仿生免疫演算法的無限制條件最佳化及應用

Unsonstrained Optimization by Developing Immune Algorithms and Applications

趙宜奕(Yi-Yi Chao)

指導教授 ： 史建中

淡江大學/工學院/機械與機電工程學系碩士班/碩士(2009年)

https://doi.org/10.6846/TKU.2009.00523

摘要

本文以基於對抗多等級病毒入侵的生物免疫系統為主要理論基礎，建構同步求解多個極值解的免疫演算模型，並模仿免疫系統的生殖、演化及記憶能力，開發非梯度搜尋方法的仿生免疫最佳化設計及程序，以求解函數全部極值點的求解方法為主要目標。免疫演算法以模仿免疫細胞的基因組成，採用體細胞高度突變及基因重組等運作模式，對應至最佳化數學型式可形成增殖、突變、辨識與重組等運算子，其中突變運算仿造免疫細胞的輕鏈、重鏈突變，可依目標函數值計算搜尋點合適的突變量。本文使用群集策略作為辨識與重整極值點的主要依據，求解過程中以目標函數值劃分多等級的極值點，具有良好的區域極值保存能力。以不同類型多極值函數進行演算法分析與探討，包含5個參數的設定與調整策略。以經過調整的參數進行數值分析，結果證實本文多極值免疫最佳化解題程序可求得全部極值點，成功仿效免疫系統對抗多等級病毒的能力。
以本文所發展的多極值免疫最佳化程序，應用於桁架拓樸設計與分析，提出求解具有限制條件的桁架型態及結構設計方法，採用二階段設計程序。第一階段取得各種排列的桁架設計型態，再經第二次型態與結構尺寸同步設計程序，最終可得到多種型態的設計結果，每種排列結構即為不同尺寸的極值點。以二維及三維桁架結構題目進行探討，證明本文的多極值求解方法相當適用，結果與文獻相同或更佳之設計結果，同時可得到數種型態的多極值解供使用者選用。
上述桁架型態與結構最佳設計程序以無限制條件的多極值免疫演算法為理論基礎，求解過程中對於不符合限制條件的搜尋點捨去，不進行限制條件的處理。設計結果顯示此處理方法為可行的，但效率性有待提升，未來研究可考慮限制條件的處理與整合成一階段的桁架求解程序，進一步應用於大型多設計變數的桁架設計題目。

關鍵字

進化式最佳化 ； 免疫系統 ； 多極值最佳化 ； 無限制條件最佳化 ； 拓樸結構設計

並列摘要

The main purpose of this thesis is to develop a non-gradient based optimization algorithm by utilizing the immune theory for solving multiple optimum points including global and local optimums in the feasible domain. The somatic hyper mutation and recombination are simulated in the algorithm development of evolutionary process for creating diversifying off springs. This evolution technique is fundamental for constructing the effective and robust optimization searching algorithm. Another critical investigation focuses on the method of locating both global and local optimums. In the thesis, a parallel clustering concept combines the regeneration and yielding to the most probable potential local optimal points. A variety functions are experimented for further improving the proposed algorithm. Five design parameters are required to setup for solving the problem. The turning strategy of selecting those parameters is under investigation in the thesis.
The developed algorithm is then applied to several topological optimization problems containing plane truss and space truss design. For applying the proposed algorithm, a two-stage design process is proposed herein. In the first stage, the structural topology is the only concern target. In the second stage, the size optimization is performed under the fixed topological structure. The final results shows the identical performances as compare to published papers in the research journal. The results of some problems appear even better performance than that in published papers.

並列關鍵字

Evolutionary optimization ； Immune system ； Multiple optimization ； Unconstrained optimization ； Topological structural design

參考文獻

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