Efficient population-based optimization for high dimensional multimodal problems by estimating hill-valley structures and distribution types

2020 Fiscal Year Final Research Report

• Project/Area Number: 17K00311
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Intelligent informatics
• Research Institution: Hiroshima City University
• Principal Investigator: Takahama Tetsuyuki 広島市立大学, 情報科学研究科, 教授 (80197194)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: 最適化アルゴリズム / 多峰性最適化 / 関数形状推定 / 山谷構造 / 近傍グラフ / 進化的計算 / 差分進化

Outline of Final Research Achievements

In this study, we conducted research on the following items in order to solve complex optimization problems that appear in various fields, especially high-dimensional multimodal optimization problems. (1) We proposed a method for determining hill and valley points using a neighborhood graph. Valley points can be considered as solution candidates. We also proposed a method of performing local search around the valley points. (2) We proposed crossover using a correlation matrix in order to generate offspring according to the dependency between variables that determine the distribution of search points. (3) We proposed a beta-relaxed relative neighborhood graph (beta-RNG), which can generate an intermediate graph between Gabriel graph and relative neighborhood graph using a parameter beta, and also proposed graph-based speciation using beta-RNG to deal with high-dimensional problems. These studies showed that evolutionary algorithms with high search efficiency can be realized.

Free Research Field

知能情報学

Academic Significance and Societal Importance of the Research Achievements

近年，様々な分野において，高次元の多峰性最適化問題を安定的に解くニーズが高まってきている。また，最適化の対象となる目的関数の評価コストや評価時間が増大する傾向にあるため，探索効率の向上も大きな課題となっている。例えば，空力設計最適化では計算流体力学シミュレーションのために１回の計算に数10時間かかる場合もある。本研究では，複数の探索点によって最適解を探索する進化的アルゴリズムにおいて，近傍グラフを用いて探索点間の隣接関係を把握し，隣接点間における関数値の大小関係から山谷構造を求め，谷点を中心とする種分化によって探索点をグループ化し，複数の最適解を探索する効率的なアルゴリズムを提案した。