使用啟發式演算法求解最佳化實驗設計

Abstract

啟發式演算法被廣泛應用於解決許多最佳實驗設計問題。在本文中, 我們運用啟發式演算法求解四種最佳化試驗設計問題的例子。首先, 我們提出並說明這四個例子, 並簡述所使用於比較的演算法, 如蝙蝠演算法, 杜鵑鳥搜索演算法, 基因演算法, 模擬退火演算法, 人工蜂群演算法, 螢火蟲演算法, 音諧搜索演算法和粒子群優化演算法。介紹完後, 我們提出四種例子的比較數值結果並進一步作討論。最後, 從數值結果顯示與其他演算法相比較下, 杜鵑鳥搜索演算法和粒子群優化演算法有最佳的性能。這些數值研究僅針對此篇文章所提出的例 子, 可能並不適用於其他的例子。

Metaheuristic algorithms are widely used in solving many optimal experimental design problems. In this paper, we demonstrate the metaheuristic algorithms to construct four optimal experimental designs. First, we proposed the four examples for optimization design problems and presented the outlines of algorithm for comparison such as bat-inspired algorithm, cuckoo search, genetic algorithm, simulated annealing, artificial bee colony algorithm, firefly algorithm, harmony search and particle swarm optimization. After stated the algorithms, the numerical results of the comparison for the four examples are presented and discussed further. Finally, the conclusion suggested that cuckoo search and particle swarm optimization have the best performance in contrast with the other algorithms from the numerical results. The conclusions are drawn from the specific numerical studies and may not apply to other examples.