混沌理論混合粒子群搜尋法之結構離散尺寸最佳化設計

戴才淇(Tsai-chi Dai)

指導教授 ： 莊德興

國立中央大學/工學院/土木工程學系/碩士(2014年)

摘要

本文主要是針對連續數計變數問題和離散設計變數問題之結構尺寸最佳化設計，提出以群體智能和混沌理論的新組合，應用在桁架與構架結構。混沌搜尋法(CSP)從許多不同的生物群體和混沌理論的靈感形成，這方法是一種多階段最佳化技巧，採用混沌理論的兩個階段，在第一階段控制粒子群搜尋法(PSO)的參數稱為(CPVPSO)，第二階段是局部搜尋(CLSPSO)，有些桁架結構利用CSP演算法與高階啟發式搜尋法的結果進行比較，展現出CSP的有效性，且和其他高階啟發式搜尋法類似，在本文中，藉由連續設計變數問題和離散設計變數問題，探討本文方法的優劣。比較算例之結果發現，在求解連續設計變數及離散設計變數之最佳化問題都有穩定表現，求解品質較佳。

關鍵字

混沌理論 ； 混沌映射 ； 混沌粒子搜尋 ； 粒子群演算(搜尋)法 ； 啟發式搜尋法

並列摘要

This article is devoted to the presentation of the optimum design with continuous and discrete variables. A new combination of swarm intelligence and chaos theory is presented for optimal design of truss structures. Here the tendency to form swarms appearing in many different organisms and chaos theory has been the source of inspiration, and the algorithm is called chaotic swarming of particles (CSP). This method is a kind of multi-phase optimization technique which employs chaos theory in two phases, in the first phase it controls the parameter values of the particle swarm optimization (CPVPSO) and the second phase is utilized for local search (CLSPSO). Some truss structures are optimized using the CSP algorithm, and the results are compared to those of the other meta-heuristic algorithms showing the effectiveness of the new method. It’s similar to other meta-heuristic algorithms. The design examples including structure design of continuous and discrete variable problems. The results show the CSP algorithm is reliable, and solution quality in the literature is comparable to oter optimal methods.

並列關鍵字

Chaos theory ； Chaotic map ； Chaotic swarming of particles ； Particle swarm optimization ； Meta-heuristic searching method

參考文獻

[1] Alatas, B., Akin, E. and Ozer, A. B., (2009) “Chaos Embedded Particle Swarm Optimization Algorithms,” Chaos Solit Fract, Vol. 40, pp. 1715–1734.

[2] Alatas, B. and Akin, E., (2009) “Chaotically Encoded Particle Swarm Optimization Algorithm and Its Applications,” Chaos Solit Fract, Vol. 41, pp. 939–950.

[3] Alatas, B., (2010a) “Chaotic Bee Colony Algorithms for Global Numerical Optimization,” Expert Syst Appl, Vol 37, pp. 5682–5687.

[4] Alatas, B., (2010b) “Chaotic Harmony Search Algorithm,” Appl Math Comput, Vol. 29(4), pp. 2687–2699.

[5] Alatas, B., (2011) “Uniform Big Bang-Chaotic Big Crunch Optimization,” Commun Nonlinear Sci Numer Simul, Vol. 16(9), pp. 3696–3703.