{"title":"An efficient iterated local search for the minimum quasi-clique partitioning problem","authors":"Qing Zhou , Tongtong Zhu , Qinghua Wu , Zhong-Zhong Jiang , Wenjie Wang","doi":"10.1016/j.cor.2025.107033","DOIUrl":null,"url":null,"abstract":"<div><div>Given a simple undirected graph <span><math><mi>G</mi></math></span> and a real constant <span><math><mrow><mi>γ</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span>, a <span><math><mi>γ</mi></math></span>-quasi-clique is defined as a subset of vertices that induces a subgraph with an edge density of at least <span><math><mi>γ</mi></math></span>. The minimum quasi-clique partitioning problem (MQCPP) seeks to identify the minimum cardinality of <span><math><mi>γ</mi></math></span>-quasi-clique partitions in <span><math><mi>G</mi></math></span>. This work presents an efficient iterated local search (ILS) method to address MQCPP by using a two-phase local search procedure for local improvement, and a greedy-based perturbation procedure for diversifying the search process. An evaluation function that records the number of intra edges of each quasi-clique is used for neighboring solution evaluation, and a fast incremental evaluation technique is employed to speed up the evaluation. Numerical results on three sets of 321 benchmark instances demonstrate the superior performance of the proposed algorithm compared with state-of-the-art approaches. Specifically, ILS reports 153 (47.7%) new upper bounds and fails to reach the best known solution for only 2 instances. Additional analysis experiments are conducted to evaluate the effects of the key components of ILS, including the two-phase local search procedure, the greedy-based perturbation procedure, and the fast incremental evaluation technique.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"179 ","pages":"Article 107033"},"PeriodicalIF":4.1000,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers & Operations Research","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0305054825000619","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
Given a simple undirected graph and a real constant , a -quasi-clique is defined as a subset of vertices that induces a subgraph with an edge density of at least . The minimum quasi-clique partitioning problem (MQCPP) seeks to identify the minimum cardinality of -quasi-clique partitions in . This work presents an efficient iterated local search (ILS) method to address MQCPP by using a two-phase local search procedure for local improvement, and a greedy-based perturbation procedure for diversifying the search process. An evaluation function that records the number of intra edges of each quasi-clique is used for neighboring solution evaluation, and a fast incremental evaluation technique is employed to speed up the evaluation. Numerical results on three sets of 321 benchmark instances demonstrate the superior performance of the proposed algorithm compared with state-of-the-art approaches. Specifically, ILS reports 153 (47.7%) new upper bounds and fails to reach the best known solution for only 2 instances. Additional analysis experiments are conducted to evaluate the effects of the key components of ILS, including the two-phase local search procedure, the greedy-based perturbation procedure, and the fast incremental evaluation technique.
期刊介绍:
Operations research and computers meet in a large number of scientific fields, many of which are of vital current concern to our troubled society. These include, among others, ecology, transportation, safety, reliability, urban planning, economics, inventory control, investment strategy and logistics (including reverse logistics). Computers & Operations Research provides an international forum for the application of computers and operations research techniques to problems in these and related fields.