{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T14:10:22Z","timestamp":1765807822121,"version":"build-2065373602"},"reference-count":79,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,5]],"date-time":"2020-09-05T00:00:00Z","timestamp":1599264000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Scheduling can be described as a decision-making process. It is applied in various applications, such as manufacturing, airports, and information processing systems. More so, the presence of symmetry is common in certain types of scheduling problems. There are three types of parallel machine scheduling problems (PMSP): uniform, identical, and unrelated parallel machine scheduling problems (UPMSPs). Recently, UPMSPs with setup time had attracted more attention due to its applications in different industries and services. In this study, we present an efficient method to address the UPMSPs while using a modified harris hawks optimizer (HHO). The new method, called MHHO, uses the salp swarm algorithm (SSA) as a local search for HHO in order to enhance its performance and to decrease its computation time. To test the performance of MHHO, several experiments are implemented using small and large problem instances. Moreover, the proposed method is compared to several state-of-art approaches used for UPMSPs. The MHHO shows better performance in both small and large problem cases.<\/jats:p>","DOI":"10.3390\/sym12091460","type":"journal-article","created":{"date-parts":[[2020,9,6]],"date-time":"2020-09-06T23:12:49Z","timestamp":1599433969000},"page":"1460","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["Modified Harris Hawks Optimizer for Solving Machine Scheduling Problems"],"prefix":"10.3390","volume":"12","author":[{"given":"Hamza","family":"Jouhari","sequence":"first","affiliation":[{"name":"School of Automation, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deming","family":"Lei","sequence":"additional","affiliation":[{"name":"School of Automation, Wuhan University of Technology, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6956-7641","authenticated-orcid":false,"given":"Mohammed A. A.","family":"Al-qaness","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed Abd","family":"Elaziz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9990-1084","authenticated-orcid":false,"given":"Robertas","family":"Dama\u0161evi\u010dius","sequence":"additional","affiliation":[{"name":"Department of Applied Informatics, Vytautas Magnus University, 44404 Kaunas, Lithuania"},{"name":"Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6002-2733","authenticated-orcid":false,"given":"Marcin","family":"Korytkowski","sequence":"additional","affiliation":[{"name":"Department of Intelligent Computer Systems, Czestochowa University of Technology, 42-200 Cz\u0119stochowa, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmed A.","family":"Ewees","sequence":"additional","affiliation":[{"name":"Department of e-Systems, University of Bisha, Bisha 61922, Saudi Arabia"},{"name":"Department of Computer, Damietta University, Damietta 34517, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,5]]},"reference":[{"key":"ref_1","unstructured":"Ostrowski, J., Anjos, M.F., and Vannelli, A. 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