{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,12]],"date-time":"2026-04-12T19:22:27Z","timestamp":1776021747453,"version":"3.50.1"},"reference-count":41,"publisher":"MIT Press - Journals","issue":"1","license":[{"start":{"date-parts":[[2021,2,5]],"date-time":"2021-02-05T00:00:00Z","timestamp":1612483200000},"content-version":"vor","delay-in-days":401,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":["direct.mit.edu"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2020,3,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Pareto-based multi-objective evolutionary algorithms experience grand challenges in solving many-objective optimization problems due to their inability to maintain both convergence and diversity in a high-dimensional objective space. Exiting approaches usually modify the selection criteria to overcome this issue. Different from them, we propose a novel meta-objective (MeO) approach that transforms the many-objective optimization problems in which the new optimization problems become easier to solve by the Pareto-based algorithms. MeO converts a given many-objective optimization problem into a new one, which has the same Pareto optimal solutions and the number of objectives with the original one. Each meta-objective in the new problem consists of two components which measure the convergence and diversity performances of a solution, respectively. Since MeO only converts the problem formulation, it can be readily incorporated within any multi-objective evolutionary algorithms, including those non-Pareto-based ones. Particularly, it can boost the Pareto-based algorithms' ability to solve many-objective optimization problems. Due to separately evaluating the convergence and diversity performances of a solution, the traditional density-based selection criteria, for example, crowding distance, will no longer mistake a solution with poor convergence performance for a solution with low density value. By penalizing a solution in term of its convergence performance in the meta-objective space, the Pareto dominance becomes much more effective for a many-objective optimization problem. Comparative study validates the competitive performance of the proposed meta-objective approach in solving many-objective optimization problems.<\/jats:p>","DOI":"10.1162\/evco_a_00243","type":"journal-article","created":{"date-parts":[[2018,11,26]],"date-time":"2018-11-26T19:54:41Z","timestamp":1543262081000},"page":"1-25","update-policy":"https:\/\/doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":23,"title":["A Meta-Objective Approach for Many-Objective Evolutionary\n          Optimization"],"prefix":"10.1162","volume":"28","author":[{"given":"Dunwei","family":"Gong","sequence":"first","affiliation":[{"name":"School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China"}]},{"given":"Yiping","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China"},{"name":"Department of Computer Science and Intelligent Systems, Graduate School of Engineering, Osaka Prefecture University, Sakai 599-8531, Japan yiping0liu@gmail.com"}]},{"given":"Gary G.","family":"Yen","sequence":"additional","affiliation":[{"name":"School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, OK 74078, USA gyen@okstate.edu"}]}],"member":"281","published-online":{"date-parts":[[2020,3,1]]},"reference":[{"key":"2022050416562507600_B1","doi-asserted-by":"crossref","unstructured":"Adra, S. F., and\n                Fleming, P.\n              J. (2011).\n            Diversity management in evolutionary many-objective\n            optimization. IEEE Transactions on Evolutionary\n            Computation,\n            15(2):183\u2013195.","DOI":"10.1109\/TEVC.2010.2058117"},{"key":"2022050416562507600_B2","doi-asserted-by":"crossref","unstructured":"Bader, J., and\n                Zitzler,\n            E. (2011).\n            HypE: An algorithm for fast hypervolume-based many-objective\n            optimization. Evolutionary Computation,\n            19(1):45\u201376.","DOI":"10.1162\/EVCO_a_00009"},{"key":"2022050416562507600_B3","doi-asserted-by":"crossref","unstructured":"Cheng, J.,\n                Yen, G. G.,\n            and Zhang,\n            G. (2015).