{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T15:47:07Z","timestamp":1770911227242,"version":"3.50.1"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T00:00:00Z","timestamp":1740441600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T00:00:00Z","timestamp":1740441600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"the Natural Science Foundation of Fujian Province","award":["2021J011205"],"award-info":[{"award-number":["2021J011205"]}]},{"name":"the Natural Science Foundation of Fujian Province","award":["2022J05285"],"award-info":[{"award-number":["2022J05285"]}]},{"name":"Xiamen University of Technology scientific research project","award":["YKJ22020R"],"award-info":[{"award-number":["YKJ22020R"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61773106"],"award-info":[{"award-number":["61773106"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cluster Comput"],"published-print":{"date-parts":[[2025,8]]},"DOI":"10.1007\/s10586-024-04944-z","type":"journal-article","created":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T14:04:37Z","timestamp":1740492277000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A constrained multi-objective evolutionary algorithm with tri-populations assisted by an additional objective function"],"prefix":"10.1007","volume":"28","author":[{"given":"Binrong","family":"Liao","sequence":"first","affiliation":[]},{"given":"Yongkuan","family":"Yang","sequence":"additional","affiliation":[]},{"given":"Jianlong","family":"Xu","sequence":"additional","affiliation":[]},{"given":"Xiangsong","family":"Kong","sequence":"additional","affiliation":[]},{"given":"Jun","family":"Su","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,2,25]]},"reference":[{"key":"4944_CR1","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2022.3155533","author":"J Liang","year":"2022","unstructured":"Liang, J., Ban, X., Yu, K., Qu, B., Qiao, K., Yue, C., Chen, K., Tan, K.: A survey on evolutionary constrained multi-objective optimization. IEEE Trans. Evolut. Comput. (2022). https:\/\/doi.org\/10.1109\/TEVC.2022.3155533","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"4944_CR2","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2018.2881190","author":"R Chai","year":"2018","unstructured":"Chai, R., Savvaris, A., Tsourdos, A., Xia, Y., Chai, S.: Solving multiobjective constrained trajectory optimization problem by an extended evolutionary algorithm. IEEE Trans. Cybern. (2018). https:\/\/doi.org\/10.1109\/TCYB.2018.2881190","journal-title":"IEEE Trans. Cybern."},{"key":"4944_CR3","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1007\/3-540-44719-9_20","volume-title":"Constrained Test Problems for Multi-objective Evolutionary Optimization","author":"K Deb","year":"2001","unstructured":"Deb, K., Pratap, A., Meyarivan, T.: Constrained Test Problems for Multi-objective Evolutionary Optimization, vol. 1993, pp. 284\u2013298. Springer, Berlin (2001). https:\/\/doi.org\/10.1007\/3-540-44719-9_20"},{"key":"4944_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/s11277-021-08627-5","author":"O Singh","year":"2021","unstructured":"Singh, O., Rishiwal, V., Chaudhry, R., Yadav, M.: Multi-objective optimization in wsn: opportunities and challenges. Wirel. Pers. Commun. (2021). https:\/\/doi.org\/10.1007\/s11277-021-08627-5","journal-title":"Wirel. Pers. Commun."},{"key":"4944_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2018.01.112","author":"J Wang","year":"2018","unstructured":"Wang, J., Yang, W., Du, P., Li, Y.: Research and application of a hybrid forecasting framework based on multi-objective optimization for electrical power system. Energy (2018). https:\/\/doi.org\/10.1016\/j.energy.2018.01.112","journal-title":"Energy"},{"key":"4944_CR6","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1007\/978-981-33-4295-8_11","volume-title":"Multi-objective Optimization Approaches for Design, Planning, and Management of Water Resource Systems","author":"A Ferdowsi","year":"2021","unstructured":"Ferdowsi, A., Singh, V., Ehteram, M., Mirjalili, S.: Multi-objective Optimization Approaches for Design, Planning, and Management of Water Resource Systems, pp. 275\u2013303. Springer, Singapore (2021). https:\/\/doi.org\/10.1007\/978-981-33-4295-8_11"},{"key":"4944_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-018-3808-3","author":"I Tariq","year":"2020","unstructured":"Tariq, I., Alsattar, H., Zaidan, A., Bahaa, B., Abu Bakar, M., Mohammed, R., Albahri, O.S., Alsalem, M.A., Albahri, A.S.: Mogsabat: a metaheuristic hybrid algorithm for solving multi-objective optimisation problems. Neural Comput. Appl. (2020). https:\/\/doi.org\/10.1007\/s00521-018-3808-3","journal-title":"Neural Comput. Appl."