Gradient-Based Simulation Optimization

We present a review of methods for simulation optimization. In particular, we focus on gradient-based techniques for continuous optimization. We demonstrate the main concepts using as an example the multidimensional newsvendor problem. We also discuss mathematical techniques and results that are useful in verifying and analyzing the simulation optimization procedures

[1]  H. Robbins A Stochastic Approximation Method , 1951 .

[2]  Michael C. Fu,et al.  Feature Article: Optimization for simulation: Theory vs. Practice , 2002, INFORMS J. Comput..

[3]  A. Shapiro Monte Carlo Sampling Methods , 2003 .

[4]  Michael C. Fu,et al.  Conditional Monte Carlo , 1997 .

[5]  Fred W. Glover,et al.  Simulation optimization: a review, new developments, and applications , 2005, Proceedings of the Winter Simulation Conference, 2005..

[6]  D. Ruppert A Newton-Raphson Version of the Multivariate Robbins-Monro Procedure , 1985 .

[7]  Michael C. Fu,et al.  A comparison of perturbation analysis techniques , 1996, WSC.

[8]  Michael A. Zazanis,et al.  Convergence Rates of Finite-Difference Sensitivity Estimates for Stochastic Systems , 1993, Oper. Res..

[9]  Huifen Chen,et al.  Stochastic root finding via retrospective approximation , 2001 .

[10]  Pierre L'Ecuyer,et al.  On the Convergence Rates of IPA and FDC Derivative Estimators , 1990, Oper. Res..

[11]  M. Fu Convergence of a stochastic approximation algorithm for the GI/G/1 queue using infinitesimal perturbation analysis , 1990 .

[12]  Michael C. Fu,et al.  Optimization via simulation: A review , 1994, Ann. Oper. Res..

[13]  Charles Leake,et al.  Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method , 1994 .

[14]  Stephen M. Robinson,et al.  Sample-path optimization of convex stochastic performance functions , 1996, Math. Program..

[15]  H. Kushner,et al.  Stochastic Approximation and Recursive Algorithms and Applications , 2003 .

[16]  J. Kiefer,et al.  Stochastic Estimation of the Maximum of a Regression Function , 1952 .

[17]  Peter W. Glynn,et al.  Optimization Of Stochastic Systems Via Simulation , 1989, 1989 Winter Simulation Conference Proceedings.

[18]  J. Banks,et al.  Handbook of Simulation , 1998 .

[19]  J. Michael Harrison,et al.  Multi-Resource Investment Strategies: Operational Hedging Under Demand Uncertainty , 1997, Eur. J. Oper. Res..

[20]  Sigrún Andradóttir,et al.  A review of simulation optimization techniques , 1998, 1998 Winter Simulation Conference. Proceedings (Cat. No.98CH36274).

[21]  P. L’Ecuyer,et al.  A Unified View of the IPA, SF, and LR Gradient Estimation Techniques , 1990 .

[22]  Alexander Shapiro,et al.  Asymptotic Behavior of Optimal Solutions in Stochastic Programming , 1993, Math. Oper. Res..

[23]  P. L’Ecuyer,et al.  On the interchange of derivative and expectation for likelihood ratio derivative estimators , 1995 .

[24]  Nils Rudi,et al.  Newsvendor Networks: Inventory Management and Capacity Investment with Discretionary Activities , 2002, Manuf. Serv. Oper. Manag..

[25]  George L. Nemhauser,et al.  Handbooks in operations research and management science , 1989 .

[26]  Paul Glasserman,et al.  Gradient Estimation Via Perturbation Analysis , 1990 .

[27]  Boris Polyak,et al.  Acceleration of stochastic approximation by averaging , 1992 .

[28]  P. Glynn,et al.  Stochastic Optimization by Simulation: Convergence Proofs for the GI/G/1 Queue in Steady-State , 1994 .

[29]  Jason H. Goodfriend,et al.  Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method , 1995 .

[30]  Farhad Azadivar,et al.  Simulation optimization methodologies , 1999, WSC '99.

[31]  Harold J. Kushner,et al.  wchastic. approximation methods for constrained and unconstrained systems , 1978 .

[32]  Philippe L. Toint,et al.  Convergence theory for nonconvex stochastic programming with an application to mixed logit , 2006, Math. Program..

[33]  R. H. Smith Optimization for Simulation : Theory vs . Practice , 2002 .

[34]  Lee W. Schruben,et al.  Retrospective simulation response optimization , 1991, 1991 Winter Simulation Conference Proceedings..

[35]  Stephen M. Robinson,et al.  Analysis of Sample-Path Optimization , 1996, Math. Oper. Res..