{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T13:50:39Z","timestamp":1765547439248,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T00:00:00Z","timestamp":1750291200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100011447","name":"key scientific and technological projects of Henan Province","doi-asserted-by":"publisher","award":["252102211072","232102210078","62102372","62072414","2024AH053415","2021BSJJ029","GXXT-2023-050","2023AH010056","2024tlxyrc019"],"award-info":[{"award-number":["252102211072","232102210078","62102372","62072414","2024AH053415","2021BSJJ029","GXXT-2023-050","2023AH010056","2024tlxyrc019"]}],"id":[{"id":"10.13039\/501100011447","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of China","award":["252102211072","232102210078","62102372","62072414","2024AH053415","2021BSJJ029","GXXT-2023-050","2023AH010056","2024tlxyrc019"],"award-info":[{"award-number":["252102211072","232102210078","62102372","62072414","2024AH053415","2021BSJJ029","GXXT-2023-050","2023AH010056","2024tlxyrc019"]}]},{"name":"Anhui Provincial Key Research and Development Project","award":["252102211072","232102210078","62102372","62072414","2024AH053415","2021BSJJ029","GXXT-2023-050","2023AH010056","2024tlxyrc019"],"award-info":[{"award-number":["252102211072","232102210078","62102372","62072414","2024AH053415","2021BSJJ029","GXXT-2023-050","2023AH010056","2024tlxyrc019"]}]},{"name":"Doctor Scientific Research Fund of Zhengzhou University of Light Industry","award":["252102211072","232102210078","62102372","62072414","2024AH053415","2021BSJJ029","GXXT-2023-050","2023AH010056","2024tlxyrc019"],"award-info":[{"award-number":["252102211072","232102210078","62102372","62072414","2024AH053415","2021BSJJ029","GXXT-2023-050","2023AH010056","2024tlxyrc019"]}]},{"name":"Anhui Province University Collaborative Innovation Project","award":["252102211072","232102210078","62102372","62072414","2024AH053415","2021BSJJ029","GXXT-2023-050","2023AH010056","2024tlxyrc019"],"award-info":[{"award-number":["252102211072","232102210078","62102372","62072414","2024AH053415","2021BSJJ029","GXXT-2023-050","2023AH010056","2024tlxyrc019"]}]},{"name":"Excellent Innovative Research Team of universities in Anhui Province","award":["252102211072","232102210078","62102372","62072414","2024AH053415","2021BSJJ029","GXXT-2023-050","2023AH010056","2024tlxyrc019"],"award-info":[{"award-number":["252102211072","232102210078","62102372","62072414","2024AH053415","2021BSJJ029","GXXT-2023-050","2023AH010056","2024tlxyrc019"]}]},{"name":"Talent Research Fund of Tongling University","award":["252102211072","232102210078","62102372","62072414","2024AH053415","2021BSJJ029","GXXT-2023-050","2023AH010056","2024tlxyrc019"],"award-info":[{"award-number":["252102211072","232102210078","62102372","62072414","2024AH053415","2021BSJJ029","GXXT-2023-050","2023AH010056","2024tlxyrc019"]}]},{"name":"School-Level Young Backbone Teacher Training Program of Zhengzhou University of Light Industry","award":["252102211072","232102210078","62102372","62072414","2024AH053415","2021BSJJ029","GXXT-2023-050","2023AH010056","2024tlxyrc019"],"award-info":[{"award-number":["252102211072","232102210078","62102372","62072414","2024AH053415","2021BSJJ029","GXXT-2023-050","2023AH010056","2024tlxyrc019"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The Dynamic Multi-objective Optimization Problem (DMOP) is one of the common problem types in academia and industry. The Dynamic Multi-Objective Evolutionary Algorithm (DMOEA) is an effective way for solving DMOPs. Despite the existence of many research works proposing a variety of DMOEAs, the demand for efficient solutions to DMOPs in drastically changing scenarios is still not well met. To this end, this paper is oriented towards DMOEA and innovatively proposes to explore the correlation between different points of the optimal frontier (PF) to improve the accuracy of predicting new PFs for new environments, which is the first attempt, to our best knowledge. Specifically, when the DMOP environment changes, this paper first constructs a spatio-temporal correlation model between various key points of the PF based on the linear regression algorithm; then, based on the constructed model, predicts a new location for each key point in the new environment; subsequently, constructs a sub-population by introducing the Gaussian noise into the predicted location to improve the generalization ability; and then, utilizes the idea of NSGA-II-B to construct another sub-population to further improve the population diversity; finally, combining the previous two sub-populations, re-initializing a new population to adapt to the new environment through a random replacement strategy. The proposed method was evaluated by experiments on the CEC 2018 test suite, and the experimental results show that the proposed method can obtain the optimal MIGD value on six DMOPs and the optimal MHVD value on five DMOPs, compared with six recent research results.