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The Equilibrium Optimizer (EO) is a recently reported physics-based metaheuristic algorithm, and it has been inspired by the models used to predict equilibrium state and dynamic state. A similar procedure is utilized in MOEO by combining models in a different target search space. The crowding distance mechanism is employed in the MOEO algorithm to balance exploitation and exploration phases as the search progresses. In addition, a non-dominated sorting strategy is also merged with the MOEO algorithm to preserve the population diversity and it has been considered as a crucial problem in multi-objective metaheuristic algorithms. An archive with an update function is used to uphold and improve the coverage of Pareto with optimal solutions. The performance of MOEO is validated for 33 contextual problems with 6 constrained, 12 unconstrained, and 15 practical constrained engineering design problems, including non-linear problems. The result obtained by the proposed MOEO algorithm is compared with other state-of-the-art multi-objective optimization algorithms. The quantitative and qualitative results indicate that the proposed MOEO provides more competitive outcomes than the different algorithms. From the results obtained for all 33 benchmark optimization problems, the efficiency, robustness, and exploration ability to solve multi-objective problems of the MOEO algorithm are well defined and clarified. The paper is further supported with extra online service and guideline at https:\/\/premkumarmanoharan.wixsite.com\/mysite.<\/jats:p>","DOI":"10.1093\/jcde\/qwab065","type":"journal-article","created":{"date-parts":[[2021,10,20]],"date-time":"2021-10-20T17:52:24Z","timestamp":1634752344000},"page":"24-50","source":"Crossref","is-referenced-by-count":52,"title":["Multi-objective equilibrium optimizer: framework and development for solving multi-objective optimization problems"],"prefix":"10.1093","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1032-4634","authenticated-orcid":false,"given":"M","family":"Premkumar","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronics Engineering, Dayananda Sager College of Engineering, Bengaluru 560078, Karnataka, India"}]},{"given":"Pradeep","family":"Jangir","sequence":"additional","affiliation":[{"name":"Rajasthan Rajya Vidyut Prasaran Nigam Ltd., Sikar 332025, Rajasthan, India"}]},{"given":"R","family":"Sowmya","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronics Engineering, National Institute of Technology, Tiruchirappalli 620015, Tamil Nadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2015-3827","authenticated-orcid":false,"given":"Hassan Haes","family":"Alhelou","sequence":"additional","affiliation":[{"name":"Department of Electrical Power Engineering, Tishreen University, 2230 Lattakia, Syria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1443-9458","authenticated-orcid":false,"given":"Seyedali","family":"Mirjalili","sequence":"additional","affiliation":[{"name":"Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, Fortitude Valley, QLD 4006, Australia"},{"name":"Yonsei Frontier Lab, Yonsei University, Seoul 03722, Korea"}]},{"given":"B Santhosh","family":"Kumar","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Guru Nanak Institute of Technology, Hyderabad 501506, Telangana, India"}]}],"member":"286","published-online":{"date-parts":[[2021,12,30]]},"reference":[{"key":"2022010106254216700_bib1","doi-asserted-by":"crossref","first-page":"10685","DOI":"10.1007\/s00521-020-04820-y","article-title":"A novel equilibrium optimization algorithm for multi-thresholding image segmentation problems","volume":"33","author":"Abdel-Basset","year":"2020","journal-title":"Neural Computing and Applications"},{"issue":"1","key":"2022010106254216700_bib3","doi-asserted-by":"crossref","first-page":"59","DOI":"10.5267\/j.dsl.2019.8.001","article-title":"A new non-dominated sorting ions motion algorithm: Development and applications","volume":"9","author":"Buch","year":"2020","journal-title":"Decision Science Letters"},{"issue":"4","key":"2022010106254216700_bib4","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/s12293-011-0072-9","article-title":"DMEA: A direction-based multiobjective evolutionary algorithm","volume":"3","author":"Bui","year":"2011","journal-title":"Memetic Computing"},{"key":"2022010106254216700_bib5","doi-asserted-by":"crossref","first-page":"1051","DOI":"10.1109\/CEC.2002.1004388","article-title":"MOPSO: A proposal for multiple objective particle swarm optimization","volume-title":"Proceedings of the 2002 Congress on Evolutionary Computation. 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