A survey and numerical comparison of factor-free penalty function constraint-handling techniques in genetic algorithms

Abstract

Numerous techniques have been proposed for handling almost all kinds of constraints in searching for solutions to constrained optimization problems. Among these methods, penalty function has been the most commonly used approach. However, a drawback of the penalty function method lies in the difficulty of setting adequate penalty factors. Thus, due to the unavailability of appropriate penalty factors, the factor-free penalty function is created to decide penalties directly by the severities of constraint violations, and is expected to capture the distance to feasibility without any user-defined factors. However, although various factor-free penalty functions have been developed, a formal comparison of these functions is short. Therefore, in order to have a clearer picture of the factor-free penalty functions and their performances, this article surveys and compares the factor-free penalty functions proposed in prior literature, and performs a numerical comparison of these (nine) functions by applying the genetic algorithm on a collection of 37 popular test problems.

對於有限最佳化的問題, 已經有許多研究提出方法來對應各式各樣的限制式以求解。 在這些方法中, 懲罰函數是最常被使用的一類。 然而懲罰函數的使用通常需搭配適當的參數, 因而成為此方法應用上的一項缺憾。 正由於適當的參數難以取得, 無參數懲罰函數於是應運而生, 藉由違反限制式的程度, 來決定一組解離合理解區域的距離。 只是, 雖然也有許多研究提出許多無參數懲罰函數, 有關這些函數的全面性績效比較卻較缺乏。 也因此, 為了對這些無參數懲罰函數的績效能有較完整的了解, 本研究探討比較既有的各種函數, 並以其中代表性的九種方法, 針對37個試驗性問題以基因演算法求解, 以比較其求解成效。

(*聯絡人: [email protected])

Keywords:

• factor-free penalty function
• constraint-handling technique
• numerical comparison
• constrained optimization problem
• genetic algorithm

Keywords:

• 關鍵詞： 無參數懲罰函數; 限制式處理方法; 成效比較; 有限最佳化問題 ; 基因演算法

Notes

(*聯絡人: [email protected])