\n            A many-objective evolutionary algorithm with enhanced mating and\n            environmental selections. IEEE Transactions on Evolutionary\n            Computation,\n            19(4):592\u2013605.","DOI":"10.1109\/TEVC.2015.2424921"},{"key":"2022050416562507600_B4","doi-asserted-by":"crossref","unstructured":"Deb, K., and\n                Jain,\n            H. (2013).\n            An evolutionary many-objective optimization algorithm using\n            reference-point based non-dominated sorting approach, part i: Solving problems with box\n            constraints. IEEE Transactions on Evolutionary\n            Computation,\n            18(4):577\u2013601.","DOI":"10.1109\/TEVC.2013.2281535"},{"key":"2022050416562507600_B5","doi-asserted-by":"crossref","unstructured":"Deb, K.,\n                Pratap, A.,\n                Agarwal,\n            S., and\n                Meyarivan,\n              T. (2002).\n            A fast and elitist multiobjective genetic algorithm:\n            NSGA-II. IEEE Transactions on Evolutionary Computation,\n            6(2):182\u2013197.","DOI":"10.1109\/4235.996017"},{"key":"2022050416562507600_B6","unstructured":"Deb, K.,\n                Thiele, L.,\n                Laumanns,\n              M., and\n                Zitzler,\n            E. (2005).\n            Scalable test problems for evolutionary multiobjective optimization.\n            New York:\n          Springer."},{"key":"2022050416562507600_B7","doi-asserted-by":"crossref","unstructured":"Goulart, F., and\n                Campelo,\n            F. (2016).\n            Preference-guided evolutionary algorithms for many-objective\n            optimization. Information Sciences,\n            329:236\u2013255.","DOI":"10.1016\/j.ins.2015.09.015"},{"key":"2022050416562507600_B8","doi-asserted-by":"crossref","unstructured":"Hadka, D., and\n                Reed,\n            P. (2012).\n            Diagnostic assessment of search controls and failure modes in\n            many-objective evolutionary optimization. Evolutionary\n            Computation,\n            20(3):423\u2013452.","DOI":"10.1162\/EVCO_a_00053"},{"key":"2022050416562507600_B9","doi-asserted-by":"crossref","unstructured":"Han, Y.,\n                Gong, D.,\n                Jin, Y.,\n            and Pan,\n            Q. (2017).\n            Evolutionary multi-objective blocking lot-streaming flow shop scheduling\n            with machine breakdowns. IEEE Transactions on\n            Cybernetics. doi:10.1109\/TCYB.2017.2771213","DOI":"10.1109\/TCYB.2017.2771213"},{"key":"2022050416562507600_B10","doi-asserted-by":"crossref","unstructured":"Han, Y.,\n                Gong, D.,\n            and Sun,\n            X. (2015).\n            A discrete artificial bee colony algorithm incorporating differential\n            evolution for the flow-shop scheduling problem with blocking.\n            Engineering Optimization,\n            47(7):927\u2013946.","DOI":"10.1080\/0305215X.2014.928817"},{"key":"2022050416562507600_B11","doi-asserted-by":"crossref","unstructured":"He, Z., and\n                Yen, G.\n            G. (2016).\n            Visualization and performance metric in many-objective\n            optimization. IEEE Transactions on Evolutionary\n            Computation,\n            20(3):386\u2013402.","DOI":"10.1109\/TEVC.2015.2472283"},{"key":"2022050416562507600_B12","doi-asserted-by":"crossref","unstructured":"He, Z.,\n                Yen, G. G.,\n            and Zhang,\n            J. (2014).\n            Fuzzy-based Pareto optimality for many-objective evolutionary\n            algorithms. IEEE Transactions on Evolutionary\n            Computation,\n            18(2):269\u2013285.","DOI":"10.1109\/TEVC.2013.2258025"},{"key":"2022050416562507600_B13","doi-asserted-by":"crossref","unstructured":"Hern\u00e1ndez G\u00f3mez, R., and\n                Coello Coello, C.\n              A. (2015).\n            Improved metaheuristic based on the r2 indicator for many-objective\n            optimization. In Proceedings of the 2015 Conference on Genetic\n            and Evolutionary Computation, pp.