Adversarial Instance Generation and Robust Training for Neural Combinatorial Optimization with Multiple Objectives

TL;DR

This paper introduces a framework combining adversarial attacks and robust training to improve the robustness and generalization of neural solvers for multi-objective combinatorial optimization problems, tested on TSP, VRP, and knapsack problems.

Contribution

It develops a preference-based adversarial attack and a hardness-aware training method to enhance neural solver robustness and out-of-distribution performance.

Findings

Attack method effectively generates hard instances for various solvers.

Defense strategy improves robustness against out-of-distribution instances.

Neural solvers show significant performance gains on hard problems.

Abstract

Deep reinforcement learning (DRL) has shown great promise in addressing multi-objective combinatorial optimization problems (MOCOPs). Nevertheless, the robustness of these learning-based solvers has remained insufficiently explored, especially across diverse and complex problem distributions. In this paper, we propose a unified robustness-oriented framework for preference-conditioned DRL solvers for MOCOPs. Within this framework, we develop a preference-based adversarial attack to generate hard instances that expose solver weaknesses, and quantify the attack impact by the resulting degradation on Pareto-front quality. We further introduce a defense strategy that integrates hardness-aware preference selection into adversarial training to reduce overfitting to restricted preference regions and improve out-of-distribution performance. The experimental results on multi-objective traveling salesman problem (MOTSP), multi-objective capacitated vehicle routing problem (MOCVRP), and multi-objective knapsack problem (MOKP) verify that our attack method successfully learns hard instances for different solvers. Furthermore, our defense method significantly strengthens the robustness and generalizability of neural solvers, delivering superior performance on hard or out-of-distribution instances.