Pareto Set Learning for Neural Multi-objective Combinatorial Optimization

TL;DR

This paper introduces a neural network-based approach to approximate the entire Pareto set in multi-objective combinatorial optimization problems, enabling efficient and high-quality solutions without extensive search.

Contribution

It develops a preference-conditioned neural model trained with reinforcement learning to generate Pareto solutions for any trade-off, extending decomposition-based evolutionary algorithms.

Findings

Outperforms existing methods on TSP, VRP, and knapsack problems.

Provides faster solution generation with higher quality.

Uses a single model for all preferences, improving efficiency.

Abstract

Multiobjective combinatorial optimization (MOCO) problems can be found in many real-world applications. However, exactly solving these problems would be very challenging, particularly when they are NP-hard. Many handcrafted heuristic methods have been proposed to tackle different MOCO problems over the past decades. In this work, we generalize the idea of neural combinatorial optimization, and develop a learning-based approach to approximate the whole Pareto set for a given MOCO problem without further search procedure. We propose a single preference-conditioned model to directly generate approximate Pareto solutions for any trade-off preference, and design an efficient multiobjective reinforcement learning algorithm to train this model. Our proposed method can be treated as a learning-based extension for the widely-used decomposition-based multiobjective evolutionary algorithm (MOEA/D). It uses a single model to accommodate all the possible preferences, whereas other methods use a finite number of solutions to approximate the Pareto set. Experimental results show that our proposed method significantly outperforms some other methods on the multiobjective traveling salesman problem, multiobjective vehicle routing problem, and multiobjective knapsack problem in terms of solution quality, speed, and model efficiency.