Abstract
The travelling salesman problem (TSP) is a very famous NP-hard problem in operations research as well as in computer science. To solve the problem several genetic algorithms (GAs) are developed which depend primarily on crossover operator. The crossover operators are classified as distance-based crossover operators and blind crossover operators. The distance-based crossover operators use distances between nodes to generate the offspring(s), whereas blind crossover operators are independent of any kind of information of the problem, except follow the problem’s constraints. Selecting better crossover operator can lead to successful GA. Several crossover operators are available in the literature for the TSP, but most of them are not leading good GA. In this study, we propose reverse greedy sequential constructive crossover (RGSCX) and then comprehensive sequential constructive crossover (CSCX) for developing better GAs for solving the TSP. The usefulness of our proposed crossover operators is shown by comparing with some distance-based crossover operators on some TSPLIB instances. It can be concluded from the comparative study that our proposed operator CSCX is the best crossover in this study for the TSP.
Highlights
The travelling Salesman Problem (TSP) is an old and famous combinatorial optimization problem in computer science and operations research which was documented in 1759 by Euler, not by that name, whose aim was to solve the Knights’ tour problem
If someone wants to verify the quality of any distance-based crossover operator, suppose SCX, the results found by the operator should be compared against the one found by another distance-based crossover operator, such as HX, GX or DPX
The crossover operators are classified as distance-based crossover operators and blind crossover operators
Summary
The travelling Salesman Problem (TSP) is an old and famous combinatorial optimization problem in computer science and operations research which was documented in 1759 by Euler, not by that name, whose aim was to solve the Knights’ tour problem. Genetic algorithm (GA) is a search process that is inspired by natural biological evolution process It was proposed by John Holland in 1970s [5]. It starts initially with a population of strings, called chromosomes, that encode solutions to a problem, and operates probably three operators - selection, crossover and mutation, to produce new and probably better populations in successive generations. Crossover is the primary operator, and numerous crossover operators have been suggested as well as improved for finding better solution to the TSP [5] In this present study, we propose first reverse greedy sequential constructive crossover (RGSCX) and comprehensive sequential constructive crossover (CSCX) by combining greedy sequential constructive crossover (GSCX) [6] with RGSCX for the TSP.
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