BS-AWA: Adaptive Weighted Aggregationの目的数に対するスケーラビリティの向上

DOI
  • 濱田 直希
    東京工業大学 大学院総合理工学研究科・日本学術振興会 特別研究員 DC(現 株式会社富士通研究所)
  • 永田 裕一
    東京工業大学 情報生命博士教育院(現 徳島大学 工学部 知能情報工学科)
  • 小林 重信
    東京工業大学 大学院総合理工学研究科(現 東京工業大学 名誉教授)
  • 小野 功
    東京工業大学 大学院総合理工学研究科

書誌事項

タイトル別名
  • BS-AWA: A More Scalable Adaptive Weighted Aggregation for Continuous Multiobjective Optimization

説明

This paper proposes a more scalable variant of Adaptive Weighted Aggregation (AWA) with respect to the number of objectives in continuous multiobjective optimization. AWA is a scalarization-based multi-start strategy for generating finite points that approximate the entire Pareto set and Pareto front, which is especially focused on many-objective problems (having four or more objectives). In our last study, we discussed a reasonable stopping criterion for AWA, the representing iteration, and analyzed the time and space complexity of AWA when the representing iteration is used as a stopping criterion. Theoretical and empirical results showed that the running time and memory consumption of AWA depends on the number of solutions found in the representing iteration, the representing number. Due to the factorial increase of the representing number for objectives, the applicability of AWA is limited to 16-objective problems. In this study, we therefore redesign two central operations in AWA, the subdivision and the relocation, in order to reduce the representing number. The new subdivision is based on the simplicial complex and its barycentric subdivision and the new relocation is based on the simplicial approximation of a mapping and its range, both of which are well-known notions in topology. We theoretically compare the new AWA, named the barycentric subdivision-based AWA (BS-AWA), with the old AWA in terms of their representing iteration, representing number and approximate memory consumption to illustrate the improvement of scalability; the result implies that BS-AWA is applicable to over 20-objective problems. Numerical experiments using 2- to 17-objective benchmark problems show that BS-AWA achieves a better coverage of obtained solutions than conventional multi-start descent methods in both the variable and objective spaces. The running time and the solution distribution of BS-AWA are also discussed.

収録刊行物

詳細情報 詳細情報について

  • CRID
    1390282680342337152
  • NII論文ID
    130004965149
  • DOI
    10.11394/tjpnsec.5.1
  • ISSN
    21857385
  • 本文言語コード
    ja
  • データソース種別
    • JaLC
    • CiNii Articles
  • 抄録ライセンスフラグ
    使用不可

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