|Abstract: ||藉著仿自然、人文與社會科學、以及動物生態行為等系統邏輯思維，族群式進化演 算法跳脫嚴謹的數學模型推導，採用簡易數學之運作方式與控制參數等特性，並利用族 群中個體間隨機相互激盪，以直接式求解全域最佳解。因為不需導數資訊，族群式進化 演算法不僅克服了數學規劃法無法求解多極值問題之弱點，同時對於高維度問題亦能達 到相當之效益與效率，使得近年來發展出不少之演算法譬如基因演算法、螞蟻演算法、 文化演算法、及鳥飛群演算法等。 回顧文獻中，發現族群式進化演算法雖有機會求得全域最佳解，由於採用簡易數學 運作模式常導致對於許多問題的求解精確度不足，以及問題變數之總數增大（n>30）， 不僅不容易求得全域最佳解且其求得之解的精確度亦隨之變差，因此總是患『維數的魔 咒』；再者，族群式進化演算法都以連續性實數型變數為主，對於離散型或NP 問題（組 合性問題）則需對變數的編碼加以轉換修改，才能使用。 鑑此，本計畫提出三年期計畫『智慧型垃圾桶決策之差分進化演算法及其應用』， 逐年地克服上述族群式演算法的弱點，所發展的演算法不僅具有完整的系統邏輯思維， 對各類型與高維數之最佳化問題均能適用性： 第一年計畫：發展『智慧型垃圾桶決策之差分進化演算法』。採用1997 年Storn 提 出差分進化演算法為族群演化基本模式，本計劃擬加入社會科學之垃圾桶決策模式。本 方法之驗證首先以國際CEC2005 的標竿問題進行搜尋性能的檢驗，再應用於結構工程 最佳化問題； 第二年計畫：進行本演算法應用於輪胎花紋排列最佳化問題。首先對輪胎花紋的噪 音譜理論分析與實際量測值進行檢討與比對，基於比對後之噪音譜分析模型下，再對第 一年所開發的新演算法提出一簡易變數轉換格式，使之適用於組合性最佳化問題 (Combination problems)－－低噪音輪胎花紋排列最佳化問題；如此，為低噪音輪胎花紋設 計建構出一最佳化程序。 第三年計畫：為克服族群式演算法的『維數的魔咒』，首先檢討此演算法於高維數 全域最佳化問題(Large scale global optimizations, LSGO)之搜尋特性以及可行性，再提出改 善策略，首先以100~ 1000 維數問題(CEC2005)檢討其搜尋性能，最後應用於系統辨識 問題之類神經網路之學習訓練。|
The population-based evolutionary algorithm, without adopting the rigorous mathematical model, has been developed generally by imitating systematical and logical thinking, such as the natural phenomena, the humanities and the social sciences as well as the animal ecology behaviors. The related algorithms having been developed based on the thinking and possessing a creditable performance include genetic algorithm, Ant Colony Optimization algorithm, Cultural Algorithm, and Particle Swarm Optimization algorithm, etc. Theses algorithms are able to solve multiple-extreme problems, which the conventional mathematical programming method fail to achieve. However, in the review literatures were found that the global optimal solution obtained by the population-based computation method sometimes fails to meet the precision acquired. Especially, as the number of design variables (n> 30) is increased, the difficulty of determining the reliable solution becomes incredibly hard to crack. The scenario is usually called as the suffering of “curse of dimensionality”. Further, the feature that the algorithm is coded literally for real variables fails to be directly applied for problems with discrete variables or for the combination problems or NP-problems, which are often found in practical wide-ranged applications, such as industrial engineering, business, and management. To deal with the problem of the curse of dimensionality and the NP problems, we propose a three-year project titled as” Study of an intelligent garbage-can decision-making model differential evolution algorithm and its applications”. In this project, the algorithm is going to be created by the system logic thinking as is the population-based evolutionary computation developed. Therefore, the work in the first year is going to develop a new algorithm able to give helpful solution to difficulties the present population-based computation algorithm faces. The new algorithm is created by incorporating a garbage-can decision-making strategy well known in social science into a difference evolutionary algorithm developed by Storn in 1997. The developed algorithm, named as IGCMDE, will be verified with benchmark problems of CEC2005, and then applied to optimizing several structural engineering problems. Applying the developed algorithm on designing a tire tread pattern with low noise as possible is the primary work in the second year. First, the tire tread's noise spectrum determined from the theoretical analysis is compared with experimental results. Then, a noise spectrum designing model out of the comparison is determined and set for the tire tread pattern to be designed. Given the model, the sequence optimization for the tire tread pattern is fundamentally a problem with discrete variables, i.e. a so-called combination problem. A variable transformation form has to be manipulated mathematically before applying the developed algorithm to the design. The design procedure for sequence optimization of the low noise tire tread pattern is set up and detailed in the work, which is believed to be a useful reference for the tire-tread designers. In the third year, we are planning to incorporate the space identification technique into the proposed algorithm IGCMDE to overcome the “curse of dimensionality” that the population-based evolutionary algorithms have encountered. To the author’s previous experiences, this additional technique to the original algorithm IGCMDE is believed to be able to solve problems with dimensions up to more than 500. In the work, we would like to raise problem dimensions up to more than 1000 while several benchmark test functions are tested. In the end, this modified algorithm is also applied to the training of weights of artificial neural network, and the performance of the modified algorithm on several case problems will be studied in the work.