DE演算法搭配適應性懲罰函數應用於限制式連續型最佳化問題之研究

許多現今的研究中，萬用啟發式演算法常常被應用於處理最佳化問題，但是大多數侷限於非限制式的最佳化問題。然而，在真實世界中，此些問題常常會伴隨著限制式而存在。本篇論文提出了一個以differential evolution (DE) 演算法為基礎的方法來處理包含限制式的最佳化問題。此DE演算法搭配了懲罰值函數的使用，將所有限制式轉換成懲罰值的型態，並將其加入於目標函式中。懲罰值函數可用於處理問題中等式限制式與非等式限制式；而在本研究中，所有的等式限制式皆轉換成非等式限制式的型態。此外，DE演算法搜尋過程中，隨機初始化(re-initialization)的方法被用於重新產生一個滿足邊界限制式的解。本研究比較了三種不同上升程度的動態懲罰值函數以及適應性懲罰值函數績效的好壞。並且使用動態允許誤差的方法處理包含等式限制式的問題。其演算法的搜尋績效的好壞是由最佳目標函數值以及其所需函數計算次數來衡量。而參數的選擇使用一連串的模擬以及實驗設計的方法來決定。最後，使用不同的標準例題來測試DE演算法搭配懲罰值函數對於最佳化問題的效用。

關鍵字

差分演算法(Differential Evolution Algorithm) ；動態懲罰函數；適應性懲罰函數；限制式連續型最佳化問題

並列摘要

The applications of Metaheuristic algorithms that used to solve optimization problems in researches are very popular, but most of them were generally for unconstrained optimization procedures. However, these normally exiting problems in real-world are always under constrained. This paper presents a differential-evolution-type algorithm for solving constrained continuous optimization problems. The proposed differential evolution (DE) algorithm is developed based upon the penalty function approach, where constraint violation is penalized by placing the constraints into the objective function. Penalty functions can deal both with equality and inequality constraints; in this study, equality constraints are transformed into inequality ones. In addition, to handle infeasibility during DE search, a random re-initialization procedure is executed to produce a new potential solution inside the allowable ranges. Three different types of increasing penalty factors and one adaptive penalty that adjust by constraint violations are compared for their performance on convergence. A dynamic tolerance allowed of equality constraints is executed, too. The performance measure includes the best objective value achieved and the number of function evaluations required. The recommendation for the selection of parameter setting in the new algorithm is given through a series of simulation optimizations and analysis by the design of experiments (DOE). The experimental results obtained by solving a variety of benchmark functions are used to demonstrate the effectiveness and efficiency of the penalty-function DE algorithm.

並列關鍵字

Differential Evolution Algorithm ； Dynamic Penalty Function ； Adaptive Penalty Function ； Constrained Continuous Global Optimization

參考文獻

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國際替代計量

DE演算法搭配適應性懲罰函數應用於限制式連續型最佳化問題之研究

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