{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T06:41:42Z","timestamp":1772001702248,"version":"3.50.1"},"reference-count":47,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2019,11,14]],"date-time":"2019-11-14T00:00:00Z","timestamp":1573689600000},"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>Inspired by the mechanism of generation and restriction among five elements in Chinese traditional culture, we present a novel Multi-Objective Five-Elements Cycle Optimization algorithm (MOFECO). During the optimization process of MOFECO, we use individuals to represent the elements. At each iteration, we first divide the population into several cycles, each of which contains several individuals. Secondly, for every individual in each cycle, we judge whether to update it according to the force exerted on it by other individuals in the cycle. In the case of an update, a local or global update is selected by a dynamically adjustable probability P s ; otherwise, the individual is retained. Next, we perform combined mutation operations on the updated individuals, so that a new population contains both the reserved and updated individuals for the selection operation. Finally, the fast non-dominated sorting method is adopted on the current population to obtain an optimal Pareto solution set. The parameters\u2019 comparison of MOFECO is given by an experiment and also the performance of MOFECO is compared with three classic evolutionary algorithms Non-dominated Sorting Genetic Algorithm II (NSGA-II), Multi-Objective Particle Swarm Optimization algorithm (MOPSO), Pareto Envelope-based Selection Algorithm II (PESA-II) and two latest algorithms Knee point-driven Evolutionary Algorithm (KnEA) and Non-dominated Sorting and Local Search (NSLS) on solving test function sets Zitzler et al\u2019s Test suite (ZDT), Deb et al\u2019s Test suite (DTLZ), Walking Fish Group (WFG) and Many objective Function (MaF). The experimental results indicate that the proposed MOFECO can approach the true Pareto-optimal front with both better diversity and convergence compared to the five other algorithms.<\/jats:p>","DOI":"10.3390\/a12110244","type":"journal-article","created":{"date-parts":[[2019,11,14]],"date-time":"2019-11-14T10:56:34Z","timestamp":1573728994000},"page":"244","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Novel Multi-Objective Five-Elements Cycle Optimization Algorithm"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2258-4620","authenticated-orcid":false,"given":"Chunling","family":"Ye","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3280-7322","authenticated-orcid":false,"given":"Zhengyan","family":"Mao","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5928-4656","authenticated-orcid":false,"given":"Mandan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1109\/TEVC.2008.920677","article-title":"Effective Evolutionary Algorithms for Many-Specifications Attainment: Application to Air Traffic Control Tracking Filters","volume":"13","author":"Garcia","year":"2009","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1109\/TEVC.2014.2378512","article-title":"A Knee Point-Driven Evolutionary Algorithm for Many-Objective Optimization","volume":"19","author":"Zhang","year":"2015","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_3","unstructured":"Deb, K., and Kalyanmoy, D. (2001). Multi-Objective Optimization Using Evolutionary Algorithms, John Wiley & Sons, Inc."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1162\/evco.1994.2.3.221","article-title":"Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms","volume":"2","author":"Srinivas","year":"1994","journal-title":"Evol. Comput."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Deb, K., Agrawal, S., Pratap, A., and Meyarivan, T. (2000). A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimization: NSGA-II. Parallel Problem Solving from Nature PPSN VI, Springer.","DOI":"10.1007\/3-540-45356-3_83"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Junhua, Y., Cuimei, B.O., Jun, L.I., and Yan, H. (2018, January 8\u201311). Multi-objective Optimization of Methyl Acetate Hydrolysis Process Based on NSGA-II Algorithm. Proceedings of the 30th Chinese Control Conference, Shenyang, China.","DOI":"10.1109\/CCDC.2018.8407249"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1109\/4235.797969","article-title":"Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach","volume":"3","author":"Zitzler","year":"2000","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_8","unstructured":"Zitzler, E., Laumanns, M., and Thiele, L. (2001). SPEA2: Improving the Strength Pareto Evolutionary Algorithm. Technical Report Tik-Report 103, Computer Engineering and Communication Networks Lab (TIK), Swiss Federal Institute of Technology (ETH)."