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Evaluation on DTLZ benchmark problems shows strong performance versus related algorithms, and application to a difficult polymer-processing problem demonstrates practical effectiveness. 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Math. Comput. Appl. 2023, 28, 17 . [https://doi.org/10.3390/](https://doi.org/10.3390/)[ ](https://doi.org/10.3390/)mca28010017  \nAcademic Editors: Carlos Coello, Erik Goodman, Kaisa Miettinen, Dhish Saxena, Oliver Schütze and Lothar Thiele  \nReceived: 6 November 2022  \nRevised: 14 January 2023  \nAccepted: 25 January 2023  \nPublished: 30 January 2023  \nCopyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([https://](https://)[ ](https://)[creativecommons.org/licenses/by/](creativecommons.org/licenses/by/)[ ](creativecommons.org/licenses/by/)[4.0/](4.0/)) .  \n1 Institute of Polymers and Composites, University of Minho, 4800-058 Guimar¢es, Portugal  \n2 Institute of Mathematics and Computer Science, University of S¢o Paulo, S¢o Paulo 05508-060, Brazil  \n* Correspondence: [agc@dep.uminho.pt](agc@dep.uminho.pt)  \nAbstract: Solving real-world multi-objective optimization problems using Multi-Objective Optimization Algorithms becomes difficult when the number of objectives is high since the types of algorithms generally used to solve these problems are based on the concept of non-dominance, which ceases to work as the number of objectives grows. This problem is known as the curse of dimensionality. Simultaneously, the existence of many objectives, a characteristic of practical optimization problems, makes choosing a solution to the problem very difficult. Different approaches are being used in the literature to reduce the number of objectives required for optimization. This work aims to propose a machine learning methodology, designated by FS-OPA, to tackle this problem. The proposed methodology was assessed using DTLZ benchmarks problems suggested in the literature and compared with similar algorithms, showing a good performance. In the end, the methodology was applied toa difficult real problem in polymer processing, showing its effectiveness. The algorithm proposed has some advantages when compared with a similar algorithm in the literature based on machine learning (NL-MVU-PCA), namely, the possibility for establishing variable–variable and objective– variable relations (not only objective–objective), and the elimination of the need to define/chose a kernel neither to optimize algorithm parameters. The collaboration with the DM(s) allows for the obtainment of explainable solutions.  \nKeywords: objectives reduction; data mining; multi-objective optimization; many objectives  \n1. Introduction  \nReal-world optimization problems are usually multiobjective, in which multiple conflicting objectives must be taken into account simultaneously. Manly, there are two ways to tackle these types of problems, scalarization functions and population-based algorithms. The use of scalarization functions presented some drawbacks, which led to the development of population-based metaheuristics that use the concept of Pareto-dominance and niching to evolve a population of solutions in the direction of the Pareto-optimal front [1,2] .  \nThere are at least three basic types of population-based algorithms commonly employed to solve Multiobjective Optimization Problems MOPs, namely, evolutionary algorithms, swarm-based methods, and colony-based algorithms, which can use the dominance concept, the metric indicators, or the decomposition strategy [3] . In most of these algorithms, a random initial population of solutions is generated and the new populations are consecutively obtained by selection and variation strategies until a stop criterion is met. It is expected ","cbCaicYrjUQtQ0HH","https://ap.wps.com/l/cbCaicYrjUQtQ0HH","pdf",4100973,"English","# Abstract\n# 1. Introduction\n## Multi-objective optimization and Pareto dominance\n## Curse of dimensionality in many-objective settings\n## Approaches to reduce the number of objectives","[{\"question\":\"Why do many-objective optimization problems become difficult with standard algorithms?\",\"answer\":\"As the number of objectives grows, non-dominated solutions become rarer, reducing the effectiveness of algorithms based on Pareto dominance. This scaling issue is referred to as the curse of dimensionality.\"},{\"question\":\"What does the proposed FS-OPA methodology aim to do?\",\"answer\":\"FS-OPA is designed to reduce the number of objectives required for optimization in many-objective settings, making solution selection and search more manageable.\"},{\"question\":\"How is FS-OPA evaluated and where is it applied?\",\"answer\":\"The methodology is tested on DTLZ benchmark problems suggested in the literature and compared with similar algorithms. It is also applied to a real polymer-processing problem to demonstrate effectiveness.\"},{\"question\":\"What advantages does the proposed algorithm claim over NL-MVU-PCA?\",\"answer\":\"It supports establishing variable–variable and objective–variable relations (not only objective–objective) and eliminates the need to define or choose a kernel when tuning algorithm parameters, enabling explainable solutions with decision makers.\"}]","Many-Objectives Optimization - A Machine Learning Approach for Reducing the Number of Objectives | PDF",48]