Abstract
Most practical optimization problems are multi-objective in nature. Moreover, the objective values are, in general, differently scaled. In order to obtain uniformly distributed set of Pareto-optimal points, the objectives must be normalized so that any distance metric computation in the objective space is meaningful. Thus, normalization becomes a crucial component of an evolutionary multi-objective optimization (EMO) algorithm. In this paper, we investigate and discuss the normalization procedure for NSGA-III, a state-of-the-art multi- and many-objective evolutionary algorithm. First, we show the importance of normalization in higher-dimensional objective spaces. Second, we provide pseudo-codes which presents a clear description of normalization methods proposed in this study. Third, we compare the proposed normalization methods on a variety of test problems up to ten objectives. The results indicate the importance of normalization for the overall algorithm performance and show the effectiveness of the originally proposed NSGA-III’s hyperplane concept in higher-dimensional objective spaces.
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Notes
- 1.
The source code is freely available at https://github.com/msu-coinlab/pymoo.
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Blank, J., Deb, K., Roy, P.C. (2019). Investigating the Normalization Procedure of NSGA-III. In: Deb, K., et al. Evolutionary Multi-Criterion Optimization. EMO 2019. Lecture Notes in Computer Science(), vol 11411. Springer, Cham. https://doi.org/10.1007/978-3-030-12598-1_19
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