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A method for simulation optimization with applications in robust process design and locating supply chain operations.

機(jī)譯：一種用于仿真優(yōu)化的方法，可用于穩(wěn)健的流程設(shè)計(jì)和定位供應(yīng)鏈運(yùn)營。

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This dissertation contains the first proof of convergence of a genetic algorithm in the context of stochastic optimization. The class of stochastic optimization problems includes formulations in which the objective is an expected value, which can be evaluated using Monte Carlo methods. Growing computer power combined with methods presented here and elsewhere makes feasible the solution of many stochastic optimization problems with applications ranging from process design to facility location.; The dissertation also describes the proposed stochastic optimization method that combines a sequential ranking and selection procedure with an elitist genetic algorithm. A batching procedure is included to assure that batch means of solutions achieve approximate normality. The proposed method is proven under the normality assumption to converge in the long run to identify and maintain solutions with objective values within an acceptable difference, Δ, from the global optimal solution with probability greater than an acceptable probability, P*. Computational results illustrate that the proposed algorithm achieves promising performance compared with alternatives for a variety of problems with minimal changes.; The first application is on the stochastic optimization for “robust” engineering process design decisions making. By robust we mean designs that maximize the expected utility taking into account variation of “noise factors”.; A methodology for robust process design is presented based on direct minimization of the expected loss in some cases using the proposed optimization heuristics. The proposed methods are compared with alternatives including methods based on Taguchi's signal-to-noise ratios. Several formulations of the loss are explored. The method is illustrated through its application to the design of robotic gas metal arc-welding parameter settings.; The second application is a simulation optimization method applied to decision making about where to locate facilities and how to transport products in a supply chain. This problem is shown to be a stochastic generalized assignment problem for which a bound is presented. We also propose a genetic algorithm, for cases in which bounds are available, that offers the possibility of stopping while guaranteeing that a solution with objective value within an acceptable difference, Δ, of the optimal value is found with probability greater than P*.
機(jī)譯：本文包含了隨機(jī)優(yōu)化情況下遺傳算法收斂性的第一個(gè)證明。一類隨機(jī)優(yōu)化問題包括目標(biāo)為期望值的公式，可以使用蒙特卡洛方法進(jìn)行評估。不斷增長的計(jì)算機(jī)功能以及在此和其他地方介紹的方法使解決許多隨機(jī)??優(yōu)化問題的方法可行，其應(yīng)用范圍從過程設(shè)計(jì)到設(shè)施定位。論文還描述了提出的隨機(jī)優(yōu)化方法，該方法將順序排序和選擇過程與精英遺傳算法相結(jié)合。包括分批過程，以確保溶液的分批均值達(dá)到近似正態(tài)。該方法在正態(tài)性假設(shè)下證明可以長期收斂，以識別和保持目標(biāo)值的解決方案與全局最優(yōu)解的可接受差值Δ在可接受的差值Δ之內(nèi)，且概率大于可接受的概率 P *。計(jì)算結(jié)果表明，與各種問題的替代方案相比，所提出的算法在變化最小的情況下具有令人滿意的性能。第一個(gè)應(yīng)用是針對“穩(wěn)健”工程流程設(shè)計(jì)決策的隨機(jī)優(yōu)化。 “健壯”是指在考慮“噪聲因素”變化的情況下最大化預(yù)期效用的設(shè)計(jì)。在某些情況下，使用擬議的優(yōu)化啟發(fā)法，基于對預(yù)期損失的直接最小化，提出了一種健壯的過程設(shè)計(jì)方法。將提出的方法與包括基于田口信噪比的方法在內(nèi)的替代方法進(jìn)行比較。探索了損失的幾種公式。通過將該方法應(yīng)用于氣體金屬自動(dòng)電弧焊參數(shù)設(shè)置設(shè)計(jì)中進(jìn)行了說明。第二個(gè)應(yīng)用程序是一種模擬優(yōu)化方法，用于決策關(guān)于在何處放置設(shè)施以及如何在供應(yīng)鏈中運(yùn)輸產(chǎn)品的決策。該問題顯示為一個(gè)隨機(jī)的廣義分配問題，給出了一個(gè)邊界。對于存在邊界的情況，我們還提出了一種遺傳算法，該算法提供了停止的可能性，同時(shí)保證找到的目標(biāo)值在最優(yōu)值的可接受差值Δ之內(nèi)的解決方案的概率大于

*。

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