Simulation-based methods for stochastic optimization
In this work we discuss stochastic optimization problems where the objective is to minimize the expected value of a function of a vector parameter, subject to constraints. We study a general framework for solving that type of problems, whose central idea is to replace the expected value in the objec...
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| Format: | Dissertation |
| Sprache: | Englisch |
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ProQuest Dissertations & Theses
01.01.1998
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| Abstract | In this work we discuss stochastic optimization problems where the objective is to minimize the expected value of a function of a vector parameter, subject to constraints. We study a general framework for solving that type of problems, whose central idea is to replace the expected value in the objective with a sample average of the function, and then to minimize the corresponding approximation by using a nonlinear programming algorithm. We discuss how to determine convenient sample sizes and stopping criteria that yield a reasonable solution without spending too much computational effort. The key for the derivation of those procedures is the use of techniques from Statistics and Simulation. We apply the proposed method to two different classes of problems. The first one is the class of 2-stage stochastic programming problems with recourse in which the random variables have continuous distributions, whereas in the second application we consider the problem of finding optimal release times of jobs in a single-line production environment where the service times at each station are random and the machines are subject to failures. Numerical results are presented for both applications suggesting efficacy of the method. We also discuss the estimation of derivatives of performance measures of systems in steady- state. An important class of processes for which the steady-state exists is that of regenerative systems . Most of the work found in the literature deals with differentiable systems, but here we consider the nondifferentiable case and present conditions for the directional derivatives to regenerate together with the original process. The significance of this result is that it allows the derivation of a procedure for estimation of the directional derivatives of the expected value function. We study other implications of these results. |
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| AbstractList | In this work we discuss stochastic optimization problems where the objective is to minimize the expected value of a function of a vector parameter, subject to constraints. We study a general framework for solving that type of problems, whose central idea is to replace the expected value in the objective with a sample average of the function, and then to minimize the corresponding approximation by using a nonlinear programming algorithm. We discuss how to determine convenient sample sizes and stopping criteria that yield a reasonable solution without spending too much computational effort. The key for the derivation of those procedures is the use of techniques from Statistics and Simulation. We apply the proposed method to two different classes of problems. The first one is the class of 2-stage stochastic programming problems with recourse in which the random variables have continuous distributions, whereas in the second application we consider the problem of finding optimal release times of jobs in a single-line production environment where the service times at each station are random and the machines are subject to failures. Numerical results are presented for both applications suggesting efficacy of the method. We also discuss the estimation of derivatives of performance measures of systems in steady- state. An important class of processes for which the steady-state exists is that of regenerative systems . Most of the work found in the literature deals with differentiable systems, but here we consider the nondifferentiable case and present conditions for the directional derivatives to regenerate together with the original process. The significance of this result is that it allows the derivation of a procedure for estimation of the directional derivatives of the expected value function. We study other implications of these results. |
| Author | Homem de Mello, Tito |
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