\n          679\u2013686.","DOI":"10.1145\/2739480.2754776"},{"key":"2022050416562507600_B14","doi-asserted-by":"crossref","unstructured":"Huband, S.,\n                Hingston,\n              P., Barone,\n                L., and\n                While,\n            L. (2006).\n            A review of multiobjective test problems and a scalable test problem\n            toolkit. IEEE Transactions on Evolutionary Computation,\n            10(5):477\u2013506.","DOI":"10.1109\/TEVC.2005.861417"},{"key":"2022050416562507600_B15","doi-asserted-by":"crossref","unstructured":"Ishibuchi, H.,\n                Masuda, H.,\n                Tanigaki,\n              Y., and\n                Nojima,\n            Y. (2015).\n            Modified distance calculation in generational distance and inverted\n            generational distance. In International Conference on\n            Evolutionary Multi-Criterion Optimization, pp.\n            110\u2013125.","DOI":"10.1007\/978-3-319-15892-1_8"},{"key":"2022050416562507600_B16","doi-asserted-by":"crossref","unstructured":"Jaimes, A. L.,\n                Aguirre,\n            H., Tanaka,\n                K., and\n                Coello, C. A.\n              C. (2010).\n            Objective space partitioning using conflict information for\n            many-objective optimization. In Parallel Problem Solving from\n            Nature, pp. 657\u2013666.","DOI":"10.1007\/978-3-642-15844-5_66"},{"key":"2022050416562507600_B17","doi-asserted-by":"crossref","unstructured":"Laumanns, M.,\n                Thiele, L.,\n                Deb, K.,\n            and Zitzler,\n            E. (2002).\n            Combining convergence and diversity in evolutionary multiobjective\n            optimization. Evolutionary Computation,\n            10(3):263\u2013282.","DOI":"10.1162\/106365602760234108"},{"key":"2022050416562507600_B18","doi-asserted-by":"crossref","unstructured":"Li, J.,\n                Sang, H.,\n                Han, Y.,\n                Wang, C.,\n            and Gao,\n            K. (2018).\n            Efficient multi-objective optimization algorithm for hybrid flow shop\n            scheduling problems with setup energy consumptions. Journal of\n            Cleaner Production, 181:584\u2013598.","DOI":"10.1016\/j.jclepro.2018.02.004"},{"key":"2022050416562507600_B19","doi-asserted-by":"crossref","unstructured":"Li, K.,\n                Kwong, S.,\n                Cao, J.,\n                Li, M.,\n                Zheng, J.,\n            and Shen,\n            R. (2012).\n            Achieving balance between proximity and diversity in multi-objective\n            evolutionary algorithm. Information Sciences,\n            182(1):220\u2013242.","DOI":"10.1016\/j.ins.2011.08.027"},{"key":"2022050416562507600_B20","doi-asserted-by":"crossref","unstructured":"Li, M.,\n                Yang, S.,\n            and Liu,\n            X. (2014).\n            Shift-based density estimation for Pareto-based algorithms in\n            many-objective optimization. IEEE Transactions on Evolutionary\n            Computation,\n            18(3):348\u2013365.","DOI":"10.1109\/TEVC.2013.2262178"},{"key":"2022050416562507600_B21","doi-asserted-by":"crossref","unstructured":"Li, M.,\n                Yang, S.,\n            and Liu,\n            X. (2015).\n            Bi-goal evolution for many-objective optimization\n            problems. Artificial Intelligence,\n            228:45\u201365.","DOI":"10.1016\/j.artint.2015.06.007"},{"key":"2022050416562507600_B22","doi-asserted-by":"crossref","unstructured":"Liu, Y.,\n                Gong, D.,\n                Sun, J.,\n            and Jin,\n            Y. (2017).\n            A many-objective evolutionary algorithm using a one-by-one selection\n            strategy. IEEE Transactions on Cybernetics,\n            47(9):2689\u20132702.","DOI":"10.1109\/TCYB.2016.2638902"},{"key":"2022050416562507600_B23","doi-asserted-by":"crossref","unstructured":"Liu, Y.,\n                Gong, D.,\n                Sun, X.,\n            and Zhang,\n            Y. (2017).\n            Many-objective evolutionary optimization based on reference\n            points. Applied Soft Computing,\n            50:344\u2013355.","DOI":"10.1016\/j.asoc.2016.11.009"},{"key":"2022050416562507600_B24","doi-asserted-by":"crossref","unstructured":"Liu, Y.,\n                Ishibuchi,\n              H., Nojima,\n                Y.,\n                Masuyama,\n              N., and\n              Shang,\n            K. (2018a).