Effective Local and Guided Variable Neighbourhood Search Methods for the Asymmetric Travelling Salesman Problem

Abstract

In this paper we present effective new local and variable neighbourhood search heuristics for the asymmetric Travelling Salesman Problem. Our local search approach, HyperOpt, is inspired by a heuristic developed for a sequencing problem arising in the manufacture of printed circuit boards. In our approach we embed an exact algorithm into a local search heuristic in order to exhaustively search promising regions of the solution space. We propose a hybrid of HyperOpt and 3-opt which allows us to benefit from the advantages of both approaches and gain better tours overall. Using this hybrid within the Variable Neighbourhood Search (VNS) metaheuristic framework, as suggested by Hansen and Mladenovific, allows us to overcome local optima and create tours of very high quality. We introduce the notion of a “guided shake” within VNS and show that this yields a heuristic which is more effective than the random shakes proposed by Hansen and Mladenovific. The heuristics presented form a continuum from very fast ones which produce reasonable results to much slower ones which produce excellent results. All of the heuristics have proven capable of handling the sort of constraints which arise for real life problems, such as those in electronics assembly.