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This research introduces a unified framework for improving the robustness of deep reinforcement learning solvers in multi-objective combinatorial optimization by using adversarial attacks to generate hard instances. The proposed defense strategy, which integrates hardness-aware preference selection into adversarial training, effectively reduces overfitting and enhances generalization on out-of-distribution problems. These findings are significant for practitioners deploying neural solvers in complex logistics and scheduling scenarios where solution reliability across diverse problem distributions is critical.
Adversarial Instance Generation and Robust Training for Neural Combinatorial Optimization with Multiple Objectives
arXiv:2601.01665v2 Announce Type: replace 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.
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.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2601.01665 [cs.LG]
(or arXiv:2601.01665v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2601.01665 Focus to learn more arXiv-issued DOI via DataCite
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