A weighted-sum method for solving the bi-objective traveling thief problem

TL;DR

This paper introduces a weighted-sum method for the bi-objective traveling thief problem, combining TSP and knapsack components, and demonstrates its effectiveness through competitive performance and new best solutions.

Contribution

It proposes a novel weighted-sum approach using randomized heuristics for the bi-objective traveling thief problem, improving solution quality over existing methods.

Findings

Outperforms competitors on 6 of 9 instances

Finds new best solutions to 379 single-objective instances

Effective in solving complex multi-component problems

Abstract

Many real-world optimization problems have multiple interacting components. Each of these can be NP-hard and they can be in conflict with each other, i.e., the optimal solution for one component does not necessarily represent an optimal solution for the other components. This can be a challenge for single-objective formulations, where the respective influence that each component has on the overall solution quality can vary from instance to instance. In this paper, we study a bi-objective formulation of the traveling thief problem, which has as components the traveling salesperson problem and the knapsack problem. We present a weighted-sum method that makes use of randomized versions of existing heuristics, that outperforms participants on 6 of 9 instances of recent competitions, and that has found new best solutions to 379 single-objective problem instances.