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"... Problems that are not aligned with the coordinate system can present difficulties to many optimization algorithms, including evolutionary algorithms, by trapping the search on a ridge. The ridge problem in single-objective optimization is understood, but until now little work has been done on unders ..."
Abstract
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Problems that are not aligned with the coordinate system can present difficulties to many optimization algorithms, including evolutionary algorithms, by trapping the search on a ridge. The ridge problem in single-objective optimization is understood, but until now little work has been done on understanding this issue in the multi-objective domain. Multiobjective problems with parameter interactions present difficulties to an optimization algorithm, which are not present in the single-objective domain. In this work, we have explained the nature of these difficulties, and investigated the behavior of the NSGA-II, which has difficulties with problems not aligned with the principle coordinate system. This study has investigated Simplex Crossover (SPX), Unimodal Normally Distributed Crossover (UNDX),Parent-CentricCrossover(PCX),andDifferentialEvolution(DE),aspossible alternatives to the Simulated Binary Crossover (SBX) operator within the NSGA-II, on problems exhibiting parameter interactions through a rotation of the coordinate system. An analysis of these operators on three rotated bi-objective test problems, and a fourand eight-objective problem is provided. New observations on the behavior of rotationally

