{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:47:07Z","timestamp":1760237227941,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,3,16]],"date-time":"2020-03-16T00:00:00Z","timestamp":1584316800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61703426"],"award-info":[{"award-number":["61703426"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the real world, multi-objective optimization problems always change over time in most projects. Once the environment changes, the distribution of the optimal solutions would also be changed in decision space. Sometimes, such change may obey the law of symmetry, i.e., the minimum of the objective function in such environment is its maximum in another environment. In such cases, the optimal solutions keep unchanged or vibrate in a small range. However, in most cases, they do not obey the law of symmetry. In order to continue the search that maintains previous search advantages in the changed environment, some prediction strategy would be used to predict the operation position of the Pareto set. Because of this, the segment and multi-directional prediction is proposed in this paper, which consists of three mechanisms. First, by segmenting the optimal solutions set, the prediction about the changes in the distribution of the Pareto front can be ensured. Second, by introducing the cloud theory, the distance error of direction prediction can be offset effectively. Third, by using extra angle search, the angle error of prediction caused by the Pareto set nonlinear variation can also be offset effectively. Finally, eight benchmark problems were used to verify the performance of the proposed algorithm and compared algorithms. The results indicate that the algorithm proposed in this paper has good convergence and distribution, as well as a quick response ability to the changed environment.<\/jats:p>","DOI":"10.3390\/sym12030465","type":"journal-article","created":{"date-parts":[[2020,3,20]],"date-time":"2020-03-20T07:29:07Z","timestamp":1584689347000},"page":"465","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A New Method for Dynamic Multi-Objective Optimization Based on Segment and Cloud Prediction"],"prefix":"10.3390","volume":"12","author":[{"given":"Peng","family":"Ni","sequence":"first","affiliation":[{"name":"Air and Missile Defense College, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiale","family":"Gao","sequence":"additional","affiliation":[{"name":"No. 95806 of PLA, Beijing 100021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0962-0671","authenticated-orcid":false,"given":"Yafei","family":"Song","sequence":"additional","affiliation":[{"name":"Air and Missile Defense College, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wen","family":"Quan","sequence":"additional","affiliation":[{"name":"Air Traffic Control and Navigation College, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qinghua","family":"Xing","sequence":"additional","affiliation":[{"name":"Air and Missile Defense College, Air Force Engineering University, Xi\u2019an 710051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.asoc.2018.02.042","article-title":"A multi-swarm particle swarm optimization algorithm based on dynamical topology and purposeful detecting","volume":"67","author":"Xia","year":"2018","journal-title":"Appl. Soft Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"105703","DOI":"10.1016\/j.asoc.2019.105703","article-title":"Divergence-based cross entropy and uncertainty measures of Atanassov\u2019s intuitionistic fuzzy sets with their application in decision making","volume":"84","author":"Song","year":"2019","journal-title":"Appl. Soft Comput. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"174210","DOI":"10.1109\/ACCESS.2019.2956017","article-title":"Combing evidence sources in time domain with decision maker\u2019s preference on time sequence","volume":"7","author":"Zhang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1985","DOI":"10.1007\/s00500-017-2912-0","article-title":"A new approach to construct similarity measure for intuitionistic fuzzy sets","volume":"23","author":"Song","year":"2019","journal-title":"Soft Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3950","DOI":"10.1007\/s10489-018-1188-0","article-title":"Sensor dynamic reliability evaluation based on evidence and intuitionistic fuzzy sets","volume":"48","author":"Song","year":"2018","journal-title":"Appl. Intell."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1007\/s10489-014-0596-z","article-title":"A novel similarity measure on intuitionistic fuzzy sets with its applications","volume":"42","author":"Song","year":"2015","journal-title":"Appl. Intell."},{"key":"ref_7","unstructured":"Lei, L., Song, Y., and Luo, X. A New Re-encoding ECOC Using a Reject Option. Appl. Intell."},{"key":"ref_8","first-page":"419","article-title":"Discovering unique, low-energy pure water isomers: memetic exploration, optimization and landscape analysis","volume":"14","author":"Soh","year":"2010","journal-title":"IEEE Trans. Comput."