差分演化參數調整對求解最佳化問題效能之影響

Performance Effects of Adjusting Parameters in Differential Evolution for Solving Optimization Problems

林豐澤(Feng-Tse Lin)

《智慧科技與應用統計學報》 10卷2期 (2012/12) Pp. 33-46

https://doi.org/10.29807/JTITAS.201212.0003

摘要

差分演化被視為是一種極有效率、隨機性、基於群體理論的最佳化方法。差分演化與演化計算以及人工生命有密切的關聯；它是基因演算法的改良變型，也是一種新的演化計算技術。最初，差分演化是用來求解切比雪夫多項式問題，它能夠找到33維度的切比雪夫多項式係數；後來發現差分演化也可以求解連續空間上複雜的最佳化問題。由於可獲得不錯的成效，差分演化被廣泛地運用在機械工具設計、資料探勘、決策支援等問題上。差分演化將每一個個體視為是一個向量，每個向量根據差分突變在偌大的空間做搜尋，經由突變向量的計算尋找更好適應值的個體，以期獲得較佳解，避免陷入區域最佳解。然而與大多數演化計算方法一樣，差分演化於求解過程仍可能會有收斂不穩定，或陷入區域最佳解等問題。本文是探討差分向量的數量、改良演化機制、以及調整參數等議題，我們想研究動態參數調整方式對於求解最佳化問題的影響程度，並提出一套求解最佳化問題的高效能動態參數調整差分演化策略。

關鍵字

差分演化 ； 差分突變 ； 突變向量 ； 差分演化策略 ； 動態參數調整

並列摘要

Differential evolution (DE) is regarded as one of the most powerful stochastic population-based optimization methods. DE is closely relevant to Evolutionary Algorithms and Artificial Life and is a variant of Genetic Algorithms. It is also to be regarded as a novel evolutionary computational technique. DE was initially invented to solve Chebyshev polynomials. It has no difficulty to find the coefficients of the 33-dimensional Chebyshev polynomial. Later, DE was found can be applied to solve complex global optimization over continuous spaces. Due to its effectiveness, DE was widely applied to mechanical unit design, data mining and decision support problems. Each individual of the population is a vector to DE. DE perturbs vectors with scaled difference of two randomly selected population vectors (i.e. differential mutation) and adds the scaled, random vector difference to a third randomly selected population vector to avoid trapping in the local optima. The advantages of DE are its simplicity, easy to use and fast convergence. However, it has the similar problems of instability for global convergence and easily trapping into local optima as most of the evolutionary algorithms had. This study investigates the number of differential vectors, evolution mechanism and parameters adjustment. We would like to find out the performance effects of dynamical adjusting parameters in DE while solving optimization problems, and to propose a dynamic, adaptive DE strategy to solve optimization problems efficiently.

並列關鍵字

differential evolution ； differential mutation ； mutation vector ； differential evolution strategy ； dynamical adjusting parameter