\n            A double-niched evolutionary algorithm and its behavior on polygon-based\n            problems. In International Conference on Parallel Problem\n            Solving from Nature, pp.\n          262\u2013273.","DOI":"10.1007\/978-3-319-99253-2_21"},{"key":"2022050416562507600_B25","doi-asserted-by":"crossref","unstructured":"Liu, Y.,\n                Ishibuchi,\n              H., Nojima,\n                Y.,\n                Masuyama,\n              N., and\n              Shang,\n            K. (2018b).\n            Improving 1by1ea to handle various shapes of Pareto\n            fronts. In International Conference on Parallel Problem Solving\n            from Nature, pp. 311\u2013322.","DOI":"10.1007\/978-3-319-99253-2_25"},{"key":"2022050416562507600_B26","doi-asserted-by":"crossref","unstructured":"Liu, Y.,\n                Yen, G. G.,\n            and Gong,\n            D. (2018).\n            A multi-modal multi-objective evolutionary algorithm using two-archive\n            and recombination strategies. IEEE Transactions on Evolutionary\n            Computation. doi:10.1109\/TEVC.2018.2879406","DOI":"10.1109\/TEVC.2018.2879406"},{"key":"2022050416562507600_B27","doi-asserted-by":"crossref","unstructured":"Qi, Y.,\n                Ma, X.,\n                Liu, F.,\n                Jiao, L.,\n                Sun, J.,\n            and Wu,\n            J. (2014).\n            MOEA\/D with adaptive weight adjustment.\n            Evolutionary Computation,\n            22(2):231\u2013264.","DOI":"10.1162\/EVCO_a_00109"},{"key":"2022050416562507600_B28","doi-asserted-by":"crossref","unstructured":"Sato, H.,\n                Aguirre,\n            H., and Tanaka,\n                K. (2011).\n            Improved S-CDAS using crossover controlling the number of crossed genes\n            for many-objective optimization. In Proceedings of the 13th\n            Annual Conference on Genetic and Evolutionary Computation, pp.\n            753\u2013760.","DOI":"10.1145\/2001576.2001679"},{"key":"2022050416562507600_B29","doi-asserted-by":"crossref","unstructured":"Takahama, T.,\n                Sakai, S.,\n            and Iwane,\n            N. (2005).\n            Constrained optimization by the \u025b constrained hybrid algorithm of particle swarm\n            optimization and genetic algorithm. AI 2005: Advances in\n            Artificial Intelligence, pp.\n          389\u2013400.","DOI":"10.1007\/11589990_41"},{"key":"2022050416562507600_B30","doi-asserted-by":"crossref","unstructured":"Tian, Y.,\n                Cheng, R.,\n                Zhang, X.,\n            and Jin,\n            Y. (2017).\n            PlatEMO: A MATLAB platform for evolutionary multi-objective\n            optimization. IEEE Computational Intelligence Magazine,\n            12(4):73\u201387.","DOI":"10.1109\/MCI.2017.2742868"},{"key":"2022050416562507600_B31","doi-asserted-by":"crossref","unstructured":"Wang, R.,\n                Ishibuchi,\n              H., Zhang,\n                Y., Zheng,\n                X., and\n                Zhang,\n            T. (2016).\n            On the effect of localized PBI method in MOEA\/D for multi-objective\n            optimization. In 2016 IEEE Symposium Series on Computational\n            Intelligence, pp. 1\u20138.","DOI":"10.1109\/SSCI.2016.7850222"},{"key":"2022050416562507600_B32","doi-asserted-by":"crossref","unstructured":"Wang, R.,\n                Zhang, Q.,\n            and Zhang,\n            T. (Early access,\n            2016). Decomposition based algorithms using Pareto adaptive\n            scalarizing methods.","DOI":"10.1109\/TEVC.2016.2521175"},{"key":"2022050416562507600_B33","doi-asserted-by":"crossref","unstructured":"Wang, R.,\n                Zhou, Z.,\n                Ishibuchi,\n              H., Liao,\n                T., and\n                Zhang,\n            T. (2018).