Stealing Items More Efficiently with Ants: A Swarm Intelligence Approach to the Travelling Thief Problem

Abstract

The travelling thief problem (TTP) is an academic combinatorial optimisation problem in which its two components, namely the travelling salesperson problem (TSP) and the knapsack problem, interact. The goal is to provide to a thief a tour across all given cities and a packing plan that defines which items should be taken in which city. The combining elements are the knapsack’s renting rate that is to be paid for the travel time, and the thief’s slowdown with increasing knapsack use. Previously, successful algorithms focussed almost exclusively on constructing packing plans for near-optimal TSP tours. Even though additional hill-climbers are used at times, this strong initial bias prevents them from finding better solutions that require longer tours that can give rise to more profitable packing plans. Our swarm intelligence approach shifts the focus away from good TSP tours to good TTP tours. In our study we observe that this is effective and computationally efficient, as we outperform state-of-the-art approaches on instances with up to 250 cities and 2000 items, sometimes by more than 10 %.