Genetic Algorithm Solution of the TSP Avoiding Special Crossover and Mutation

Ordinary representations of permutations in Genetic Algorithms (GA) is handicapped with producing offspring which aze not permutations at all. The conventional solution for crossover and mutation operations of permutations is to device ‘special’ operators. Unfortunately these operators suffer from violating the nature of crossover. Namely, considering the gene positions on the chromosome, these methods do not allow n-point crossover techniques which are known to favour building-block formations. In this work, an inversion sequence is proposed as the representation of a permutation. This sequence allows repetitive values and hence is robust under ordinary (n-point) crossover. There is a one-to-one mapping from ordinary permutation representation to the inversion sequence representation. The proposed method is used for solving TSPs and is compared to the well known PMX special crossover method. It is observed that this method outperforms PMX in convergence rate by a factor which can be as high as 1...