Application of The Temperature Parallel Simulated Annealing to Continuous Optimization Problems
نویسندگان
چکیده
連続設計変数を持つ最適化問題に対しては, これまで非線形数理計画法による解法が主流で あった.設計空間が単峰で,しかも目的関数の 勾配が連続である場合にはこのアプロ-チは極 めて有効であるが,そうでない場合には遺伝的 アルゴリズム(GA),シミュレーテッドアニー リング(SA),あるいはタブーサーチ(TS)な ど,ヒューリスティックサーチ(heuristic search) [1]とよばれる方法が用いられることも多くなっ てきた.なかでも,GAとSAはこのような手法 の双璧であり,連続最適化問題に対しても多く の研究が行われてきた[2].一般的に,設計空間 内にサイズの大きい局所解領域が多く存在する 場合にはGAが有効であり,設計空間全域的には 単峰に近いが,サイズの小さい局所解領域が無 数に存在する場合にはSAが有効である[3]. SA[4]は,炉内の固体の熱的平衡状態をシミュ レーションするための単純なアルゴリズム[5]を 基本として最適化問題を解く方法であり,多く の組合せ最適化問題の解法として有用である[6]. SAの長所は,(a) ほとんど任意の非線形性を持つ コスト関数を処理できる,(b) ほとんど任意の境 界条件や制約条件が処理できる,(c) 他の非線形 最適化アルゴリズムと比較してコード化が容易 である,(d) 最適解の発見が統計的に保証されて いる,ことである.一方,SAの短所は,(a) 計算 時間が長い,(b) 特定の問題に対してチューニン グするのが容易でない,(c) 過大評価されて用い られ,結果の解釈が間違っている場合がある, (d) 誤った利用によりエルゴード性を失う,すな わち冷却が早く,シミュレーテッドクエンチン グ(simulated quenching)になっている.この場 合は最適解が求められる統計的な保証はない, ことである[7].要するに,GAより単純なアルゴ リズムで,計算機へのインプリメントも容易で あるが,良い最適解を得るには非常に長い時間
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