Solving Multiobjective Combinatorial Optimization via Learning to Improve Method

Abstract

Recently, neural combinatorial optimization (NCO) methods have been prevailing for solving multiobjective combinatorial optimization problems (MOCOPs). Most NCO methods are based on the “Learning to Construct” (L2C) paradigm, where the trained model(s) can directly generate a set of approximate Pareto optimal solutions. However, these methods still suffer from insufficient proximity and poor diversity towards the true Pareto front. In this paper, following the “Learning to Improve” (L2I) paradigm, we propose weight-related policy network (WRPN), a learning-based improvement method for solving MOCOPs. WRPN is incorporated into multiobjective evolutionary algorithm (MOEA) frameworks to effectively guide the search direction. A shared baseline for proximal policy optimization is presented to reduce variance in model training. A quality enhancement mechanism is designed to further refine the Pareto set during model inference. Computational experiments conducted on two classic MOCOPs, i.e., multiobjective traveling salesman problem and multiobjective vehicle routing problem, indicate that our method achieves remarkable results. Notably, our WRPN module can be easily integrated into various MOEA frameworks such as NSGA-II, MOEA/D and MOGLS, providing versatility and applicability across different problem domains.