{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T14:52:42Z","timestamp":1774363962476,"version":"3.50.1"},"reference-count":52,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,10,30]],"date-time":"2023-10-30T00:00:00Z","timestamp":1698624000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001321","name":"National Research Foundation (NRF) of South Africa","doi-asserted-by":"publisher","award":["46712"],"award-info":[{"award-number":["46712"]}],"id":[{"id":"10.13039\/501100001321","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001321","name":"National Research Foundation (NRF) of South Africa","doi-asserted-by":"publisher","award":["105743"],"award-info":[{"award-number":["105743"]}],"id":[{"id":"10.13039\/501100001321","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Dynamic multi-objective optimization problems (DMOPs) are optimization problems where elements of the problems, such as the objective functions and\/or constraints, change with time. These problems are characterized by two or more objective functions, where at least two objective functions are in conflict with one another. When solving real-world problems, the incorporation of human decision-makers (DMs)\u2019 preferences or expert knowledge into the optimization process and thereby restricting the search to a specific region of the Pareto-optimal Front (POF) may result in more preferred or suitable solutions. This study proposes approaches that enable DMs to influence the search process with their preferences by reformulating the optimization problems as constrained problems. The subsequent constrained problems are solved using various constraint handling approaches, such as the penalization of infeasible solutions and the restriction of the search to the feasible region of the search space. The proposed constraint handling approaches are compared by incorporating the approaches into a differential evolution (DE) algorithm and measuring the algorithm\u2019s performance using both standard performance measures for dynamic multi-objective optimization (DMOO), as well as newly proposed measures for constrained DMOPs. The new measures indicate how well an algorithm was able to find solutions in the objective space that best reflect the DM\u2019s preferences and the Pareto-optimality goal of dynamic multi-objective optimization algorithms (DMOAs). The results indicate that the constraint handling approaches are effective in finding Pareto-optimal solutions that satisfy the preference constraints of a DM.<\/jats:p>","DOI":"10.3390\/a16110504","type":"journal-article","created":{"date-parts":[[2023,10,30]],"date-time":"2023-10-30T13:20:07Z","timestamp":1698672007000},"page":"504","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Decision-Maker\u2019s Preference-Driven Dynamic Multi-Objective Optimization"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5803-5615","authenticated-orcid":false,"given":"Adekunle Rotimi","family":"Adekoya","sequence":"first","affiliation":[{"name":"Computer Science Division, Stellenbosch University, Stellenbosch 7600, South Africa"},{"name":"Department of Computer Science, University of Pretoria, Hatfield 0002, South Africa"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4907-0662","authenticated-orcid":false,"given":"Mard\u00e9","family":"Helbig","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Pretoria, Hatfield 0002, South Africa"},{"name":"School of ICT, Griffith University, Southport 4215, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Helbig, M., and Engelbrecht, A.P. (2013, January 20\u201323). Analysing the performance of dynamic multi-objective optimisation algorithms. Proceedings of the IEEE Congress on Evolutionary Computation, Cancun, Mexico.","DOI":"10.1109\/CEC.2013.6557744"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Jiang, S., and Yang, S. (2014, January 8\u201310). A benchmark generator for dynamic multi-objective optimization problems. Proceedings of the UK Workshop on Computational Intelligence (UKCI), Bradford, UK.","DOI":"10.1109\/UKCI.2014.6930171"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Azzouz, R., Bechikh, S., and Said, L.B. (2017). Recent Advances in Evolutionary Multi-objective Optimization, Springer.","DOI":"10.1007\/978-3-319-42978-6"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.swevo.2012.05.001","article-title":"Evolutionary dynamic optimization: A survey of the state of the art","volume":"6","author":"Nguyen","year":"2012","journal-title":"Swarm Evol. Comput."},{"key":"ref_5","first-page":"287","article-title":"Multi-Objective Particle Swarm Optimizers: A Survey of the State-of-the-Art","volume":"2","year":"2006","journal-title":"Int. J. Comput. Intell. Res."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Pareto, V. (1964). Cours D\u2019Economie Politique, Librairie Droz.","DOI":"10.3917\/droz.paret.1964.01"},{"key":"ref_7","unstructured":"Deb, K. (2001). Multi-Objective Optimization Using Evolutionary Algorithms, John Wiley & Sons, Inc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"121368","DOI":"10.1016\/j.apenergy.2023.121368","article-title":"A CFD multi-objective optimization framework to design a wall-type heat recovery and ventilation unit with phase change material","volume":"347","author":"Bianco","year":"2023","journal-title":"Appl. Energy"},{"key":"ref_9","unstructured":"Deb, K., Bhaskara Rao, N.U., and Karthik, S. (2007, January 5\u20138). Dynamic Multi-objective Optimization and Decision-making Using Modified NSGA-II: A Case Study on Hydro-thermal Power Scheduling. Proceedings of the International Conference on Evolutionary Multi-Criterion Optimization, EMO\u201907, Matsushima, Japan."