PSO-SA混合法於結構多目標最佳化之應用

Multiobjective Optimization of Structure by Hybrid PSO-SA Method

黃宗鴻(Zong-Hong Huang)

指導教授 ： 張永康

淡江大學/工學院/航空太空工程學系碩士班/碩士(2013年)

https://doi.org/10.6846/TKU.2013.00838

摘要

本研究應用PSO-SA混合法於結構多目標最佳化設計中，粒子群演算法是種模仿自然界鳥類覓食的現象進行問題求解之步驟，屬於仿生演算法一種，此演算法具有快速搜尋且較為簡易設定的優點並具有全域搜尋之特色。模擬退火法主要是根據統計熱力學的原理，模擬材料在進行退火的過程中，逐漸達到最低溫狀態的現象，並透過波茲曼函數判斷問題解被接受機率，如此能有助於跳脫區域最佳解往全域最佳解靠近的機會。

本研究將結構多目標最佳化問題轉換為數學函數，利用線性遞減式慣性權重更新搜尋速度及位置以獲得最佳值，再應用模擬退火法判斷是否跳脫此最佳解以避免落入區域最佳解之中。在求解過程中，發現本方法應用於多目標結構最佳化設計問題時，能有效的在多目標問題中搜尋出最佳解並且同時滿足限制條件。

本研究以FORTRAN程式與ANSYS有限元素分析軟體中的APDL語法結合成一系統程式。並透過六個不同範例驗證了PSO-SA混合法於結構多目標最佳化設計上皆有不錯之成效。

關鍵字

粒子群演算法 ； 模擬退火法 ； 多目標最佳化

並列摘要

The PSO-SA hybrid method was applied to multiobjective optimum design of structure in this study. Particle Swarm Optimization is to mimic the behavior of birds finding a good path to the food, which is one of the artificial biological algorithms. Thus, it has the merits of converge efficiently and programming easily. The advantage of Particle Swarm Optimization (PSO) is it global search technique. The Simulated Annealing (SA) method is based on the principle of statistical thermodynamic. That is material during the annealing process can be reached most cryogenic state phenomenon. The possibility of local optimum jump to global optimum can be determined by the probability of the Bozeman function.
The structural optimization problem can be transformed into a mathematical function. The new design can be obtained by using the linear decreasing inertia weight to update velocity and position of particles. After the optimal solution was obtained, the strategy of SA method is initiated to determine whether this optimal solution should be neglected or not . In the Numerical examples, the study showed that the computational efficiency can be improved and the constraint is satisfied.
　　A systematic program was developed by FORTRAN and APDL of ANSYS software. The optimum results of six different multiobjective examples showed that the PSO-SA hybrid methods are reasonable compared to other references.

並列關鍵字

Particle Swarm Optimization ； Simulated Annealing ； Multiobjective Optimization

參考文獻

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