},{"key":"4944_CR8","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2019.2943973","author":"Z Ma","year":"2019","unstructured":"Ma, Z., Wang, Y., Song, W.: A new fitness function with two rankings for evolutionary constrained multiobjective optimization. IEEE Trans. Syst. Man Cybern.: Syst. (2019). https:\/\/doi.org\/10.1109\/TSMC.2019.2943973","journal-title":"IEEE Trans. Syst. Man Cybern.: Syst."},{"key":"4944_CR9","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/j.ins.2013.04.001","volume":"241","author":"C-H Lin","year":"2013","unstructured":"Lin, C.-H.: A rough penalty genetic algorithm for constrained optimization. Inf. Sci. 241, 119\u2013137 (2013). https:\/\/doi.org\/10.1016\/j.ins.2013.04.001","journal-title":"Inf. Sci."},{"issue":"2\u20134","key":"4944_CR10","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1016\/S0045-7825(99)00389-8","volume":"186","author":"K Deb","year":"2000","unstructured":"Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186(2\u20134), 311\u2013338 (2000)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"4944_CR11","doi-asserted-by":"publisher","unstructured":"Takahama, T., Sakai, S.: Constrained optimization by the $$\\epsilon$$ constrained differential evolution with gradient-based mutation and feasible elites, pp. 1\u20138. (2006). https:\/\/doi.org\/10.1109\/CEC.2006.1688283","DOI":"10.1109\/CEC.2006.1688283"},{"key":"4944_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-018-3087-z","author":"Y Lin","year":"2019","unstructured":"Lin, Y., Du, W., Du, W.: Multi-objective differential evolution with dynamic hybrid constraint handling mechanism. Soft Comput. (2019). https:\/\/doi.org\/10.1007\/s00500-018-3087-z","journal-title":"Soft Comput."},{"key":"4944_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2017.06.053","author":"C Peng","year":"2017","unstructured":"Peng, C., Liu, H.-L., Gu, F.: An evolutionary algorithm with directed weights for constrained multi-objective optimization. Appl. Soft Comput. (2017). https:\/\/doi.org\/10.1016\/j.asoc.2017.06.053","journal-title":"Appl. Soft Comput."},{"key":"4944_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2022.109904","volume":"132","author":"Y Yongkuan","year":"2022","unstructured":"Yongkuan, Y., Huang, P., Kong, X., Zhao, J.: A constrained multi-objective evolutionary algorithm assisted by an additional objective function. Appl. Soft Comput. 132, 109904 (2022). https:\/\/doi.org\/10.1016\/j.asoc.2022.109904","journal-title":"Appl. Soft Comput."},{"key":"4944_CR15","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2021.07.048","author":"R Jiao","year":"2021","unstructured":"Jiao, R., Zeng, S., Li, C., Ong, Y.-S.: Two-type weight adjustments in moea\/d for highly constrained many-objective optimization. Inf. Sci. (2021). https:\/\/doi.org\/10.1016\/j.ins.2021.07.048","journal-title":"Inf. Sci."},{"key":"4944_CR16","doi-asserted-by":"publisher","unstructured":"Isaacs, A., Ray, T., Smith, W.: Blessings of maintaining infeasible solutions for constrained multi-objective optimization problems, pp. 2780\u20132787. (2008). https:\/\/doi.org\/10.1109\/CEC.2008.4631171","DOI":"10.1109\/CEC.2008.4631171"},{"key":"4944_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-019-03794-x","author":"Z Fan","year":"2019","unstructured":"Fan, Z., Li, W., Cai, X., Huang, H., Fang, Y., Yugen, Y., Mo, J., Wei, C., Goodman, E.: An improved epsilon constraint-handling method in moea\/d for cmops with large infeasible regions. Soft Comput. (2019). https:\/\/doi.org\/10.1007\/s00500-019-03794-x","journal-title":"Soft Comput."},{"key":"4944_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2018.08.017","author":"Z Fan","year":"2017","unstructured":"Fan, Z., Li, W., Cai, X., Li, H., Wei, C., Zhang, Q., Deb, K., Goodman, E.: Push and pull search for solving constrained multi-objective optimization problems. Swarm Evolut. Comput. (2017). https:\/\/doi.org\/10.1016\/j.swevo.2018.08.017","journal-title":"Swarm Evolut. Comput."},{"key":"4944_CR19","unstructured":"Hoffmeister, F., Gmbh, E., Sprave, J.: Problem-independent handling of constraints by use of metric penalty functions (1996)"},{"key":"4944_CR20","unstructured":"Joines, J., Houck, C.: On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with ga\u2019s. In: IEEE Conference on Evolutionary Computation\u2014Proceedings (1996)"},{"issue":"2","key":"4944_CR21","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1109\/4235.996017","volume":"6","author":"K Deb","year":"2002","unstructured":"Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Trans. Evolut. Comput. 