Abstract
Genetic algorithms are widely used metaheuristic algorithms to solve combinatorial optimization problems that are constructed on the survival of the fittest theory. They obtain near optimal solution in a reasonable computational time, but do not guarantee the optimality of the solution. They start with random initial population of chromosomes, and operate three different operators, namely, selection, crossover and mutation, to produce new and hopefully better populations in consecutive generations. Out of the three operators, crossover operator is the most important operator. There are many existing crossover operators in the literature. In this paper, we propose a new crossover operator, named adaptive sequential constructive crossover, to solve the benchmark travelling salesman problem. We then compare the efficiency of the proposed crossover operator with some existing crossover operators like greedy crossover, sequential constructive crossover, partially mapped crossover operators, etc., under same genetic settings, for solving the problem on some benchmark TSPLIB instances. The experimental study shows the effectiveness of our proposed crossover operator for the problem and it is found to be the best crossover operator.
Highlights
The usual travelling salesman problem (TSP) is very famous combinatorial optimization problem that finds a least cost Hamiltonian cycle in a network
We have proposed a new crossover operator, named adaptive SCX (ASCX), for the TSP
We focused on some blind crossover operators, namely, PMX, OX, AEX and CX, and distance-based crossover operators, namely, GX, SCX and BCSCX along with ASCX
Summary
The usual travelling salesman problem (TSP) is very famous combinatorial optimization problem that finds a least cost Hamiltonian cycle in a network. The TSP became popular at that time due to the new subject of linear programming and attempts to solve combinatorial optimization problems. Based on the structure of the cost matrix, the TSPs are classified into two types as symmetric and asymmetric. The number of possible solutions in both types is very large for any size, n; so, a complete search is very difficult, if it is not impossible. The TSP has been researched by several researchers for mainly three reasons NP-hard problems are equivalent to each other; so, if one can develop efficient algorithm for solving one of them, one could develop efficient algorithm for others
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call