{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T15:20:26Z","timestamp":1778858426471,"version":"3.51.4"},"reference-count":35,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T00:00:00Z","timestamp":1741824000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>For large-scale multi-objective optimization, it is particularly challenging for evolutionary algorithms to converge to the Pareto Front. Most existing multi-objective evolutionary algorithms (MOEAs) handle convergence and diversity in a mutually dependent manner during the evolution process. In this case, the performance degradation of one solution may lead to the deterioration of the performance of the other solution. This paper proposes a two-stage multi-objective optimization algorithm based on decision variable clustering (LSMOEA-VT) to solve large-scale optimization problems. In LSMOEA-VT, decision variables are divided into two categories and use dimensionality reduction methods to optimize the variables that affect evolutionary convergence. Following this, we performed an interdependence analysis to break down the convergence variables into multiple subcomponents that are more tractable. Furthermore, a non-dominated dynamic weight aggregation method is used to enhance the diversity of the population. To evaluate the performance of our proposed algorithm, we performed extensive comparative experiments against four optimization algorithms across a diverse set of benchmark problems, including eight multi-objective optimization problems and nine large-scale optimization problems. The experimental results show that our proposed algorithm performs well on some test functions and has certain competitiveness.<\/jats:p>","DOI":"10.3390\/a18030164","type":"journal-article","created":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T12:06:59Z","timestamp":1741867619000},"page":"164","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Two-Stage Multi-Objective Optimization Algorithm for Solving Large-Scale Optimization Problems"],"prefix":"10.3390","volume":"18","author":[{"given":"Jiaqi","family":"Liu","sequence":"first","affiliation":[{"name":"College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0741-4743","authenticated-orcid":false,"given":"Tianyu","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/4235.996017","article-title":"A fast and elitist multiobjective genetic algorithm: NSGA-II","volume":"6","author":"Deb","year":"2002","journal-title":"IEEE Trans. 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