分組式差分進化演算法及其應用於模糊系統最佳化設計

Abstract

本篇論文主要分為兩個部分，第一部分，我們提出分組式差分進化演算法解決函數最佳化問題。該進化演算法使用兩種不同類型的突變運算，可解決傳統演算法常遇到的停滯問題，進而達到良好的演化搜尋能力。在演化程序中，依照個體之適應值，所有個體被區分為優等組與劣等組。優等組進行區域性的突變運算，劣等組進行全域性的突變運算。再藉由交配和選擇運算以產生新的子代。我們也提出一個新的適應學習策略為了避免人為設定參數問題，該策略能自動的找到最佳設定參數。在模擬中，我們測試13個函數最佳化問題。本論文所提出的演算法皆呈現良好的搜尋效能。第二部分，我們將分組式差分進化演算法應用在函數聯結之模糊系統最佳化設計上。在架構學習中，使用凝聚分群演算法自動地給予模糊系統最適合的模糊規則數。在參數學習中，群體將被拆善成數個子群體且每個子群體各自進化，最後可獲得最佳化的函數聯結之模糊系統。我們將與其他方法比較，以證實所提出的網路架構及其相關演算法之有效性。

This dissertation consists of two major parts. In the first part, we propose a group-based differential evolution (GDE) algorithm for numerical optimization problems. The proposed GDE algorithm employs two different mutation operations to solve the stagnation problem and achieve good performance. Initially, all individuals in population are grouped into an inferior group and a superior group based on their fitness value. The inferior group uses the global mutation model. The superior group employs the local mutation model. Subsequently, crossover and selection operations are employed for the next generation. An adaptive strategy is also proposed to automatically find good parameters in the GDE algorithm. To validate the performance of the GDE algorithm, 13 numerical benchmark functions are tested. The simulation results indicate that the approach is effective and efficient. In the second part, we apply the GDE algorithm to function-link fuzzy system (FLFS) optimization. For structure learning, an agglomerative clustering algorithm is proposed to find the optimal number of fuzzy rules. For parameter learning, we use symbiotic learning method and GDE algorithm. The population is separated as subpopulations. Each subpopulation performs GDE algorithm to search the optimal parameter. The FLFS model with GDE learning algorithm (FLFS-GDE) is applied in real world prediction problems. Results of this dissertation demonstrate the effectiveness of the proposed methods.