Global Optimization by Generalized Random Tunneling Algorithm (4th Report, Application to the Nonlinear Optimum Design Problem of the Mixed Design Variables)

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  • KITAYAMA Satoshi
    Department of Human & Mechanical Systems Engineering, Kanazawa University
  • YAMAZAKI Koetsu
    Department of Human & Mechanical Systems Engineering, Kanazawa University

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  • 一般化ランダム・トンネリング・アルゴリズムによる大域的最適化（第４報，混合変数非線形最適設計問題への適用）
  • イッパンカ ランダム トンネリング アルゴリズム ニ ヨル タイイキテキ サイテキカ ダイ4ホウ コンゴウ ヘンスウ ヒセンケイ サイテキ セッケイ モンダイ エ ノ テキヨウ
  • 4th Report, Application to the Nonlinear Optimum Design Problem of the Mixed Design Variables
  • 第4報, 混合変数非線形最適設計問題への適用

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This paper presents a method for global or quasi-optimum for the discrete and continuous design variables, based on Branching Generalized Random Tunneling Algorithm (BGRTA). By treating the discrete design variables as penalty function, the augmented objective function is constructed. As a result, all design variables can be treated as the continuous design variables. The augmented objective function becomes non-convex, and has many local minima. That is, finding optimum of discrete design variables is transformed into finding global optimum of this augmented objective function. Then BGRTA is applied to this augmented objective function, subject to the behavior and side constraints. We also propose the new update scheme of penalty parameter for the penalty function of discrete design variables in this paper. The proposed update scheme of penalty parameter utilizes the information of the penalty function of discrete design variables. By utilizing the characteristics of BGRTA, some optima are obtained. The validity of the proposed method is examined through typical benchmark problems.

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