<\/jats:p>","DOI":"10.3390\/a18060372","type":"journal-article","created":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T09:57:48Z","timestamp":1750327068000},"page":"372","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Linear Regression Prediction-Based Dynamic Multi-Objective Evolutionary Algorithm with Correlations of Pareto Front Points"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3373-7394","authenticated-orcid":false,"given":"Junxia","family":"Ma","sequence":"first","affiliation":[{"name":"College of Software Engineering, Zhengzhou University of Light Industry, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongxuan","family":"Sang","sequence":"additional","affiliation":[{"name":"College of Software Engineering, Zhengzhou University of Light Industry, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yaoli","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Software Engineering, Zhengzhou University of Light Industry, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3598-5359","authenticated-orcid":false,"given":"Bo","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Software Engineering, Zhengzhou University of Light Industry, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhao, Y., Shen, X., and Ge, Z. (2024). A Knowledge-Guided Multi-Objective Shuffled Frog Leaping Algorithm for Dynamic Multi-Depot Multi-Trip Vehicle Routing Problem. Symmetry, 16.","DOI":"10.3390\/sym16060697"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2379","DOI":"10.1007\/s11069-023-06280-8","article-title":"A dynamic multi-objective model for emergency shelter relief system design integrating the supply and demand sides","volume":"120","author":"Geng","year":"2024","journal-title":"Nat. Hazards"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"110369","DOI":"10.1016\/j.anucene.2024.110369","article-title":"Dynamic multi-objective path-order planning research in nuclear power plant decommissioning based on NSGA-II","volume":"199","author":"Zhang","year":"2024","journal-title":"Ann. Nucl. Energy"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhang, X., Zhang, G., Zhang, D., and Zhang, L. (2023). Dynamic Multi-Objective Optimization in Brazier-Type Gasification and Carbonization Furnace. Materials, 16.","DOI":"10.3390\/ma16031164"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1145\/3524495","article-title":"Evolutionary Dynamic Multi-objective Optimisation: A Survey","volume":"55","author":"Jiang","year":"2023","journal-title":"ACM Comput. Surv."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Qiu, X., Chen, Y., Lin, Y., and Huang, B. (2024, January 22\u201324). Enhancing Stability in Real Nor-Flash Compute-In-Memory Chips: A Narrowing Output Range Approach Using Elastic Net Regularization. Proceedings of the 2024 International Symposium on Integrated Circuit Design and Integrated Systems (ICDIS\u201924), Xiamen, China.","DOI":"10.1145\/3702191.3702197"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Vultureanu-Albi\u015fi, A., and B\u0103dic\u0103, C. (June, January 29). The Model of Regularization Coefficient in Polynomial Regression for Modelling the Spread of COVID-19 in Romania. Proceedings of the 2022 23rd International Carpathian Control Conference (ICCC), Sinaia, Romania.","DOI":"10.1109\/ICCC54292.2022.9805938"},{"key":"ref_8","unstructured":"Goodfellow, I., Bengio, Y., and Courville, A. (2016). Deep Learning, MIT Press. Available online: http:\/\/www.deeplearningbook.org."},{"key":"ref_9","unstructured":"Jiang, S., Yang, S., Yao, X., Tan, K., Kaiser, M., and Krasnogor, N. (2025, June 17). Benchmark Problems for CEC\u20192018 Competition on Dynamic Multiobjective Optimisation. Available online: http:\/\/homepages.cs.ncl.ac.uk\/shouyong.jiang\/cec2018\/CEC2018_Tech_Rep_DMOP.pdf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"111114","DOI":"10.1016\/j.asoc.2023.111114","article-title":"A framework based on generational and environmental response strategies for dynamic multi-objective optimization","volume":"152","author":"Li","year":"2024","journal-title":"Appl. Soft Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2862","DOI":"10.1109\/TCYB.2015.2490738","article-title":"Evolutionary Dynamic Multiobjective Optimization Via Kalman Filter Prediction","volume":"46","author":"Muruganantham","year":"2016","journal-title":"IEEE Trans. Cybern."