Multi-objective Pointer Network for Combinatorial Optimization

TL;DR

This paper introduces MOPN, a deep reinforcement learning framework that efficiently solves multi-objective combinatorial optimization problems, outperforming classical methods in speed and scalability.

Contribution

The study proposes a novel single-model DRL framework, MOPN, with improved input structure and training strategies for multi-objective combinatorial optimization.

Findings

MOPN outperforms state-of-the-art models and classical meta-heuristics.

MOPN requires only 20-40% of the training time of DRL-MOA.

MOPN is insensitive to problem scale, handling different sizes effectively.

Abstract

Multi-objective combinatorial optimization problems (MOCOPs), one type of complex optimization problems, widely exist in various real applications. Although meta-heuristics have been successfully applied to address MOCOPs, the calculation time is often much longer. Recently, a number of deep reinforcement learning (DRL) methods have been proposed to generate approximate optimal solutions to the combinatorial optimization problems. However, the existing studies on DRL have seldom focused on MOCOPs. This study proposes a single-model deep reinforcement learning framework, called multi-objective Pointer Network (MOPN), where the input structure of PN is effectively improved so that the single PN is capable of solving MOCOPs. In addition, two training strategies, based on representative model and transfer learning, respectively, are proposed to further enhance the performance of MOPN in different application scenarios. Moreover, compared to classical meta-heuristics, MOPN only consumes much less time on forward propagation to obtain the Pareto front. Meanwhile, MOPN is insensitive to problem scale, meaning that a trained MOPN is able to address MOCOPs with different scales. To verify the performance of MOPN, extensive experiments are conducted on three multi-objective traveling salesman problems, in comparison with one state-of-the-art model DRL-MOA and three classical multi-objective meta-heuristics. Experimental results demonstrate that the proposed model outperforms all the comparative methods with only 20\% to 40\% training time of DRL-MOA.