Adaptation of Scalarizing Functions in MOEA/D: An Adaptive Scalarizing Function-Based Multiobjective Evolutionary Algorithm

  • Authors:

  • Hisao Ishibuchi;Yuji Sakane;Noritaka Tsukamoto;Yusuke Nojima

  • Affiliations:

  • Department of Computer Science and Intelligent Systems, Graduate School of Engineering, Osaka Prefecture University, Osaka, Japan 599-8531;Department of Computer Science and Intelligent Systems, Graduate School of Engineering, Osaka Prefecture University, Osaka, Japan 599-8531;Department of Computer Science and Intelligent Systems, Graduate School of Engineering, Osaka Prefecture University, Osaka, Japan 599-8531;Department of Computer Science and Intelligent Systems, Graduate School of Engineering, Osaka Prefecture University, Osaka, Japan 599-8531

  • Venue:
  • EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
  • Year:
  • 2009

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Abstract

It is well-known that multiobjective problems with many objectives are difficult for Pareto dominance-based algorithms such as NSGA-II and SPEA. This is because almost all individuals in a population are non-dominated with each other in the presence of many objectives. In such a population, the Pareto dominance relation can generate no strong selection pressure toward the Pareto front. This leads to poor search ability of Pareto dominance-based algorithms for many-objective problems. Recently it has been reported that better results can be obtained for many-objective problems by the use of scalarizing functions. The weighted sum usually works well in scalarizing function-based algorithms when the Pareto front is convex. However, we need other functions such as the weighted Tchebycheff when the Pareto front is non-convex. In this paper, we propose an idea of automatically choosing between the weighted sum and the weighted Tchebycheff for each individual in each generation. The characteristic feature of the proposed idea is to use the weighted Tchebycheff only when it is needed for individuals along non-convex regions of the Pareto front. The weighted sum is used for the other individuals in each generation. The proposed idea is combined with a high-performance scalarizing function-based algorithm called MOEA/D (multiobjective evolutionary algorithm based on decomposition) of Zhang and Li (2007). Effectiveness of the proposed idea is demonstrated through computational experiments on modified multiobjective knapsack problems with non-convex Pareto fronts.