徳島大学 教育・研究者情報データベース(EDB)

1. (日) 濱田 直希

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2. 永田 裕一([徳島大学.大学院社会産業理工学研究部.理工学域.知能情報系.情報工学分野]/[徳島大学.理工学部.理工学科.知能情報コース.情報工学講座])

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3. (日) 小林 重信

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4. 小野 功

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(英) BS-AWA: A More Scalable Adaptive Weighted Aggregation for Continuous Multiobjective Optimization

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

(英) 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 <em>representing iteration</em>, 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 <em>representing number</em>. 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 <em>subdivision</em> and the <em>relocation</em>, 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 <em>barycentric subdivision-based AWA (BS-AWA)</em>, 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.

1. (英) multi-objective optimization
2. (英) continuous optimization
3. (英) scalarization
4. (英) multi-start search
5. (英) weight adaptation