開發改良式螞蟻演算法求解連續型最佳化問題

最佳化的應用在日常生活中比比皆是。所謂的最佳化是利用數學方法在函式限制式中找到最佳最好的數值。然而真實世界最佳化問題常常是高階且非線性的數學問題，傳統的數學理論跟方法無法求出確實的理論解。近年來啟發式演算法逐漸受到重視，因為這個演算法可以用來解決複雜的最佳化問題。在許多不同的啟發式演算法中，螞蟻演算法(ACO)在非連續型問題中是常被使用的熱門方法之一。本研究將演化式策略加入螞蟻演算法中，開發並提出運用於實數的連續型螞蟻演算法。經過不同的實測，本方法在穩定度跟精確度上都有優質的表現，證實本研究的方法可以運用到大維度的最佳化問題。

關鍵字

螞蟻演算法(ACO) ；非連續型問題；演化式策略

並列摘要

Optimization applications can be found easily in our daily life. Optimization is a mathematical practice that focuses on the finding the functional minima (or maxima) subject to functional constraints. However, most real life applications are high orders and nonlinear after converting to mathematical formula. Traditional and theoretical mathematical approaches fail to the solutions to these problems. On the other hand, heuristic algorithm has gained more attentions as it can be used to fit this requirement and solve the complex optimization problems. Among the heuristic algorithms, the Ant Colony Optimization (ACO) is one of the popular methods use for optimization problems with discrete domain. In this study, we embed the evolutionary mechanism and develop an enhanced method to make ACO suitable for continuous optimization problem. Various benchmark problems have been tested to verify the robustness and accuracy. The results show this proposed approach can be applied to large dimensional optimization problem with continuous domain.