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- W2082972783 abstract "Decomposition-based methods are often cited as the solution to multi-objective nonconvex optimization problems with an increased number of objectives. These methods employ a scalarizing function to reduce the multi-objective problem into a set of single objective problems, which upon solution yield a good approximation of the set of optimal solutions. This set is commonly referred to as Pareto front. In this work we explore the implications of using decomposition-based methods over Pareto-based methods on algorithm convergence from a probabilistic point of view. Namely, we investigate whether there is an advantage of using a decomposition-based method, for example using the Chebyshev scalarizing function, over Pareto-based methods. We find that, under mild conditions on the objective function, the Chebyshev scalarizing function has an almost identical effect to Pareto-dominance relations when we consider the probability of finding superior solutions for algorithms that follow a balanced trajectory. We propose the hypothesis that this seemingly contradicting result compared with currently available empirical evidence, signals that the disparity in performance between Pareto-based and decomposition-based methods is due to the inability of the former class of algorithms to follow a balanced trajectory. We also link generalized decomposition to the results in this work and show how to obtain optimal scalarizing functions for a given problem, subject to prior assumptions on the Pareto front geometry." @default.
- W2082972783 created "2016-06-24" @default.
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- W2082972783 date "2015-02-01" @default.
- W2082972783 modified "2023-10-11" @default.
- W2082972783 title "Methods for multi-objective optimization: An analysis" @default.
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- W2082972783 doi "https://doi.org/10.1016/j.ins.2014.08.071" @default.
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