Adaptive Sequential Constructive Crossover Operator in a Genetic Algorithm for Solving the Traveling Salesman Problem

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.

Genetic Algorithms for the Multiple Travelling Salesman Problem

“…In [17], a modified version of the SCX, named adaptive SCX (ASCX), is developed for the TSP which creates only one offspring adaptively, either in forward or backward or mixed direction depending on next city"s distance. Eight neighbour (four from each parent) cities of any current city is considered, of which best city in either direction is selected for the offspring.…”

“…In the recent years, several GAs have been developed successfully for various difficult optimization problems, for example the quadratic assignment problem [15], the minimum spanning tree problem [16], and the TSP [17]. GAs first developed by John Holland in 1970s that are based on survival-of-the-fittest theory among different species created by arbitrary variations in the chromosomes" structure in the biology.…”

“…Selecting good crossover can lead to a successful GA. An experimental study reported on six crossover operators in [19] showed that sequential constructive crossover (SCX) is the best operator. Recently, several modified versions of SCX, namely adaptive SCX (ASCX) [17], greedy SCX (GSCX) [20], reverse greedy SCX (RGSCX) [21] and comprehensive SCX (CSCX) [21], and were suggested for the TSP which showed very good results for the TSP.…”

Experimental Study of a Hybrid Genetic Algorithm for the Multiple Travelling Salesman Problem

“…However, if any infeasible offspring chromosome is created, then it exchanges selected cities to create a feasible chromosome. Al-Furhud and Ahmed [55] developed simple GAs using the original SCX and some modified SCX operators, namely, adaptive SCX [56], greedy SCX [57], reverse greedy SCX [58], and comprehensive SCX [58] for solving the problem, and found that the comprehensive SCX is the best one. However, in this study, we consider the original SCX as the crossover operator in our proposed hybrid GA. Algorithm 3 reports the algorithm for the SCX [54,55].…”

“…In the past few years, for some difficult optimization problems, like the quadratic assignment problem [16], the minimum spanning tree problem [17], and the TSP [18], several GAs have been successfully developed. GAs are developed based on imitating the "survival of the fittest" theory amongst various species formed by random changes in the structure of chromosomes in natural biology.…”