发表机构
The Ohio State University; Michigan State University; University of Colorado at Boulder; Los Alamos National Laboratory; University of Michigan（俄亥俄州立大学; 密歇根州立大学; 科罗拉多大学博尔德分校; 洛斯阿拉莫斯国家实验室; 密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出可并行化的多目标二次组合优化算法MO-QUCO及pMO-QUCO，将多目标最大割约简为偏好条件下单目标带符号权重最大割问题，实验显示其在运行时间、目标质量上优于SOTA精确、启发式及量子方法。
AI 中文摘要
多目标组合优化广泛存在于各类问题与应用中，包括经典的多目标最大割问题。近期，可微的单实例二次方法在单目标组合优化中取得了显著性能。本文中，我们结合基于邻接的二次公式与线性标量化，开发了一种面向多目标最大割的可微框架，从而将该问题约简为偏好条件下的单目标带符号权重最大割问题。理论上，我们刻画了所得带符号权重公式的驻点，并证明这些驻点如何在帕累托前沿上诱导偏好条件下的不动点。计算上，与传统启发式方法和分支定界方法不同，我们的方法可在GPU上并行化，因此能获得显著的性能加速。我们将该算法命名为多目标二次组合优化（MO-QUCO），其并行变体命名为pMO-QUCO。实验中，在不同的多层图（及权重分布）上，我们的仅CPU算法和基于GPU的算法均在挂钟运行时间和目标质量上优于SOTA精确方法与启发式方法。尽管在不同计算设置下运行，MO-QUCO也优于SOTA量子方法。
英文摘要
Multi-objective combinatorial optimization arises in a wide range of problems and applications, including the canonical multi-objective MaxCut problem. Differentiable single-instance quadratic methods have recently achieved remarkable performance in single-objective combinatorial optimization. In this paper, we develop a differentiable framework for multi-objective MaxCut by combining an adjacency-based quadratic formulation with linear scalarization, thereby reducing the problem to a preference-conditioned single-objective signed-weight MaxCut problem. Theoretically, we characterize projected gradient ascent (PGA) fixed points and their local dynamics under the signed-weight adjacency formulation. We further characterize how these fixed points depend on preferences and establish their connection to Pareto optimality. Computationally, unlike conventional heuristics and branch-and-bound methods, our approach is GPU-parallelizable and can therefore benefit from substantial performance speedups. We term our algorithm Multi-objective QUadratic Combinatorial Optimization (MO-QUCO) and its parallelized variant pMO-QUCO. Empirically, we evaluate our methods on multi-layered graphs with different sizes and edge-weight distributions. Both our CPU-only and GPU-based algorithms outperform state-of-the-art exact and heuristic methods in terms of wall-clock runtime and objective quality. Despite operating under different computational settings, MO-QUCO also outperforms the SOTA quantum method.
