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

Many real-world optimization problems have multiple interacting components. Each of these can be an NP -hard problem, 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.