Most of existing neural methods for multi-objective combinatorial optimization (MOCO) problems solely rely on decomposition, which often leads to repetitive solutions for the respective subproblems, thus a limited Pareto set. Beyond decomposition, we propose a novel neural heuristic with diversity enhancement (NHDE) to produce more Pareto solutions from two perspectives. On the one hand, to hinder duplicated solutions for different subproblems, we propose an indicator-enhanced deep reinforcement learning method to guide the model, and design a heterogeneous graph attention mechanism to capture the relations between the instance graph and the Pareto front graph. On the other hand, to excavate more solutions in the neighborhood of each subproblem, we present a multiple Pareto optima strategy to sample and preserve desirable solutions. Experimental results on classic MOCO problems show that our NHDE is able to generate a Pareto front with higher diversity, thereby achieving superior overall performance. Moreover, our NHDE is generic and can be applied to different neural methods for MOCO.

翻译：现有的大多数神经方法在处理多目标组合优化（MOCO）问题时，仅依赖分解策略，这往往导致各子问题产生重复解，从而限制了帕累托集合的多样性。为突破分解的局限性，我们提出了一种新颖的、带有多样性增强（NHDE）的神经启发式方法，从两个角度生成更多帕累托解。一方面，为阻止不同子问题产生重复解，我们提出了一种指标增强的深度强化学习方法引导模型，并设计了一种异构图注意力机制，以捕捉实例图与帕累托前沿图之间的关系。另一方面，为挖掘每个子问题邻域内的更多解，我们提出了一种多帕累托最优策略，用于采样并保留理想的解。在经典MOCO问题上的实验结果表明，我们的NHDE能够生成多样性更强的帕累托前沿，从而获得更优的整体性能。此外，我们的NHDE具有通用性，可适用于不同的MOCO神经求解方法。