Title: Decomposition-based Neural Multi-objective Combinatorial Optimization with Graph-Filter based Multi-Head Attention
Primary area: optimization
Keywords: Multi-Objective Combinatorial Optimization, Neural Combinatorial Optimization, Deep Reinforcement Learning, Encoder-Decoder

Abstract: Recent decomposition-based neural multi-objective combinatorial optimization (MOCO) methods have achieved remarkable success in solving Multi-Objective Combinatorial Optimization Problems (MOCOPs). However, existing methods either overlook the relationships between weights and instances of the subproblems, or cannot sufficiently capture their relationships. This may lead to poor synergy between weights and instances, which impairs the ability of learning the Pareto fronts. To address this limitation, we propose a novel framework that can more effectively characterize the relationships between weights and instances while mitigating the over-smoothing problem. Specifically, we have designed a cross-attention-based weight embedding model, which treats weight vectors and node vectors as two separate sequences to gain deeper insights into their interdependencies. Additionally, we employ a graph-filter-based multi-head attention module that optimizes attention computations to prevent the loss of critical information during backpropagation. We validated the effectiveness and versatility of our method on several classic MOCOP benchmarks. Experimental results show that our method outperforms existing state-of-the-art approaches with significant superiority and strong generalization capabilities.