Optimization via simulation: A review

The possibilities of combining simulation and optimization are vast and the appropriate design highly depends on the problem characteristics. Therefore, it is very important to have a good overview of the different approaches. The taxonomies and classifications proposed in the literature do not cover the complete range of methods and overlook some important criteria. We provide a taxonomy that aims at giving an overview of the full spectrum of current simulation-optimization approaches. Our study may guide researchers who want to use one of the existing methods, give insights into the cross-fertilization of the ideas applied in those methods and create a standard for a better communication in the scientific community. Future reviews can use the taxonomy here described to classify both general approaches and methods for specific application fields.

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“…However, only a single replicate is used to obtain each estimate. The procedure switches to a pure SA when the optimum is approached [6].…”

Section: Gradient Surface Methods (Gsm)mentioning

confidence: 99%

“…Other frameworks focused on the optimization problem, i.e. the solution space and objective function [6,7,8,9]. Shanthikumar and Sargent [10] suggested a classification schema, according to the hierarchical structure of both simulation and optimization models.…”

Section: Introductionmentioning

confidence: 99%

Hybrid simulation–optimization methods: A taxonomy and discussion

Figueira¹,

Almada-Lobo²

2014

Simulation Modelling Practice and Theory

213

104

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“…12) whereK is a large index in S and t(K) is a count number of indexes in the summation term. Sincê f N∞ is bounded below (Assumption 2), we know thatf N∞ (xK) −f N∞ (xK +1 ) is a finite value.…”

Section: Convergence Analysis Of the Algorithmmentioning

confidence: 99%

“…Historically, the parameters are chosen by selecting the best from a set of candidate parameter settings. Simulation-based optimization [12,13,20] is an emerging field which integrates optimization techniques into simulation analysis. The corresponding objective function is an associated measurement of an experimental simulation.…”

Section: Introductionmentioning

confidence: 99%

Variable-Number Sample-Path Optimization

Deng

Ferris

2007

Math. Program.

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The sample-path method is one of the most important tools in simulation-based optimization. The basic idea of the method is to approximate the expected simulation output by the average of sample observations with a common random number sequence. In this paper, we describe a new variant of Powell's UOBYQA (Unconstrained Optimization BY Quadratic Approximation) method, which integrates a Bayesian Variable-Number Sample-Path (VNSP) scheme to choose appropriate number of samples at each iteration. The statistically accurate scheme determines the number of simulation runs, and guarantees the global convergence of the algorithm. The VNSP scheme saves a significant amount of simulation operations compared to general purpose 'fixed-number' sample-path methods. We present numerical results based on the new algorithm.Keywords sample-path method, simulation-based optimization, Bayesian analysis, trust region method Dedication This paper is dedicated to Stephen Robinson on the occasion of his 65th birthday. The authors are grateful for his encouragement and guidance over the past two decades, and the inspirational work he has done in the topic of this paper.

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“…Most of the early works concerned variants of the stochastic approximation (SA) technique; see Ref. 10 and the references therein for a survey. In particular, we mention the pioneering works in Refs.…”

mentioning

confidence: 99%

Convergence analysis of gradient descent stochastic algorithms

Shapiro

Wardi

1996

J Optim Theory Appl

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Abstract. This paper proves convergence of a sample-path based stochastic gradient-descent algorithm for optimizing expected-value performance measures in discrete event systems. The algorithm uses increasing precision at successive iterations, and it moves against the direction of a generalized gradient of the computed sample performance function. Two convergence results are established: one, for the case where the expected-value function is continuously differentiable; and the other, when that function is nondifferentiable but the sample performance functions are convex. The proofs are based on a version of the uniform law of large numbers which is provable for many discrete event systems where infinitesimal perturbation analysis is known to be strongly consistent.

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Optimization via simulation: A review

Cited by 337 publications

References 94 publications

Hybrid simulation–optimization methods: A taxonomy and discussion

Hybrid simulation–optimization methods: A taxonomy and discussion

Variable-Number Sample-Path Optimization

Convergence analysis of gradient descent stochastic algorithms

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