Efficient preprocessing methods for tabu search: an application on asymmetric travelling salesman problem

Abstract

This paper presents efficient methods of combining preprocessing methods and tabu search metaheuristic for solving large instances of the asymmetric travelling salesman problem (ATSP) with a focus on applications which require one to solve repeatedly different instances of ATSP and where for each instance one needs a reasonably good-quality solution quickly. For such applications, we present two hybrid metaheuristics, namely GA-SAG and RGC-SAG that, respectively, use genetic algorithm (GA) and randomized greedy contract (RGC) algorithm as preprocessing mechanisms, to sparsify a dense graph and apply an implementation of tabu search specifically designed for sparse asymmetric graphs (SAG) to further improve the solution quality. Our computational experience shows that both GA-SAG and RGC-SAG clearly outperform the conventional implementation of pure tabu search. Moreover, for benchmark instances, RGC-SAG reaches a solution within 1%–5% of the optimal solution much faster than the best known heuristics on benchmark problem instances. RGC-SAG provides tour values better than those obtained by PATCH or KP heuristic on 50% and 75% of the benchmark instances, respectively. Although the quality of the solutions obtained in Helsgaun or in the paper by doubly rooted stem and cycle ejection chain algorithm is marginally better than RGC-SAG on most of the benchmark instances, RGC-SAG establishes its potential with a significant reduction in computational time.