6(2), 182\u2013197 (2002)","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"4944_CR22","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2019.2894743","author":"Z Liu","year":"2019","unstructured":"Liu, Z., Wang, Y.: Handling constrained multiobjective optimization problems with constraints in both the decision and objective spaces. IEEE Trans. Evolut. Comput. (2019). https:\/\/doi.org\/10.1109\/TEVC.2019.2894743","journal-title":"IEEE Trans. Evolut. Comput."},{"issue":"2","key":"4944_CR23","doi-asserted-by":"publisher","first-page":"1011","DOI":"10.1007\/s10878-022-00870-1","volume":"44","author":"N Ouertani","year":"2022","unstructured":"Ouertani, N., Ben-Romdhane, H., Krichen, S., Nouaouri, I.: A vector evaluated evolutionary algorithm with exploitation reinforcement for the dynamic pollution routing problem. J. Comb. Optim. 44(2), 1011\u20131038 (2022)","journal-title":"J. Comb. Optim."},{"key":"4944_CR24","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1109\/TEVC.2013.2281534","volume":"18","author":"H Jain","year":"2014","unstructured":"Jain, H., Deb, K.: An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part ii: Handling constraints and extending to an adaptive approach. Evolut. Comput. IEEE Trans. 18, 602\u2013622 (2014). https:\/\/doi.org\/10.1109\/TEVC.2013.2281534","journal-title":"Evolut. Comput. IEEE Trans."},{"key":"4944_CR25","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2016.2519378","author":"R Cheng","year":"2016","unstructured":"Cheng, R., Jin, Y., Olhofer, M., Sendhoff, B.: A reference vector guided evolutionary algorithm for many-objective optimization. IEEE Trans. Evolut. Comput. (2016). https:\/\/doi.org\/10.1109\/TEVC.2016.2519378","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"4944_CR26","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2018.06.063","author":"Z Liu","year":"2017","unstructured":"Liu, Z., Wang, Y., Huang, P.: A many-objective evolutionary algorithm with angle-based selection and shift-based density estimation. Inf. Sci. (2017). https:\/\/doi.org\/10.1016\/j.ins.2018.06.063","journal-title":"Inf. Sci."},{"key":"4944_CR27","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2018.2848254","author":"C Liu","year":"2018","unstructured":"Liu, C., Zhao, Q., Yan, B., Elsayed, S., Ray, T., Sarker, R.: Adaptive sorting-based evolutionary algorithm for many-objective optimization. IEEE Trans. Evolut. Comput. (2018). https:\/\/doi.org\/10.1109\/TEVC.2018.2848254","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"4944_CR28","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2018.2855411","author":"K Li","year":"2018","unstructured":"Li, K., Chen, R., Fu, G., Yao, X.: Two-archive evolutionary algorithm for constrained multi-objective optimization. IEEE Trans. Evolut. Comput. (2018). https:\/\/doi.org\/10.1109\/TEVC.2018.2855411","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"4944_CR29","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2021.3056176","author":"Z Liu","year":"2021","unstructured":"Liu, Z., Wang, B.-C., Tang, K.: Handling constrained multiobjective optimization problems via bidirectional coevolution. IEEE Trans. Cybern. (2021). https:\/\/doi.org\/10.1109\/TCYB.2021.3056176","journal-title":"IEEE Trans. Cybern."},{"issue":"1","key":"4944_CR30","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1109\/TEVC.2020.3004012","volume":"25","author":"Y Tian","year":"2021","unstructured":"Tian, Y., Zhang, T., Xiao, J., Zhang, X., Jin, Y.: A coevolutionary framework for constrained multiobjective optimization problems. IEEE Trans. Evolut. Comput. 25(1), 102\u2013116 (2021). https:\/\/doi.org\/10.1109\/TEVC.2020.3004012","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"4944_CR31","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2023.3300181","author":"Z Song","year":"2023","unstructured":"Song, Z., Wang, H., Xue, B., Zhang, M., Jin, Y.: Balancing objective optimization and constraint satisfaction in expensive constrained evolutionary multi-objective optimization. IEEE Trans. Evolut. Comput. (2023). https:\/\/doi.org\/10.1109\/TEVC.2023.3300181","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"4944_CR32","doi-asserted-by":"crossref","unstructured":"Ray, T., Singh, H.K., Isaacs, A., Smith, W.: Infeasibility driven evolutionary algorithm for constrained optimization. In: Constraint-Handling in Evolutionary Optimization, pp. 145\u2013165. (2009)","DOI":"10.1007\/978-3-642-00619-7_7"},{"key":"4944_CR33","unstructured":"Zitzler, E., Laumanns, M., Thiele, L.: Spea2: improving the strength pareto evolutionary algorithm. TIK-Report 103 (2001)"},{"key":"4944_CR34","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2019.2896967","author":"Z Ma","year":"2019","unstructured":"Ma, Z., Wang, Y.: Evolutionary constrained multiobjective optimization: test suite construction and performance comparisons. IEEE Trans. Evolut. Comput. (2019). https:\/\/doi.org\/10.1109\/TEVC.2019.2896967","journal-title":"IEEE Trans. Evolut. Comput."