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Wu, X., Cao, W., Wang, D., and Ding, M. (2018, January 8\u201311). Multi objective optimization based on SPEA for the microgrid energy dispatch. Proceedings of the 30th Chinese Control Conference, Shenyang, China.","DOI":"10.23919\/ChiCC.2018.8483695"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Corne, D., Knowles, J.D., and Oates, M.J. (2000, January 18\u201320). The Pareto Envelope-Based Selection Algorithm for Multi-objective Optimisation. Proceedings of the 6th International Conference on Parallel Problem Solving from Nature PPSN VI, Paris, Prance.","DOI":"10.1007\/3-540-45356-3_82"},{"key":"ref_11","unstructured":"Corne, D.W., Jerram, N.R., Knowles, J.D., and Oates, M.J. (2001, January 7\u201311). PESA-II: Region-based Selection in Evolutionary Multiobjective Optimization. Proceedings of the 3rd Annual Conference on Genetic and Evolutionary Computation, San Francisco, CA, USA."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Coello Coello, C.A., and Lechuga, M.S. (2002, January 12\u201317). MOPSO: A proposal for multiple objective particle swarm optimization. Proceedings of the 2002 Congress on Evolutionary Computation, Honolulu, HI, USA. CEC\u201902 (Cat. No.02TH8600).","DOI":"10.1109\/CEC.2002.1004388"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Patil, M.B., Naidu, M.N., Vasan, A., and Varma, M.R.R. (2019). Water Distribution System Design Using Multi-Objective Particle Swarm Optimisation. arXiv.","DOI":"10.1007\/s12046-019-1258-y"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.comnet.2019.04.009","article-title":"Location Management in LTE Networks using Multi-Objective Particle Swarm Optimization","volume":"157","author":"Hashim","year":"2019","journal-title":"Comput. Netw."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1109\/TEVC.2014.2301794","article-title":"A New Local Search-Based Multiobjective Optimization Algorithm","volume":"19","author":"Chen","year":"2015","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1979","DOI":"10.1109\/TII.2017.2677939","article-title":"Multi-Objective Evolutionary Algorithm Based On Non-Dominated Sorting and Bidirectional Local Search for Big Data","volume":"13","author":"Fan","year":"2017","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1109\/TEVC.2015.2504730","article-title":"Pareto or Non-Pareto: Bi-Criterion Evolution in Multi-Objective Optimization","volume":"20","author":"Li","year":"2016","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Tian, Y., Zhang, X., Cheng, R., and Jin, Y. (2016, January 24\u201329). A multi-objective evolutionary algorithm based on an enhanced inverted generational distance metric. Proceedings of the 2016 IEEE Congress on Evolutionary Computation (CEC), Vancouver, BC, Canada.","DOI":"10.1109\/CEC.2016.7748352"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Liu, M. (2017, January 10\u201312). Five-elements cycle optimization algorithm for the travelling salesman problem. Proceedings of the 2017 18th International Conference on Advanced Robotics (ICAR), Hong Kong, China.","DOI":"10.1109\/ICAR.2017.8023672"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Liu, M. (2017, January 22\u201324). Five-elements cycle optimization algorithm for solving continuous optimization problems. Proceedings of the 2017 IEEE 4th International Conference on Soft Computing Machine Intelligence (ISCMI), Balaclava, Mauritius.","DOI":"10.1109\/ISCMI.2017.8279601"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1109\/TEVC.2014.2339823","article-title":"A Decomposition Based Evolutionary Algorithm for Many Objective Optimization","volume":"19","author":"Asafuddoula","year":"2015","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_22","unstructured":"Schaffer, J.D. (1984). Some Experiments in Machine Learning Using Vector Evaluated Genetic Algorithms (Artificial Intelligence, Optimization, Adaptation, Pattern Recognition). [Ph.D. Thesis, Vanderbilt University]."},{"key":"ref_23","first-page":"49","article-title":"Improved diversity maintenance strategy in NSGA-II","volume":"46","author":"Wen","year":"2010","journal-title":"Comput. Eng. Appl."},{"key":"ref_24","unstructured":"Lei, R., and Cheng, Y. (2010, January 26\u201328). A pareto-based differential evolution algorithm for multi-objective optimization problems. Proceedings of the 2010 Chinese Control and Decision Conference, Xuzhou, China."},{"key":"ref_25","unstructured":"Wen, S. (2009). The Research on Mutation Operators for Multi-Objective Evolutionary Algorithms. [Ph.D. Thesis, Xiangtan University]."},{"key":"ref_26","unstructured":"Schaffer, J.D. (1985, January 24\u201326). Multiple Objective Optimization with Vector Evaluated Genetic Algorithms. Proceedings of the 1st International Conference on Genetic Algorithms, Pittsburgh, PA, USA."},{"key":"ref_27","unstructured":"Knowles, J., and Corne, D. (1999, January 6\u20139). The Pareto Archived Evolution Strategy: A New Baseline Algorithm for Pareto Multiobjective Optimisation. Proceedings of the Congress on Evolutionary Computation, Washington, DC, USA."},{"key":"ref_28","unstructured":"Kim, Y., Street, W.N., and Menczer, F. (2001, January 27\u201330). An evolutionary multi-objective local selection algorithm for customer targeting. Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546), Seoul, Korea."},{"key":"ref_29","unstructured":"Horn, J., Nafpliotis, N., and Goldberg, D.E. (July, January 29). A niched Pareto genetic algorithm for multiobjective optimization. Proceedings of the First IEEE Conference on Evolutionary Computation, Orlando, FL, USA."},{"key":"ref_30","unstructured":"Fonseca, C.M., and Fleming, P.J. (1993, January 17\u201321). Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization. Proceedings of the 5th International Conference on Genetic Algorithms, Urbana-Champaign, IL, USA."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Wagner, M., and Neumann, F. (2013, January 6\u201310). A Fast Approximation-guided Evolutionary Multi-objective Algorithm. Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, Amsterdam, The Netherlands.","DOI":"10.1145\/2463372.2463448"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Zitzler, E., and K\u00fcnzli, S. (2004). Indicator-Based Selection in Multiobjective Search. Parallel Problem Solving from Nature\u2014PPSN VIII, Springer.","DOI":"10.1007\/978-3-540-30217-9_84"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1109\/TEVC.2013.2281535","article-title":"An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints","volume":"18","author":"Deb","year":"2014","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1109\/TEVC.2014.2373386","article-title":"An Evolutionary Many-Objective Optimization Algorithm Based on Dominance and Decomposition","volume":"19","author":"Li","year":"2015","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_35","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle swarm optimization. Proceedings of the ICNN\u201995\u2014International Conference on Neural Networks, Perth, Australia."},{"key":"ref_36","first-page":"627","article-title":"Research of mutation operator in evolutionary programming and evolutionary strategies","volume":"33","author":"Lin","year":"2000","journal-title":"J. Tianjin Univ. Sci. Technol. Ed."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1162\/106365600568202","article-title":"Comparison of Multiobjective Evolutionary Algorithms: Empirical Results","volume":"8","author":"Zitzler","year":"2000","journal-title":"Evol. Comput."},{"key":"ref_38","unstructured":"Deb, K., Thiele, L., Laumanns, M., and Zitzler, E. (2005). Scalable Test Problems for Evolutionary Multiobjective Optimization. Evolutionary Multiobjective Optimization: Theoretical Advances and Applications, Springer."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1109\/TEVC.2005.861417","article-title":"A review of multiobjective test problems and a scalable test problem toolkit","volume":"10","author":"Huband","year":"2006","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s40747-017-0039-7","article-title":"A benchmark test suite for evolutionary many-objective optimization","volume":"3","author":"Cheng","year":"2017","journal-title":"Complex Intell. Syst."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1109\/MCI.2017.2742868","article-title":"PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization","volume":"12","author":"Ye","year":"2017","journal-title":"IEEE Comput. Intell. Mag."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s00500-008-0394-9","article-title":"Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure","volume":"14","author":"Wang","year":"2010","journal-title":"Soft Comput."},{"key":"ref_43","unstructured":"Vanveldhuizen, D.A., and Lamont, G.B. (1998, January 13\u201316). Evolutionary computation and convergence to a Pareto front. Proceedings of the Late Breaking Papers at the Genetic Programming 1998 Conference, Stanford University, CA, USA."},{"key":"ref_44","unstructured":"Schott, J.R. (1995). Fault Tolerant Design Using Single and Multi-Criteria Genetic Algorithm Optimization. [Ph.D. Thesis, Massachusetts Institute of Technology]."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1006\/jeem.1993.1004","article-title":"On the Measurement of Biological Diversity","volume":"24","author":"Solow","year":"1993","journal-title":"J. Environ. Econ. Manag."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1109\/TEVC.2005.851275","article-title":"A faster algorithm for calculating hypervolume","volume":"10","author":"While","year":"2006","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1109\/TEVC.2003.810758","article-title":"Performance Assessment of Multiobjective Optimizers: An Analysis and Review","volume":"7","author":"Zitzler","year":"2003","journal-title":"IEEE Trans. Evol. Comput."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/11\/244\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:34:29Z","timestamp":1760189669000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/11\/244"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,14]]},"references-count":47,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2019,11]]}},"alternative-id":["a12110244"],"URL":"https:\/\/doi.org\/10.3390\/a12110244","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,14]]}}}