Variant of partially mapped crossover for the Travelling Salesman problems

In this paper a variant of partially mapped crossover (VPMX) is designed using cut point positions and is tested for its performance with the existing partially mapped crossover (PMX).In order to test the performance ,two mutation operators are used. These mutation operators are inverted displacement and inversion mutations. Partially mapped crossover (PMX) with inversion and with inverted displacement and a variant of partially mapped crossover (VPMX) with inversion and with inverted displacement are programmed in C++ and implemented on a set of ten benchmark problems taken from the Travelling salesman problem library (TSPLIB). The results indicate that the designed variant of PMX is superior by showing a better performance in eight instances in combination with the inverted displacement mutation. In two instances PMX has obtained a better result. One is PMX with inversion mutation and the other is PMX with inverted displacement mutation.