\n            Localized weighted sum method for many-objective\n            optimization. IEEE Transactions on Evolutionary\n            Computation,\n            22(1):3\u201318.","DOI":"10.1109\/TEVC.2016.2611642"},{"key":"2022050416562507600_B34","doi-asserted-by":"crossref","unstructured":"Wang, Y., and\n                Cai,\n            Z. (2012).\n            Combining multiobjective optimization with differential evolution to\n            solve constrained optimization problems. IEEE Transactions on\n            Evolutionary Computation,\n            16(1):117\u2013134.","DOI":"10.1109\/TEVC.2010.2093582"},{"key":"2022050416562507600_B35","doi-asserted-by":"crossref","unstructured":"Wang, Y.,\n                Li, H.,\n                Yen, G. G.,\n            and Song,\n            W. (2015).\n            Mommop: Multiobjective optimization for locating multiple optimal\n            solutions of multimodal optimization problems. IEEE Transactions\n            on Cybernetics,\n            45(4):830\u2013843.","DOI":"10.1109\/TCYB.2014.2337117"},{"key":"2022050416562507600_B36","doi-asserted-by":"crossref","unstructured":"Yang, S.,\n                Li, M.,\n                Liu, X.,\n            and Zheng,\n            J. (2013).\n            A grid-based evolutionary algorithm for many-objective\n            optimization. IEEE Transactions on Evolutionary\n            Computation,\n            17(5):721\u2013736.","DOI":"10.1109\/TEVC.2012.2227145"},{"key":"2022050416562507600_B37","doi-asserted-by":"crossref","unstructured":"Yuan, Y.,\n                Xu, H.,\n                Wang, B.,\n                Zhang, B.,\n            and Yao,\n            X. (2016).\n            Balancing convergence and diversity in decomposition-based many-objective\n            optimizers. IEEE Transactions on Evolutionary\n            Computation,\n            20(6):180\u2013198.","DOI":"10.1109\/TEVC.2015.2443001"},{"key":"2022050416562507600_B38","doi-asserted-by":"crossref","unstructured":"Zhang, Q., and\n                Li,\n            H. (2007).\n            MOEA\/D: A multiobjective evolutionary algorithm based on\n            decomposition. IEEE Transactions on Evolutionary\n            Computation,\n            11(6):712\u2013731.","DOI":"10.1109\/TEVC.2007.892759"},{"key":"2022050416562507600_B39","doi-asserted-by":"crossref","unstructured":"Zhang, X.,\n                Tian, Y.,\n            and Jin,\n            Y. (2015).\n            A knee point driven evolutionary algorithm for many-objective\n            optimization. IEEE Transactions on Evolutionary\n            Computation,\n            19(6):761\u2013776.","DOI":"10.1109\/TEVC.2014.2378512"},{"key":"2022050416562507600_B40","doi-asserted-by":"crossref","unstructured":"Zitzler, E., and\n                K\u00fcnzli,\n            S. (2004).\n            Indicator-based selection in multiobjective search. In\n            Parallel Problem Solving from Nature, pp.\n            832\u2013842.","DOI":"10.1007\/978-3-540-30217-9_84"},{"key":"2022050416562507600_B41","unstructured":"Zitzler, E.,\n                Laumanns,\n              M., and\n                Thiele,\n            L. (2001).\n            SPEA2: Improving the strength Pareto evolutionary algorithm.\n            Technical Report. Eidgen\u00f6ssische Technische Hochschule Z\u00fcrich (ETH), Institut\n            f\u00fcr Technische Informatik und Kommunikationsnetze (TIK)."}],"container-title":["Evolutionary Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/direct.mit.edu\/evco\/article-pdf\/28\/1\/1\/2020344\/evco_a_00243.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/direct.mit.edu\/evco\/article-pdf\/28\/1\/1\/2020344\/evco_a_00243.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,4]],"date-time":"2022-05-04T16:57:01Z","timestamp":1651683421000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/evco\/article\/28\/1\/1\/94980\/A-Meta-Objective-Approach-for-Many-Objective"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"references-count":41,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,3,1]]},"published-print":{"date-parts":[[2020,3,1]]}},"URL":"https:\/\/doi.org\/10.1162\/evco_a_00243","relation":{},"ISSN":["1530-9304"],"issn-type":[{"value":"1530-9304","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020]]},"published":{"date-parts":[[2020]]}}}