Investigating the Normalization Procedure of NSGA-III
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.
KeywordsMany-objective optimization NSGA-III Normalization
- 1.Moeaframework. http://moeaframework.org. Accessed 26 Sept 2018
- 7.Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multiobjective optimization. In: Abraham, A., Jain, L., Goldberg, R. (eds.) Evolutionary Multiobjective Optimization. AI&KP, pp. 105–145. Springer, London (2005). https://doi.org/10.1007/1-84628-137-7_6CrossRefzbMATHGoogle Scholar
- 8.Durillo, J., Nebro, A., Alba, E.: The jmetal framework for multi-objective optimization: design and architecture. In: CEC 2010, Barcelona, Spain, pp. 4138–4325, July 2010Google Scholar
- 9.Gaur, A., Talukder, A.K.M.K., Deb, K., Tiwari, S., Xu, S., Jones, D.: Finding near-optimum and diverse solutions for a large-scale engineering design problem. In: 2017 IEEE Symposium Series on Computational Intelligence (SSCI), pp. 1–8, November 2017Google Scholar
- 10.Ibrahim, A., Rahnamayan, S., Martin, M.V., Deb, K.: EliteNSGA-III: an improved evolutionary many-objective optimization algorithm. In: 2016 IEEE Congress on Evolutionary Computation (CEC), pp. 973–982, July 2016Google Scholar