{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T03:44:57Z","timestamp":1774928697179,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,1]],"date-time":"2020-04-01T00:00:00Z","timestamp":1585699200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71501181;71871185"],"award-info":[{"award-number":["71501181;71871185"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>To certain degree, multi-objective optimization problems obey the law of symmetry, for instance, the minimum of one objective function corresponds to the maximum of another objective. To provide effective support for the multi-objective operation of the aerospace product shell production line, this paper studies multi-objective aerospace shell production scheduling problems. Firstly, a multi-objective optimization model for the production scheduling of aerospace product shell production lines is established. In the presented model, the maximum completion time and the cost of production line construction are optimized simultaneously. Secondly, to tackle the characteristics of discreteness, non-convexity and strong NP difficulty of the multi-objective problem, a knowledge-driven multi-objective evolutionary algorithm is designed to solve the problem. In the proposed approach, structural features of the scheduling plan are extracted during the optimization process and used to guide the subsequent optimization process. Finally, a set of test instances is generated to illustrate the addressed problem and test the proposed approach. The experimental results show that the knowledge-driven multi-objective evolutionary algorithm designed in this paper has better performance than the two classic multi-objective optimization methods.<\/jats:p>","DOI":"10.3390\/sym12040509","type":"journal-article","created":{"date-parts":[[2020,4,2]],"date-time":"2020-04-02T13:39:34Z","timestamp":1585834774000},"page":"509","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["An Improved Multi-Objective Evolutionary Approach for Aerospace Shell Production Scheduling Problem"],"prefix":"10.3390","volume":"12","author":[{"given":"Qing","family":"Wang","sequence":"first","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoshuang","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Information Communication, National University of Defense Technology, Wuhan 430014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiwei","family":"Luo","sequence":"additional","affiliation":[{"name":"Capital Aerospace Machinery Corporation Limited, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Xiong","sequence":"additional","affiliation":[{"name":"School of Business Administration, Southwestern University of Finance and Economics, Chengdu 610074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1080\/01605682.2018.1452537","article-title":"A multistage graph-based procedure for solving a just-in-time flexible job-shop scheduling problem with machine and time-dependent processing costs","volume":"70","author":"Corominas","year":"2018","journal-title":"J. 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