A Guided Local Search Approach for the Travelling Thief Problem

Abstract

Real-world problems complexity is often a consequence of the interdependence of the sub-problems that compose them. The Travelling Thief Problem (TTP) is a novel benchmark problem that aims to be a good model of this interdependence. It combines two classical well known problems: The Travelling Salesman Problem (TSP) and the Knapsack Problem (KP). Some state-of-the-art techniques, after a complex initialization, alternate between two different optimization stages, one focused on the tour and the other one on the selection of items. The optimization of the tour usually involves a simple trajectory-based search, meaning that important drawbacks might appear when the initial optimized TSP tours are not suitable for the TTP problem. In this paper a Guided Local Search (GLS) approach is proposed to improve further the tour optimization and compared against state-of-the-art techniques. Experimental validation shows the important benefits provided by our proposal, meaning that in fact many state-of-the-art techniques are too focused in a subset of the search space. Although at the moment the computational cost of our method is large, meaning that this approach does not scale well, new best-known solutions were generated in three well-known TTP instances. The main benefits were obtained in small and medium-sized instances.