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5003","DOI":"10.1007\/s00500-021-05668-7","article-title":"Dynamic multi-objective evolutionary algorithm with center point prediction strategy using ensemble Kalman filter","volume":"25","author":"Chen","year":"2021","journal-title":"Soft Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"127241","DOI":"10.1016\/j.neucom.2024.127241","article-title":"A learnable population filter for dynamic multi-objective optimization","volume":"574","author":"Fang","year":"2024","journal-title":"Neurocomputing"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1115","DOI":"10.1007\/s10489-022-03353-2","article-title":"A two stages prediction strategy for evolutionary dynamic multi-objective optimization","volume":"53","author":"Sun","year":"2023","journal-title":"Appl. Intell."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"121532","DOI":"10.1016\/j.eswa.2023.121532","article-title":"Novel strategies based on a gradient boosting regression tree predictor for dynamic multi-objective optimization","volume":"237","author":"Gao","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_16","unstructured":"Ishibuchi, H., Masuda, H., Tanigaki, Y., and Nojima, Y. (April, January 29). Modified Distance Calculation in Generational Distance and Inverted Generational Distance. Proceedings of the Evolutionary Multi-Criterion Optimization, Guimar\u00e3es, Portugal."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"110333","DOI":"10.1016\/j.asoc.2023.110333","article-title":"A dynamic multi-objective evolutionary algorithm based on two-stage dimensionality reduction and a region Gauss adaptation prediction strategy","volume":"142","author":"Yang","year":"2023","journal-title":"Appl. Soft Comput."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"110359","DOI":"10.1016\/j.asoc.2023.110359","article-title":"A dynamic multi-objective evolutionary algorithm based on Niche prediction strategy","volume":"142","author":"Zheng","year":"2023","journal-title":"Appl. Soft Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/4235.996017","article-title":"A fast and elitist multiobjective genetic algorithm: NSGA-II","volume":"6","author":"Deb","year":"2002","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1215","DOI":"10.1007\/s00500-023-09157-x","article-title":"An acceleration-based prediction strategy for dynamic multi-objective optimization","volume":"28","author":"Zhang","year":"2024","journal-title":"Soft Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1007\/s11227-024-06480-4","article-title":"A dynamic multi-objective optimization evolutionary algorithm based on classification of environmental change intensity and collaborative prediction strategy","volume":"81","author":"Wang","year":"2025","journal-title":"J. Supercomput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1109\/TEVC.2004.826067","article-title":"Handling multiple objectives with particle swarm optimization","volume":"8","author":"Coello","year":"2004","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_23","unstructured":"Zitzler, E., Laumanns, M., and Thiele, L. (2001). SPEA2: Improving the Strength Pareto Evolutionary Algorithm, ETH Zurich."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Zhang, H., Wang, G.G., Dong, J., and Gandomi, A.H. (2021). Improved NSGA-III with Second-Order Difference Random Strategy for Dynamic Multi-Objective Optimization. Processes, 9.","DOI":"10.3390\/pr9060911"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"129291","DOI":"10.1016\/j.neucom.2024.129291","article-title":"A new prediction strategy for dynamic multi-objective optimization using hybrid Fuzzy C-Means and support vector machine","volume":"621","author":"Zhang","year":"2025","journal-title":"Neurocomputing"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1007\/s11227-024-06832-0","article-title":"A dynamic multi-objective optimization algorithm based on probability-driven prediction and correlation-guided individual transfer","volume":"81","author":"Ge","year":"2025","journal-title":"J. Supercomput."},{"key":"ref_27","first-page":"32","article-title":"An Improved Parallel Biobjective Hybrid Real-Coded Genetic Algorithm with Clustering-Based Selection","volume":"24","author":"Akopov","year":"2024","journal-title":"Cybern. Inf. Technol."},{"key":"ref_28","first-page":"9420460","article-title":"A Review of Surrogate Assisted Multiobjective Evolutionary Algorithms","volume":"2016","author":"Toscano","year":"2016","journal-title":"Comput. Intell. Neurosci."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/6\/372\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:55:10Z","timestamp":1760032510000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/6\/372"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,19]]},"references-count":28,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["a18060372"],"URL":"https:\/\/doi.org\/10.3390\/a18060372","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2025,6,19]]}}}