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1109\/TEVC.2004.831456","article-title":"Dynamic multiobjective optimization problem: Test cases, approximation, and applications","volume":"8","author":"Farina","year":"2004","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1002\/mcda.290","article-title":"A dynamic interval goal programming approach to the regulation of a lake\u2013river system","volume":"10","year":"2001","journal-title":"J. Multi-Criteria Decis. Anal."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0377-2217(01)00282-X","article-title":"Dynamic multi-objective heating optimization","volume":"142","year":"2002","journal-title":"Eur. J. Oper. Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2370","DOI":"10.1016\/j.ins.2010.12.015","article-title":"Dynamic multi-objective optimization based on membrane computing for control of time-varying unstable plants","volume":"181","author":"Huang","year":"2011","journal-title":"Inf. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Zhang, X., Zhang, G., Zhang, D., Zhang, L., and Qian, F. (2023). Dynamic Multi-Objective Optimization in Brazier-Type Gasification and Carbonization Furnace. Materials, 16.","DOI":"10.3390\/ma16031164"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"109613","DOI":"10.1016\/j.asoc.2022.109613","article-title":"Dynamic multi-objective optimization and fuzzy AHP for copper removal process of zinc hydrometallurgy","volume":"129","author":"Zhou","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Fang, Y., Liu, F., Li, M., and Cui, H. (2022). Domain Generalization-Based Dynamic Multiobjective Optimization: A Case Study on Disassembly Line Balancing. IEEE Trans. Evol. Comput., 1.","DOI":"10.1109\/TEVC.2022.3233642"},{"key":"ref_17","first-page":"203","article-title":"Computational Intelligence Systems in Industrial Engineering","volume":"6","author":"Iris","year":"2012","journal-title":"Comput. Intell. Syst. Ind. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Smith, A.E. (2022). Women in Computational Intelligence: Key Advances and Perspectives on Emerging Topics, Springer International Publishing.","DOI":"10.1007\/978-3-030-79092-9"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Jaimes, A.L., Monta\u00f1o, A.A., and Coello Coello, C.A. (2011, January 5\u20138). Preference incorporation to solve many-objective airfoil design problems. Proceedings of the IEEE Congress of Evolutionary Computation (CEC), New Orleans, LA, USA.","DOI":"10.1109\/CEC.2011.5949807"},{"key":"ref_20","unstructured":"Coello, C.A.C., Lamont, G.B., and Veldhuizen, D.A.V. (2007). Evolutionary Algorithms for Solving Multi-Objective Problems, Springer."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Castillo, O., Melin, P., Pedrycz, W., and Kacprzyk, J. (2014). Recent Advances on Hybrid Approaches for Designing Intelligent Systems, Springer International Publishing.","DOI":"10.1007\/978-3-319-05170-3"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.asoc.2016.10.037","article-title":"Incorporation of implicit decision-maker preferences in multi-objective evolutionary optimization using a multi-criteria classification method","volume":"50","author":"Fernandez","year":"2017","journal-title":"Appl. Soft Comput. J."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.infsof.2017.05.003","article-title":"Incorporating user preferences in search-based software engineering: A systematic mapping study","volume":"90","author":"Ferreira","year":"2017","journal-title":"Inf. Softw. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1016\/j.ins.2014.10.031","article-title":"A novel preference articulation operator for the Evolutionary Multi-Objective Optimisation of classifiers in concealed weapons detection","volume":"295","author":"Rostami","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/j.ins.2015.09.015","article-title":"Preference-guided evolutionary algorithms for many-objective optimization","volume":"329","author":"Goulart","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Sudenga, S., and Wattanapongsakornb, N. (2014, January 9\u201312). Incorporating decision maker preference in multiobjective evolutionary algorithm. Proceedings of the IEEE Symposium on Computational Intelligence for Engineering Solutions (CIES), Orlando, FL, USA.","DOI":"10.1109\/CIES.2014.7011826"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1162\/evco.2009.17.3.411","article-title":"A Preference-Based Evolutionary Algorithm for Multi-Objective Optimization","volume":"17","author":"Thiele","year":"2009","journal-title":"Evol. Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.swevo.2011.10.001","article-title":"Constraint-handling in nature-inspired numerical optimization: Past, present and future","volume":"1","year":"2011","journal-title":"Swarm Evol. Comput."},{"key":"ref_29","unstructured":"Kennedy, J., and Eberhart, R. (1997, January 12\u201315). A discrete binary version of the particle swarm algorithm. Proceedings of the 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation, Orlando, FL, USA."},{"key":"ref_30","unstructured":"Jensen, P.A., and Bard, J.F. (2003). Operations Research Models and Methods, John Wiley & Sons."},{"key":"ref_31","first-page":"135","article-title":"A Survey of Constraint Handling Techniques in Evolutionary Computation Methods","volume":"4","author":"Methods","year":"1995","journal-title":"Evol. Program."