Efficient Meta Neural Heuristic for Multi-Objective Combinatorial Optimization

TL;DR

This paper introduces an efficient meta neural heuristic that improves learning efficiency and solution quality for multi-objective combinatorial optimization problems by combining meta-model training, parallel learning, and systematic fine-tuning.

Contribution

The paper proposes a novel meta neural heuristic with a shared multi-task model and hierarchical fine-tuning, significantly enhancing performance and efficiency over existing neural heuristics.

Findings

Outperforms state-of-the-art neural heuristics in solution quality.

Achieves faster training and solution times.

Provides competitive results compared to traditional heuristics.

Abstract

Recently, neural heuristics based on deep reinforcement learning have exhibited promise in solving multi-objective combinatorial optimization problems (MOCOPs). However, they are still struggling to achieve high learning efficiency and solution quality. To tackle this issue, we propose an efficient meta neural heuristic (EMNH), in which a meta-model is first trained and then fine-tuned with a few steps to solve corresponding single-objective subproblems. Specifically, for the training process, a (partial) architecture-shared multi-task model is leveraged to achieve parallel learning for the meta-model, so as to speed up the training; meanwhile, a scaled symmetric sampling method with respect to the weight vectors is designed to stabilize the training. For the fine-tuning process, an efficient hierarchical method is proposed to systematically tackle all the subproblems. Experimental results on the multi-objective traveling salesman problem (MOTSP), multi-objective capacitated vehicle routing problem (MOCVRP), and multi-objective knapsack problem (MOKP) show that, EMNH is able to outperform the state-of-the-art neural heuristics in terms of solution quality and learning efficiency, and yield competitive solutions to the strong traditional heuristics while consuming much shorter time.