{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T01:57:42Z","timestamp":1768442262414,"version":"3.49.0"},"reference-count":19,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,10,25]],"date-time":"2021-10-25T00:00:00Z","timestamp":1635120000000},"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>This paper investigated the flexible job-shop scheduling problem with the heat treatment process. To solve this problem, we built an unified mathematical model of the heat treatment process and machining process. Up to now, this problem has not been investigated much. Based on the features of this problem, we are intended to minimize Cmax, maximize the space utilization rate of heat treatment equipment, and minimize the total delay penalty to optimize the scheduling. By taking the dynamic process arrival under consideration, this paper proposed a set of decoding rules based on the heat treatment equipment volume and job delivery date to achieve a hybrid dynamic scheduling solution during one scheduling procedure. When the utilization rate of heat treatment equipment volume is maximized, and the job delivery date is taken under consideration, it is preferred to minimize the number of workpiece batches in the same job, and reduce the waiting time of the pending job. In combination with the improved adaptive non-dominated genetic algorithm, we worked out the solution. Furthermore, we verified the effectiveness of the proposed decoding rules and improved algorithm through algorithm comparison and calculation results. Finally, a software system for algorithm verification and algorithm comparison was developed to verify the validity of our proposed algorithm.<\/jats:p>","DOI":"10.3390\/a14110310","type":"journal-article","created":{"date-parts":[[2021,10,25]],"date-time":"2021-10-25T21:40:21Z","timestamp":1635198021000},"page":"310","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Non-Dominated Genetic Algorithm Based on Decoding Rule of Heat Treatment Equipment Volume and Job Delivery Date"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2787-6454","authenticated-orcid":false,"given":"Yan","family":"Liang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China"},{"name":"Beijing Xinfeng Aerospace Equipment Co., Ltd., Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingdong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/0167-6377(86)90104-5","article-title":"Efficient scheduling algorithms for a single batch processing machine","volume":"5","author":"Ikura","year":"1986","journal-title":"Oper. 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Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1016\/j.jclepro.2018.02.224","article-title":"Multi-object optimization of flexible flow shop scheduling with batch process\u2014Consideration total electricity consumption and material wastage","volume":"183","author":"Zeng","year":"2018","journal-title":"J. Clean. Prod."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1016\/j.ejor.2020.01.065","article-title":"Exact algorithms to minimize makespan on single and parallel batch processing machines","volume":"285","author":"Muter","year":"2020","journal-title":"Eur. J. Oper. Res."},{"key":"ref_16","unstructured":"Fengping, S., Jingjing, L., and Yulong, Y. (2021, September 24). Heat Treatment Batch Scheduling Model and PSO Solution for the Minimum Waiting Time. Available online: https:\/\/tow.cnki.net\/kcms\/detail\/detail.aspx?filename=JSJZ202004042&dbcode=CRJT_CJFD&dbname=CJFDLAST2020&v=."},{"key":"ref_17","unstructured":"Rong, L., Lin, Z., and Chao, W. (2021, September 24). Research on Flexible Job-Shop Scheduling Problem with the Parallel Batch Processor. Available online: https:\/\/xueshu.baidu.com\/usercenter\/paper\/show?paperid=1e4g0xp0pr5k0pt0ps4f0pd0w5584347."},{"key":"ref_18","unstructured":"Jiangxu, Q. (2011). Integrated Scheduling Method of Machine-Heat Treatment in Complex Manufacturing System. [Ph.D. Thesis, Beijing Institute of Technology]."},{"key":"ref_19","unstructured":"Li, H. (2021). Research on Batch Scheduling Methods of the Flexible Flow Shop Based on DES-GEP. [Ph.D. Thesis, Dalian University of Technology]."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/11\/310\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:23:21Z","timestamp":1760167401000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/11\/310"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,25]]},"references-count":19,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["a14110310"],"URL":"https:\/\/doi.org\/10.3390\/a14110310","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,25]]}}}