本研究主要是提出一個源自於梯度搜尋方法之萬用演算法。梯度的最佳化方法主要應用於尋找極值以及最佳解，本研究將梯度方法進行修改，並建構一個以梯度定理為基礎更新規則的萬用演算法。此方法名為梯度進化演算法(gradient evolution (GE) algorithm)，其透過一組向量來搜尋搜索空間，包含下列三個步驟：向量之更新、跳躍及重整。向量更新為梯度進化法的主要更新法則，搜尋方向是以牛頓逼近法(Newton-Raphson)來決定；向量之跳躍與重整能夠避免陷入區域最佳解。本研究分別執行三項實驗及運用十五種測試函式驗證梯度進化演算法。首先，評估各參數設定對於結果的影響程度，同時選定最佳參數設定。後續對原始與修正過的萬用演算法進行比較，實驗結果顯示，於大多數標竿資料測試的結果中，相較於粒子群最佳化演算法(particle swarm optimization algorithm)、差分進化法(differential evolution algorithm)、人工蜂群演算法(artificial bee colony algorithm)及連續型基因演算法(continuous genetic algorithm)，梯度進化演算法能擁有優於或是與上列方法一樣好的表現。最後，將梯度進化演算法加入K平均演算法(K-means algorithm)，應用於解決分群問題。本研究提出兩種分群方法，分別為單目標和多目標分群方法，運用標竿資料集測試之實驗結果顯示，以梯度進化演算法為基礎之K平均分群法(GE-based K-means algorithm)能取得比其他以萬用演算法為基礎之分群法更佳的分群結果。

This study presents a new metaheuristic method that is derived from the gradient-based searching method. In an exact optimization method, the gradient is used to find extreme points as well as the optimal point. This study modifies the gradient method and creates a new metaheuristic method that uses a gradient theorem as its basic updating rule. This new method is named gradient evolution (GE) algorithm which explores the search space using a set of vectors and includes three major operators: vector updating, jumping and refreshing. Vector updating is the main updating rule in the GE algorithm. The search direction is determined using the Newton-Raphson method. Vector jumping and refreshing allow this method to avoid local optima. In order to evaluate the performance of the GE algorithm, three different experiments are conducted by using fifteen test functions. The first experiment determines the influence of parameter settings on the result. It also determines the best parameter setting. There follows a comparison between the basic and improved metaheuristic methods. The experimental results show that the GE algorithm performs better than, or as well as other metaheuristics, such as particle swarm optimization algorithm, differential evolution algorithm, artificial bee colony algorithm and continuous genetic algorithm, for most of the benchmark problems tested. Furthermore, the proposed GE algorithm is applied to clustering problem. In order to solve the clustering problem, the GE algorithm is embedded with K-means algorithm. There are two clustering approaches presented in this study, single-objective and multi-objective clustering methods. The experimental results using benchmark datasets indicate that GE-based K-means algorithm outperforms other metaheuristic-based K-means algorithms.

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