臺灣博碩士論文加值系統

微分演化演算技術是一種有效且具強健性找尋全域最適解的方法。本法近年來雖已有不少成功的應用案例，但收斂速度不佳，收斂過於耗時，一直是其主要缺點。針對此一缺失，本研究嘗試以Babu與Angria所提出的改良式微分演化演算法為骨幹，藉由排除一定數量較差之標的向量，取代以同數量，以當下最佳標的向量周圍區域，所新生成之新標的向量。以進一步強化當下最佳值附近的搜尋，藉此提升整體收斂速度。透過求解數個標準測試樣板問題的結果得知：此局部取代策略確可大幅降低目標函數呼叫的次數，有效提昇收斂效率。由於，在100次利用不同起始向量的運算中，仍能保有高成功率。證明結合局部取代策略的改良式微分演化法依然保有不錯的強健性。此外，本研究也利用此改良後之微分演算法，求解化學工程中之程序設計與整合的最佳化問題。測試結果顯示：改良後之方法，不僅可快速收斂，強健性佳之外，在不同精確度要求下，仍可維持極佳的數值品質。

Differential evolution (DE) algorithm is a very effective and robust global optimizer. Even there are any successful applications proposed in the past several years, however, the basic DE like other meta-heuristics also encounters the difficulty of too slow convergence. Based on the modified differential evolution proposed by Babu and Angria, we suggest in this study replacing a proportion of worse target vectors by the same numbers of new ones randomly generated from the neighborhood of the current best target vector. The improvement is named as local replacement policy.By testing a lot of benchmark problems, the resuts show that such improvement may largely reduce the numbers of function evaluation.After 100 tests with different initial guesses, the high successful rate also justifies the modified DE with local replacement strategy still keeps the robustness.
We also apply the proposed method to optimize the process design and synthesis problems in chemical engineering. The results show that besides having very nice convergent rate, the proposed method may acquire the solutions with very nice numerical accuacy.

第一章 緒論 1
1.1. 研究動機 1
1.2. 文獻回顧 2
1.3. 章節配置 6
第二章 介紹 7
2.1. 基本微分演化演算法 7
2.1.1. 基本DE演算流程 12
2.2. 改良式微分演化演算法 14
2.2.1. MDE演算流程 16
2.3. 改良對策 17
2.3.1. 基本DE整合局部取代後之演算流程 19
2.3.2. MDE整合局部取代後之演算流程 22
第三章 效能評估 25
3.1. 無約束條件最適問題之測試及評估 27
3.1.1. 演算法結果探討 27
第四章 程序整合與設計問題 95
4.1. 各類具約束條件之最適化問題分類 96
4.2. 具(不)等式約束條件之非線性最適化問題 98
4.2.1. 具(不)等式約束條件最適化問題之求解 102
4.3. 具整數之非線性最適化問題 136
4.3.1. 整數規劃問題之結果探討 137
第五章 結論 169
參考文獻 171

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