On the computational complexity of ordinal multi-objective unconstrained combinatorial optimization

IF 0.8 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Letters Pub Date : 2025-05-06 DOI:10.1016/j.orl.2025.107302

José Rui Figueira , Kathrin Klamroth , Michael Stiglmayr , Julia Sudhoff Santos

引用次数: 0

Abstract

Multi-objective unconstrained combinatorial optimization problems (MUCO) are in general hard to solve, i.e., the corresponding decision problem is NP-hard and the outcome set is intractable. In this paper we explore special cases of MUCO problems that are actually easy, i.e., solvable in polynomial time. More precisely, we show that MUCO problems with up to two ordinal objective functions plus one real-valued objective function are tractable, and that their complete nondominated set can be computed in polynomial time. For MUCO problems with one ordinal and a second ordinal or real-valued objective function we present an even more efficient algorithm that applies a greedy strategy multiple times.

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有序多目标无约束组合优化的计算复杂度

多目标无约束组合优化问题（MUCO）一般是难以解决的问题，即相应的决策问题是np困难的，结果集是难以处理的。在本文中，我们探讨了MUCO问题的特殊情况，这些问题实际上很容易，即在多项式时间内可解。更精确地说，我们证明了包含两个有序目标函数和一个实值目标函数的MUCO问题是可处理的，并且它们的完全非支配集可以在多项式时间内计算出来。对于具有一个序数和一个二阶序数或实值目标函数的MUCO问题，我们提出了一种更有效的算法，该算法多次应用贪婪策略。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Operations Research Letters 管理科学-运筹学与管理科学

CiteScore

2.10

自引率

9.10%

发文量

111

审稿时长

83 days

期刊介绍： Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.