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Adaptive Weighted Aggregation 2: More scalable AWA for multiobjective function optimization

Adaptive Weighted Aggregation 2: More scalable AWA for multiobjective function optimization,10.1109/CEC.2011.5949911,Naoki Hamada,Yuichi Nagata,Shigen

Adaptive Weighted Aggregation 2: More scalable AWA for multiobjective function optimization  
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Adaptive Weighted Aggregation (AWA) is a frame- work of multi-starting optimization methods based on scalariza- tion for solving multiobjective function optimization problems. It progressively generates new solutions to refine the approximation of the Pareto set or the Pareto front by the subdivision, and itera- tively estimates the appropriate weight vector for scalarization in each search by the weight adaptation. Our recent study shows that AWA's solution set combinatorially increases for the number of objectives. In this paper, we propose a new subdivision and weight adaptation scheme of AWA to improve its scalability. Numerical experiments show the effectiveness of the proposed method. I. INTRODUCTION To obtain good approximate solutions from both view- points of precision and coverage, we have proposed Adaptive Weighted Aggregation (AWA) (6), a framework of multi- starting optimization methods based on scalarization, which estimates the appropriate weight vector for scalarization in each search by the operation called the weight adaptation. Recently, we have analyzed the scalability of AWA (7). In this analysis, it has been theoretically shown that AWA's solution set combinatorially increases for the number of objectives while the experiments in the paper has been shown that AWA succeeds in solving 9-objective problems. This increase of solutions is done by the operation called the subdivision. In this paper, we propose a new subdivision and weight adaptation scheme of AWA to improve its scalability for the number of objectives. We also show that the effectiveness of the new AWA by comparing with some conventional multi- starting descent methods in numerical experiments. The rest of this paper is organized as follows. In Section II, we define the multiobjective function optimization problem and related notions. Section III introduces the conventional AWA and discusses its scalability problem. To remedy the problem discussed in Section III, we propose a new AWA that employs a new subdivision and weight adaptation scheme in Section IV. In Section V, some experiments are conducted to show the effectiveness of the proposed method. Section VI concludes the paper and discusses future work.
Published in 2011.
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