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1109\/TCYB.2013.2250956","article-title":"Constrained Optimization Via Artificial Immune System","volume":"44","author":"Zhang","year":"2014","journal-title":"IEEE Trans. Cybern."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Azzouz, R., Bechikh, S., and Said, L.B. (2012, January 7\u20139). Articulating Decision Maker\u2019s Preference Information within Multiobjective Artificial Immune Systems. Proceedings of the 2012 IEEE 24th International Conference on Tools with Artificial Intelligence, Athens, Greece.","DOI":"10.1109\/ICTAI.2012.52"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1109\/TEVC.2010.2059031","article-title":"Differential Evolution: A Survey of the State-of-the-Art","volume":"15","author":"Das","year":"2011","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_35","unstructured":"Schoenauer, M., Deb, K., Rudolph, G., Yao, X., Lutton, E., Merelo, J.J., and Schwefel, H.P. (2020, January 18\u201320). A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimization: NSGA-II. Proceedings of the Parallel Problem Solving from Nature PPSN VI, Paris, France."},{"key":"ref_36","unstructured":"Adekunle, R.A., and Helbig, M. (December, January 27). A differential evolution algorithm for dynamic multi-objective optimization. Proceedings of the IEEE Symposium Series on Computational Intelligence (SSCI), Honolulu, HI, USA."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Helbig, M., and Engelbrecht, A.P. (2013, January 16\u201319). Issues with performance measures for dynamic multi-objective optimisation. Proceedings of the IEEE Symposium on Computational Intelligence in Dynamic and Uncertain Environments (CIDUE), Singapore.","DOI":"10.1109\/CIDUE.2013.6595767"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Helbig, M. (2012). Solving Dynamic Multi-Objective Optimisation Problems Using Vector Evaluated Particle Swarm Optimisation. [Ph.D. Thesis, University of Pretoria].","DOI":"10.1109\/CEC.2011.5949867"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1109\/TEVC.2008.920671","article-title":"A competitive-cooperative coevolutionary paradigm for dynamic multiobjective optimization","volume":"13","author":"Goh","year":"2009","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1007\/s10589-015-9752-6","article-title":"Feasibility preserving constraint-handling strategies for real parameter evolutionary optimization","volume":"62","author":"Padhye","year":"2015","journal-title":"Comput. Optim. Appl."},{"key":"ref_41","first-page":"783","article-title":"On the disruption-level of polynomial mutation for evolutionary multi-objective optimisation algorithms","volume":"29","author":"Hamdan","year":"2010","journal-title":"Comput. Inform."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Engelbrecht, A.P. (2007). Computational Intelligence: An Introduction, John Wiley & Sons.","DOI":"10.1002\/9780470512517"},{"key":"ref_43","first-page":"293","article-title":"A Parameter Study for Differential Evolution","volume":"10","author":"Gaemperle","year":"2002","journal-title":"Adv. Intell. Syst. Fuzzy Syst. Evol. Comput."},{"key":"ref_44","unstructured":"Ronkkonen, J., Kukkonen, S., and Price, K. (2005, January 2\u20135). Real-parameter optimization with differential evolution. Proceedings of the IEEE Congress on Evolutionary Computation, Scotland, UK."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Zelinka, I., Sn\u00e1\u0161el, V., and Abraham, A. (2013). Handbook of Optimization: From Classical to Modern Approach, Springer.","DOI":"10.1007\/978-3-642-30504-7"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/A:1008202821328","article-title":"Differential Evolution\u2014A Simple and Efficient Heuristic for global Optimization over Continuous Spaces","volume":"11","author":"Storn","year":"1997","journal-title":"J. Glob. Optim."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"3570","DOI":"10.1016\/j.neucom.2008.12.041","article-title":"A Single Front Genetic Algorithm for Parallel Multi-objective Optimization in Dynamic Environments","volume":"72","author":"Ortega","year":"2009","journal-title":"Neurocomputing"},{"key":"ref_48","unstructured":"Van Veldhuizen, D. (1999). Multiobjective Evolutionary Algorithms: Classification, Analyses, and New Innovations. [Ph.D. Thesis, Faculty of the Graduate School of Engineering, Air Force Institute of Technology, Air University]."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.ins.2013.06.051","article-title":"Performance measures for dynamic multi-objective optimisation algorithms","volume":"250","author":"Helbig","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_50","unstructured":"Sola, M.C. (2010). Parallel Processing for Dynamic Multi-Objective Optimization. [Ph.D. Thesis, Universidad de Granada]."},{"key":"ref_51","unstructured":"R Core Team (2017). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing."},{"key":"ref_52","unstructured":"Buyya, R., Hernandez, S.M., Kovvur, R.M.R., and Sarma, T.H. Dynamic Multi-objective Optimization Using Computational Intelligence Algorithms. Proceedings of the Computational Intelligence and Data Analytics."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/11\/504\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:14:24Z","timestamp":1760130864000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/11\/504"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,30]]},"references-count":52,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["a16110504"],"URL":"https:\/\/doi.org\/10.3390\/a16110504","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,30]]}}}