{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T21:38:26Z","timestamp":1790631506843,"version":"4.1.0"},"reference-count":121,"publisher":"Public Library of Science (PLoS)","issue":"1","license":[{"start":{"date-parts":[[2023,1,3]],"date-time":"2023-01-03T00:00:00Z","timestamp":1672704000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS ONE"],"abstract":"<jats:p>Monkey king evolution (MKE) is a population-based differential evolutionary algorithm in which the single evolution strategy and the control parameter affect the convergence and the balance between exploration and exploitation. Since evolution strategies have a considerable impact on the performance of algorithms, collaborating multiple strategies can significantly enhance the abilities of algorithms. This is our motivation to propose a multi-trial vector-based monkey king evolution algorithm named MMKE. It introduces novel best-history trial vector producer (BTVP) and random trial vector producer (RTVP) that can effectively collaborate with canonical MKE (MKE-TVP) using a multi-trial vector approach to tackle various real-world optimization problems with diverse challenges. It is expected that the proposed MMKE can improve the global search capability, strike a balance between exploration and exploitation, and prevent the original MKE algorithm from converging prematurely during the optimization process. The performance of the MMKE was assessed using CEC 2018 test functions, and the results were compared with eight metaheuristic algorithms. As a result of the experiments, it is demonstrated that the MMKE algorithm is capable of producing competitive and superior results in terms of accuracy and convergence rate in comparison to comparative algorithms. Additionally, the Friedman test was used to examine the gained experimental results statistically, proving that MMKE is significantly superior to comparative algorithms. Furthermore, four real-world engineering design problems and the optimal power flow (OPF) problem for the IEEE 30-bus system are optimized to demonstrate MMKE\u2019s real applicability. The results showed that MMKE can effectively handle the difficulties associated with engineering problems and is able to solve single and multi-objective OPF problems with better solutions than comparative algorithms.<\/jats:p>","DOI":"10.1371\/journal.pone.0280006","type":"journal-article","created":{"date-parts":[[2023,1,3]],"date-time":"2023-01-03T14:05:00Z","timestamp":1672754700000},"page":"e0280006","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":53,"title":["MMKE: Multi-trial vector-based monkey king evolution algorithm and its applications for engineering optimization problems"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0135-1115","authenticated-orcid":true,"given":"Mohammad H.","family":"Nadimi-Shahraki","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8872-8455","authenticated-orcid":true,"given":"Shokooh","family":"Taghian","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0444-4509","authenticated-orcid":true,"given":"Hoda","family":"Zamani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Seyedali","family":"Mirjalili","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohamed Abd","family":"Elaziz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2023,1,3]]},"reference":[{"key":"pone.0280006.ref001","doi-asserted-by":"crossref","DOI":"10.1002\/9780470496916","volume-title":"Metaheuristics: from design to implementation","author":"E.-G. 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