permutation Gene Representation

A permutation gene is a named list with at least the following elements:

• $gene1: The gene must be a permutation vector.

• $fit: The fitness value of the gene (for EvalGeneDet and EvalGeneU) or the mean fitness (for stochastic functions evaluated with EvalGeneStoch).

• $evaluated: Boolean. Has the gene been evaluated?

• $evalFail: Boolean. Has the evaluation of the gene failed?

Abstract Interface of a Problem Environment for the TSP

A problem environment penv for the TSP must provide:

• $name(): Returns the name of the problem environment.

• $genelength(): The number of bits of the binary coded real parameter vector. Used in InitGene.

• $dist(): The distance matrix of the TSP.

• $cities(): A list of city names or 1:numberOfCities.

• $f(permutation, gene, lF): Returns the fitness of the permutation (the length of a tour).

• $solution(): The minimal tour length (if known).

• $path(): An optimal TSP tour.

• $show(permutation): Prints the tour with the distances and the cumulative distances between the cities.

• TSP Heuristics:

  • $greedy(startposition, k): Computes a greedy tour of length k.

  • $kBestgreedy(k): Computes the best greedy tour of length k.

  • $rnd2Opt(permutation, maxTries): Generate a new permutation by a random 2-change. maxTries is the maximal number of trials to find a better permutation. $rnd2Opt either returns a better permutation or, if no better permutation can be found in maxTries attempts, the original permutation.

  • $LinKernighan(permutation, maxTries): Returns a permutation generated by a random sequence of 2-changes with improving performance. The optimality criterion of the k Lin-Kernighan heuristics is replaced by the necessity of finding a sequence of random 2-changes with strictly increasing performance.

Abstract Interface of Mutation Functions

Each mutation function has the following function signature:

newGene<-Mutate(gene, lF)

All local parameters of the mutation function configured are expected in the local configuration lF.

Local Constants of Mutation Functions

The local constants of a mutation function determine the the behavior of the function.

Constant	Default	Used in
lF$BitMutationRate1()	0.005	xegaPermMutateGeneOrderBased
lF$Lambda()	0.05	xegaPermMutateGenekInversion
		xegaPermMutateGenekGreedy
		xegaPermMutateGeneBestGreedy
lF$max2Opt()	100	xegaPermMutateGene2Opt
		xegaPermMutateGenekOptLK

Abstract Interface of Crossover Functions

The signatures of the abstract interface to the 2 families of crossover functions are:

ListOfTwoGenes<-Crossover2(gene1, gene2, lF)

newGene<-Crossover(gene1, gene2, lF)

The Architecture of the xegaX-Packages

The xegaX-packages are a family of R-packages which implement eXtended Evolutionary and Genetic Algorithms (xega). The architecture has 3 layers, namely the user interface layer, the population layer, and the gene layer:

• The user interface layer (package xega) provides a function call interface and configuration support for several algorithms: genetic algorithms (sga), permutation-based genetic algorithms (sgPerm), derivation free algorithms as e.g. differential evolution (sgde), grammar-based genetic programming (sgp) and grammatical evolution (sge).

• The population layer (package xegaPopulation) contains population related functionality as well as support for population statistics dependent adaptive mechanisms and parallelization.

• The gene layer is split in a representation independent and a representation dependent part:

  1. The representation indendent part (package xegaSelectGene) is responsible for variants of selection operators, evaluation strategies for genes, as well as profiling and timing capabilities.

  2. The representation dependent part consists of the following packages:

     • xegaGaGene for binary coded genetic algorithms.

     • xegaPermGene for permutation-based genetic algorithms.

     • xegaDfGene for derivation free algorithms as e.g. differential evolution.

     • xegaGpGene for grammar-based genetic algorithms.

     • xegaGeGene for grammatical evolution algorithms.

     The packages xegaDerivationTrees and xegaBNF support the last two packages: xegaBNF essentially provides a grammar compiler and xegaDerivationTrees an abstract data type for derivation trees.

Copyright

(c) 2023 Andreas Geyer-Schulz

License

MIT

URL

<https://github.com/ageyerschulz/xegaPermGene>

Installation

From CRAN by install.packages('xegaPermGene')

Author(s)

Andreas Geyer-Schulz