Context-aware Diversity Enhancement for Neural Multi-Objective Combinatorial Optimization

TL;DR

This paper introduces CDE, a context-aware diversity enhancement algorithm for neural multi-objective combinatorial optimization, which improves solution diversity by modeling context at node and solution levels, outperforming existing methods.

Contribution

The paper proposes a novel CDE algorithm that leverages autoregressive sequence modeling and hypervolume-based feedback to enhance diversity in neural MOCO solutions.

Findings

CDE outperforms state-of-the-art baselines on three MOCO problems.

The hypervolume residual update improves Pareto front capturing.

Context-aware modeling enhances diversity and solution quality.

Abstract

Multi-objective combinatorial optimization (MOCO) problems are prevalent in various real-world applications. Most existing neural MOCO methods rely on problem decomposition to transform an MOCO problem into a series of singe-objective combinatorial optimization (SOCO) problems and train attention models based on a single-step and deterministic greedy rollout. However, inappropriate decomposition and undesirable short-sighted behaviors of previous methods tend to induce a decline in diversity. To address the above limitation, we design a Context-aware Diversity Enhancement algorithm named CDE, which casts the neural MOCO problems as conditional sequence modeling via autoregression (node-level context awareness) and establishes a direct relationship between the mapping of preferences and diversity indicator of reward based on hypervolume expectation maximization (solution-level context awareness). Based on the solution-level context awareness, we further propose a hypervolume residual update strategy to enable the Pareto attention model to capture both local and non-local information of the Pareto set/front. The proposed CDE can effectively and efficiently grasp the context information, resulting in diversity enhancement. Experimental results on three classic MOCO problems demonstrate that our CDE outperforms several state-of-the-art baselines.