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1007\/s11241-017-9291-6","article-title":"Energy-efficient real-time scheduling for two-type heterogeneous multiprocessors","volume":"54","author":"Thammawichai","year":"2018","journal-title":"Real Time Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"7141","DOI":"10.1109\/TIE.2014.2314075","article-title":"Bi-velocity discrete particle swarm optimization and its application to multicast routing problem in communication networks","volume":"61","author":"Shen","year":"2014","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_11","unstructured":"Deb, K., and Karthik, S. (2007). Dynamic multiobjective optimization and decision-making using modified NSGA-II: A case study on hydro-thermal power scheduling. Proceedings of the 4th International Conference on Evolutionary Multi-Criterion Optimization, Matsushima, Japan, 5\u20138 March 2007, Springer."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Azevedo, C.R.B., and Araujo, A.F.R. (2011, January 5\u20138). Generalized immigration schemes for dynamic evolutionary multiobjective optimization. Proceedings of the IEEE Congress on Evolutionary Computation, New Orleans, LA, USA.","DOI":"10.1109\/CEC.2011.5949865"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2700","DOI":"10.1360\/jos182700","article-title":"An immune clonal algorithm for dynamic multi-objective optimization","volume":"18","author":"Shang","year":"2007","journal-title":"J. Softw."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1002\/ecj.10097","article-title":"A new genetic algorithm with diploid chromosomes by using probability decoding for adaptation to various environments","volume":"93","author":"Kominami","year":"2010","journal-title":"Electron. Commun. Jpn."},{"key":"ref_15","unstructured":"Yang, S. (2006, January 16\u201321). On the Design of Diploid Genetic Algorithms for Problem Optimization in Dynamic Environments. Proceedings of the 2006 Congress on Evolutionary Computation, Vancouver, BD, Canada."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1571","DOI":"10.3724\/SP.J.1001.2013.04311","article-title":"Memory enhanced dynamic multi-objective evolutionary algorithm based on decomposition","volume":"24","author":"Liu","year":"2013","journal-title":"J. Softw."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Hatzakis, I., and Wallace, D. (2006, January 8\u201312). Dynamic multi-objective optimization with evolutionary algorithms: A forward-looking approach. Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, Washington, DC, USA.","DOI":"10.1145\/1143997.1144187"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1109\/TCYB.2013.2245892","article-title":"A population prediction strategy for evolutionary dynamic multiobjective optimization","volume":"44","author":"Zhou","year":"2014","journal-title":"IEEE Trans. Cybern."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3221","DOI":"10.1007\/s00500-014-1477-4","article-title":"A directed search strategy for evolutionary dynamic multiobjetive optimization","volume":"19","author":"Wu","year":"2015","journal-title":"Soft Comput."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Rong, M., Gong, D., Zhang, Y., Jin, Y., and Pedrycz, W. (2016). Multidirectional prediction approach for dynamic multiobjective optimization problems. Intelligent Computing Methodologies, ICIC 2016 Lecture Notes in Computer Science, Springer.","DOI":"10.1007\/978-3-319-42297-8_58"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Li, Q., Zou, J., Yang, S., Zheng, J., and Ruan, G. (2018). A predictive strategy based on special points for evolutionary dynamic multi-objective optimization. Soft Comput., 1\u201317.","DOI":"10.1007\/s00500-018-3033-0"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1016\/j.asoc.2017.05.008","article-title":"The effect of diversity maintenance on prediction in dynamic multi-objective optimization","volume":"56","author":"Ruan","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_23","first-page":"461","article-title":"A benchmark test suite for dynamic evolutionary multiobjective optimization","volume":"47","author":"Gee","year":"2017","journal-title":"IEEE Trans. Cybern."},{"key":"ref_24","first-page":"182","article-title":"A fast and elitist multiobjective genetic algorithm: NSGA-II","volume":"6","author":"Deb","year":"2002","journal-title":"IEEE Trans. Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1109\/TCYB.2015.2510698","article-title":"Evolutionary dynamic multiobjective optimization: bencmarks and algorithm comparisons","volume":"47","author":"Jiang","year":"2017","journal-title":"IEEE Trans. Cybern."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1109\/TEVC.2007.892759","article-title":"MOEA\/D: A multiobjective evolutionary algorithm based on decomposition","volume":"11","author":"Zhang","year":"2007","journal-title":"IEEE Trans. Evol. Comput."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/3\/465\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:07:12Z","timestamp":1760173632000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/3\/465"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,16]]},"references-count":26,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["sym12030465"],"URL":"https:\/\/doi.org\/10.3390\/sym12030465","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,3,16]]}}}