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      Multi-Ojective Optimization Problem Scalarization using Pairing Functions

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            Abstract

            Optimization problems concern exploration of the best possible solutions to a given problem. The feasible solutions are termed good or bad based on the respective values of the objective function. For optimization problems involving more than one objective functions, absolute comparison among feasible solutions is not as straight forward as is the case with problems involving single objective functions. It can be shown that comparison among all the feasible solutions cannot be accomplished for problems involving more than one objective functions, due to lack of total order among the solutions. Scalarization is the process of transforming the multi-objective vector into a single scalar objective value. Scalarization is a popular approach for solving multi-objective optimization problems. The most prevalent scalarization technique is weighted sum method, which has been shown to be unsuitable for MOO problems having non-convex Pareto Front. It has been shown that non-convex optimization problems can be transformed into better structured problems through monotonic transformations of the objective functions. This work proposes Pairing Functions as an efficient scalarization method. Pairing functions are monotonic, bijective transformations from R2 → R. This makes pairing functions as strictly monotonic functions, which guarantee unique single-valued aggregated objective for unique combinations of the multiple objectives. The effectiveness of the pairing function based scalarization has been demonstrated on bench-mark MOO problems.

            Content

            Author and article information

            Journal
            ScienceOpen Preprints
            ScienceOpen
            12 December 2023
            Affiliations
            [1 ] Homi Bhabha National Institute, Mumbai, India;
            [2 ] Bhabha Atomic Research Centre, Mumbai, India;
            Author notes
            Author information
            https://orcid.org/0000-0003-0223-8381
            Article
            10.14293/PR2199.000547.v1
            c7a8add5-7419-4c56-890d-002e478ffedf

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .

            History
            : 12 December 2023
            Categories

            Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
            Applied mathematics,General engineering,Mathematics
            Pairing Functions,Scalarization,Multiobjective Optimization

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