集合覆盖问题：算法与应用

doi:10.3778/j.issn.1002-8331.2507-0352

摘要/Abstract

摘要： 集合覆盖问题作为组合优化领域的核心基础问题，因其NP-hard复杂性，广泛应用于无线网络基站部署、物流配送路径规划等工程领域，具有重要的实际应用价值。近年来，针对其求解的算法研究不断推进，主要包括启发式算法、群智能优化算法、进化算法、机器学习以及基于实际应用的算法等。系统地梳理集合覆盖问题的研究现状与算法发展脉络，从算法设计原理、结构适应性、性能对比等方面展开综述。总结各类算法的优势与局限，归纳适用场景与发展趋势，并展望集合覆盖问题在大规模数据集下的研究方向，旨在为相关研究提供理论支持与方法指导。

关键词: 集合覆盖问题（SCP）, 群智能优化算法, 进化算法, 启发式算法, 机器学习

Abstract: The set covering problem, as a core foundational problem in combinatorial optimization, due to its NP-hard complexity, is widely applied in engineering fields such as wireless network base station deployment and logistics routing, and has significant practical application value. In recent years, research on algorithms for solving this problem has advanced continuously, primarily including heuristic algorithms, swarm intelligence optimization algorithms, evolutionary algorithms, machine learning, and application-specific algorithms. This paper systematically reviews the research status and algorithmic development of the set covering problem, focusing on aspects such as algorithm design principles, structural adaptability, and performance comparisons. It summarizes the advantages and limitations of various algorithms, categorizes their applicable scenarios, and discusses the development trends. Furthermore, the paper looks ahead to the research directions for the set covering problem in large-scale datasets, aiming to provide theoretical support and methodological guidance for related research.

Key words: set covering problem (SCP), swarm intelligence optimization algorithms, evolutionary algorithms, heuristic algorithms, machine learning

锁小娜, 王晓峰, 颜冬, 胡思敏, 宋家欢. 集合覆盖问题：算法与应用[J]. 计算机工程与应用, 2026, 62(8): 1-20.

SUO Xiaona, WANG Xiaofeng, YAN Dong, HU Simin, SONG Jiahuan. Set Covering Problem: Algorithms and Applications[J]. Computer Engineering and Applications, 2026, 62(8): 1-20.

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