Optimal allocation of simulation experiments in discrete stochastic optimization and approximative algorithms |
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| Institution: | 1. Institut für Statistik, Operations Research und Computerverfahren, Universität Wien, Universitätsstraβe 5/9, A-1010 Vienna, Austria;2. IIASA, Laxenburg, Austria;1. Institute of Applied Mathematics, College of Science, Huazhong Agricultural University, Wuhan 430070, China;2. Faculty of Science and Technology, University of Macau, Macau 999078, China;1. School of E-commerce and Logistics Management, Henan University of Economics and Law, Zhengzhou, Henan 450000, China;2. Department of Electronics and Information, Zhengzhou Sias University, Zhengzhou, Henan 450000, China;3. EED, Arian Company, Yerevan, Armenia;1. Department of Electrical Engineering, Iran University of Science and Technology, Iran;2. Department of Management & Innovation Systems, University of Salerno Via Giovanni Paolo II, 132, Fisciano (SA) - 84084 Italy;3. Department of Electrical and Electronic Engineering Science, University of Johannesburg, Johannesburg, South Africa |
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| Abstract: | Approximate solutions for discrete stochastic optimization problems are often obtained via simulation. It is reasonable to complement these solutions by confidence regions for the argmin-set. We address the question how a certain total number of random draws should be distributed among the set of alternatives. Two goals are considered: the minimization of the costs caused by using a statistical estimate of the true argmin, and the minimization of the expected size of the confidence sets. We show that an asymptotically optimal sampling strategy in the case of normal errors can be obtained by solving a convex optimization problem. To reduce the computational effort we propose a regularization that leads to a simple one-step allocation rule. |
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