本研究為解決非線性可靠度限制式之最佳化問題(Reliability Based Design Optimization)，簡稱RBDO，有單迴圈(Single loop)、雙迴圈(Double loop)及去偶合(decouple)的模式，本研究利用雙迴圈解決目前遇到的問題，其外部迴圈為最佳化程式、內部迴圈為可靠度分析。
實務上桿件尺寸一般是選用標準規格之桿件，自訂規格訂製困難，導致成本提高，造成問題之設計參數呈間斷型態，再加上搜尋空間相當龐大、桿件尺寸的誤差、外力之不確定性。傳統利用微分進行求解的方法有Sequential quadratic programming (SQP) algorithm及Generalized Reduced Gradient (GRG) algorithm，本研究有考慮桿件挫屈的情形，無法使用微分求解的演算法。種種不利傳統方法進行求解的因素，故本研究使用四種超啟發式(Meta-heuristic)演算法相互進行比較，分別為基因演算法(GA)、質群演算法(PSO)、禁忌搜尋(TS)、模擬退火(SA)，把可靠度評估之機率加入成本考量中，以失效成本與材料成本為目標，比較各方法在這類問題上之適用性及求解表現。
本研究桿件之設計參數參考中國國家標準(CNS)所頒布之CNS 4435,G 3102桿件尺寸列表，對於一個十桿桁架結構進行討論，來判斷所提出之四種超啟發式演算法，在解決這種問題上之優劣程度。經過進行比較後發現模擬退火法與禁忌搜尋法有較高的機會搜尋到成本低的答案，主要取決於其搜尋機制為鄰近搜尋，在一定計算時間內更新最佳解次數較多。

Normally when solving Reliability Based Design Optimization (RBDO) problems. There are three common methods single loop, Double loop and decouple.In this paper we utilize double loops to solve the encountering problems. Using the outer loop as the optimization program, and the inner loop as the reliability analysis.
In field applications member bars are usually standard customized. Creating custom made parts is extremely difficult. In result, making the costs go higher and causing the problem design parameters to be discrete. Not mentioning it might also create large search spaces, inaccurate sized member bars or unexpected outer force.
Traditional methods like Sequential quadratic programming (SQP) algorithm and Generalized Reduced Gradient (GRG) algorithm use differential methods to approach the solution. This paper has considered that buckling in the member bars are unable to use differential algorithms to solve the problem. And after considering the disadvantages of traditional methods. This paper uses four Meta-heuristic algorithms and conducts a comparison among them. The four methods are Genetic Algorithm , Practical Swarm Optimization, Taboo Search (TS)、Simulated Annealing (SA). Including the probability of reliability evaluation into consideration. Establishing failure costs and material costs as the major objectives. And comparing the applicability and solving performance among each of the methods.
The member bar design parameters conducted in this paper are under CNS (Chinese National Standards) 4435 and G 3102 member bar standards. In this paper we discuss under the framework of ten rigid girders. Determine the advantages and disadvantages of the four Meta-heuristic algorithms. And judge which have a better performance in this sort of problem.

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