Robust parameter design optimization of simulation experiments using stochastic perturbation methods

Stochastic perturbation methods can be applied to problems for which either the objective function is represented analytically, or the objective function is the result of a simulation experiment. The Simultaneous Perturbation Stochastic Approximation (SPSA) method has the advantage over similar methods of requiring only two measurements at each iteration of the search. This feature makes SPSA attractive for robust parameter design (RPD) problems where some factors affect the variance of the response(s) of interest. In this paper, the feasibility of SPSA as a RPD optimizer is presented, first when the objective function is known, and then when the objective function is estimated by means of a discrete-event simulation.

[1]  Csaba Szepesvári,et al.  Universal parameter optimisation in games based on SPSA , 2006, Machine Learning.

[2]  Vincent D. Blondel,et al.  Proceedings of the 2000 American Control Conference , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[3]  Elsayed A. Elsayed,et al.  Analysis and control of production systems , 1993 .

[4]  Madhav Erraguntla,et al.  Using Simulation for Robust System Design , 1995, Simul..

[5]  J. Spall.  Multivariate stochastic approximation using a simultaneous perturbation gradient approximation , 1992 .

[6]  L. Gerencsér.  SPSA with state-dependent noise-a tool for direct adaptive control , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[7]  So Young Sohn,et al.  Robust design of server capability in M/M/1 queues with both partly random arrival and service rates , 2002, Comput. Oper. Res..

[8]  Julian Scott Yeomans,et al.  Automatic generation of efficient policy alternatives via simulation-optimization , 2002, J. Oper. Res. Soc..

[9]  Bernhard Sendhoff,et al.  Robust Optimization - A Comprehensive Survey , 2007 .

[10]  Ana Karina,et al.  Stochastic Perturbation Methods for Robust Optimization of Simulation Experiments , 2008 .

[11]  James C. Spall,et al.  Introduction to stochastic search and optimization - estimation, simulation, and control , 2003, Wiley-Interscience series in discrete mathematics and optimization.

[12]  M. Fu,et al.  Optimization of discrete event systems via simultaneous perturbation stochastic approximation , 1997 .

[13]  R. J. Mayer,et al.  Using the Taguchi paradigm for manufacturing design using simulation experiments , 1992 .

[14]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[15]  Waraporn. Ittiwattana,et al.  A Method for Simulation Optimization with Applications in Robust Process Design and Locating Supply Chain Operations , 2002 .

[16]  R. D. Hurrion,et al.  An example of simulation optimisation using a neural network metamodel: finding the optimum number of kanbans in a manufacturing system , 1997 .

[17]  G. Pflug.  Optimization of Discrete-Event Systems , 1993 .

[18]  C. N Bouza,et al.  Spall, J.C. Introduction to stochastic search and optimization. Estimation, simulation and control. Wiley Interscience Series in Discrete Mathematics and Optimization, 2003 , 2004 .

[19]  Fahimeh Rezayat.  On the use of an SPSA-based model-free controller in quality improvement , 1995, Autom..

[20]  D. C. Chin,et al.  Comparative study of stochastic algorithms for system optimization based on gradient approximations , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[21]  Michel Verhaegen,et al.  Proceedings of the 37th IEEE Conference on Decision and Control , 1998 .

[22]  Daniel E. Rivera,et al.  Simulation-based optimization of process control policies for inventory management in supply chains , 2006, Autom..

[23]  D. Hutchison.  On an Efficient Distribution of Perturbations for Simulation Optimization using Simultaneous Perturbation Stochastic Approximation , 2002 .

[24]  Enrique Del Castillo,et al.  Process Optimization: A Statistical Approach , 2007 .

[25]  Joseph J. Pignatiello,et al.  An experimental design strategy for designing robust systems using discrete-event simulation , 1991, Simul..

[26]  Jorge J. Moré,et al.  Testing Unconstrained Optimization Software , 1981, TOMS.

[27]  L. Gerencsér,et al.  Stochastic approximation on discrete sets using simultaneous difference approximations , 2004, Proceedings of the 2004 American Control Conference.

[28]  Payman Sadegh,et al.  Constrained optimization via stochastic approximation with a simultaneous perturbation gradient approximation , 1997, Autom..

[29]  James C. Spall,et al.  A neural network controller for systems with unmodeled dynamics with applications to wastewater treatment , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[30]  Christos G. Cassandras,et al.  Ordinal optimisation and simulation , 2000, J. Oper. Res. Soc..

[31]  Liya Wang,et al.  Augmented Simultaneous Perturbation Stochastic Approximation (ASPSA) for Discrete Supply Chain Inventory Optimization Problems , 2006 .

[32]  F. Cupertino,et al.  An experimental implementation of SPSA algorithms for induction motor adaptive control , 2006, 2006 IEEE Mountain Workshop on Adaptive and Learning Systems.