},{"key":"4944_CR35","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1162\/evco_a_00259","volume":"28","author":"Z Fan","year":"2019","unstructured":"Fan, Z., Li, W., Cai, X., Li, H., Wei, C., Zhang, Q., Deb, K., Goodman, E.: Difficulty adjustable and scalable constrained multi-objective test problem toolkit. Evolut. Comput. 28, 1\u201328 (2019). https:\/\/doi.org\/10.1162\/evco_a_00259","journal-title":"Evolut. Comput."},{"key":"4944_CR36","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2021.100961","volume":"67","author":"A Kumar","year":"2021","unstructured":"Kumar, A., Wu, G., Ali, M., Luo, Q., Mallipeddi, R., Suganthan, P., Das, S.: A benchmark-suite of real-world constrained multi-objective optimization problems and some baseline results. Swarm Evolut. Comput. 67, 100961 (2021). https:\/\/doi.org\/10.1016\/j.swevo.2021.100961","journal-title":"Swarm Evolut. Comput."},{"key":"4944_CR37","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1109\/MCI.2017.2742868","volume":"12","author":"Y Tian","year":"2017","unstructured":"Tian, Y., Cheng, R., Zhang, X., Jin, Y.: Platemo: a matlab platform for evolutionary multi-objective optimization. IEEE Comput. Intell. Mag. 12, 73\u201387 (2017). https:\/\/doi.org\/10.1109\/MCI.2017.2742868","journal-title":"IEEE Comput. Intell. Mag."},{"key":"4944_CR38","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-24694-7_71","volume-title":"A Study of the Parallelization of a Coevolutionary Multi-objective Evolutionary Algorithm","author":"C Coello","year":"2004","unstructured":"Coello, C., Reyes Sierra, M.: A Study of the Parallelization of a Coevolutionary Multi-objective Evolutionary Algorithm, vol. 2972. Springer, Berlin (2004). https:\/\/doi.org\/10.1007\/978-3-540-24694-7_71"},{"key":"4944_CR39","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1109\/4235.797969","volume":"3","author":"E Zitzler","year":"1999","unstructured":"Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans. Evolut. Comput. 3, 257\u2013271 (1999)","journal-title":"IEEE Trans. Evolut. Comput."},{"issue":"6","key":"4944_CR40","doi-asserted-by":"publisher","first-page":"80","DOI":"10.2307\/3001968","volume":"1","author":"F Wilcoxon","year":"1944","unstructured":"Wilcoxon, F.: Individual comparisons by ranking methods. Biometrics 1(6), 80\u201383 (1944)","journal-title":"Biometrics"},{"key":"4944_CR41","doi-asserted-by":"publisher","DOI":"10.1007\/s12065-024-00932-9","author":"Y Yang","year":"2024","unstructured":"Yang, Y., Yang, Y., Liao, B.: Dual population multi-objective evolutionary algorithm for dynamic co-transformations. Evolut. Intell. (2024). https:\/\/doi.org\/10.1007\/s12065-024-00932-9","journal-title":"Evolut. Intell."}],"container-title":["Cluster Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10586-024-04944-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10586-024-04944-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10586-024-04944-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T06:34:16Z","timestamp":1757140456000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10586-024-04944-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,25]]},"references-count":41,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,8]]}},"alternative-id":["4944"],"URL":"https:\/\/doi.org\/10.1007\/s10586-024-04944-z","relation":{},"ISSN":["1386-7857","1573-7543"],"issn-type":[{"value":"1386-7857","type":"print"},{"value":"1573-7543","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,25]]},"assertion":[{"value":"29 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 October 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 November 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 February 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"All authors read and approved the final version of the manuscript.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"All authors contributed to this work.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to participate"}},{"value":"All authors have checked the manuscript and have agreed to the submission.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}}],"article-number":"261"}}