Constrained optimization in expensive simulation: Novel approach

This article presents a novel heuristic for constrained optimization of computationally expensive random simulation models. One output is selected as objective to be minimized, while other outputs must satisfy given threshold values. Moreover, the simulation inputs must be integer and satisfy linear or nonlinear constraints. The heuristic combines (i) sequentialized experimental designs to specify the simulation input combinations, (ii) Kriging (or Gaussian process or spatial correlation modeling) to analyze the global simulation input/output data resulting from these designs, and (iii) integer nonlinear programming to estimate the optimal solution from the Kriging metamodels. The heuristic is applied to an (s,S) inventory system and a call-center simulation, and compared with the popular commercial heuristic OptQuest embedded in the Arena versions 11 and 12. In these two applications the novel heuristic outperforms OptQuest in terms of number of simulated input combinations and quality of the estimated optimum.

[1]  N. Zheng,et al.  Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models , 2006, J. Glob. Optim..

[2]  K. Ng,et al.  Kriging model with modified nugget effect for random simulation with heterogeneous variances , 2008, 2008 IEEE International Conference on Industrial Engineering and Engineering Management.

[3]  James P. Kelly.  Simulation Optimization is Evolving , 2002, INFORMS J. Comput..

[4]  Jack P. C. Kleijnen,et al.  Customized sequential designs for random simulation experiments: Kriging metamodeling and bootstrapping , 2008, Eur. J. Oper. Res..

[5]  Daniel Atkins,et al.  Revolutionizing Science and Engineering Through Cyberinfrastructure: Report of the National Science Foundation Blue-Ribbon Advisory Panel on Cyberinfrastructure , 2003 .

[6]  J. Kleijnen,et al.  Response surface methodology revisited , 2002, Proceedings of the Winter Simulation Conference.

[7]  Raghu Pasupathy,et al.  A Testbed of Simulation-Optimization Problems , 2006, Proceedings of the 2006 Winter Simulation Conference.

[8]  Ron S. Kenett,et al.  Achieving Robust Design from Computer Simulations , 2006 .

[9]  Jack P. C. Kleijnen,et al.  Kriging Metamodeling in Simulation: A Review , 2007, Eur. J. Oper. Res..

[10]  Shane G. Henderson,et al.  Optimizing Call Center Staffing Using Simulation and Analytic Center Cutting-Plane Methods , 2008, Manag. Sci..

[11]  Jack P. C. Kleijnen,et al.  Optimization of simulated systems: OptQuest and alternatives , 2007, Simul. Model. Pract. Theory.

[12]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

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

[14]  T. Simpson,et al.  Use of Kriging Models to Approximate Deterministic Computer Models , 2005 .

[15]  Antonio Arreola-Risa,et al.  Production , Manufacturing and Logistics Optimizing stochastic production-inventory systems : A heuristic based on simulation and regression analysis , 2011 .

[16]  Jack P. C. Kleijnen,et al.  Kriging metamodeling in constrained simulation optimization: an explorative study , 2007, 2007 Winter Simulation Conference.

[17]  T. Simpson,et al.  A Monte Carlo Simulation of the Kriging Model , 2004 .

[18]  Herbert Hamers,et al.  Why Methods for Optimization Problems with Time-Consuming Function Evaluations and Integer Variables Should Use Global Approximation Models , 2006 .

[19]  Michael C. Fu,et al.  Optimization for Simulation: Theory vs. Practice , 2002 .

[20]  Jack P. C. Kleijnen.  Design and Analysis of Simulation Experiments , 2007 .

[21]  Thomas W. Lucas,et al.  Efficient Nearly Orthogonal and Space-Filling Latin Hypercubes , 2007, Technometrics.

[22]  Jack P. C. Kleijnen,et al.  The correct Kriging variance estimated by bootstrapping , 2006, J. Oper. Res. Soc..

[23]  Noel A Cressie,et al.  Statistics for Spatial Data, Revised Edition. , 1994 .

[24]  Catherine M. Harmonosky,et al.  Optimization of systems with multiple performance measures via simulation: Survey and recommendations , 2008, Comput. Ind. Eng..

[25]  Jürgen Branke,et al.  Selecting a Selection Procedure , 2007, Manag. Sci..

[26]  T. M. Cioppa,et al.  Efficient Nearly Orthogonal and Space-Filling , 2007 .

[27]  Pierre L'Ecuyer,et al.  Staffing Multiskill Call Centers via Linear Programming and Simulation , 2008, Manag. Sci..

[28]  Herbert Hamers,et al.  On D-optimality based trust regions for black-box optimization problems , 2006 .

[29]  Marianthi G. Ierapetritou,et al.  A kriging based method for the solution of mixed-integer nonlinear programs containing black-box functions , 2009, J. Glob. Optim..

[30]  Hans Wackernagel,et al.  Multivariate Geostatistics: An Introduction with Applications , 1996 .

[31]  J. Chilès,et al.  Geostatistics: Modeling Spatial Uncertainty , 1999 .

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

[33]  Jack P. C. Kleijnen,et al.  Expected Improvement in Efficient Global Optimization Through Bootstrapped Kriging , 2011 .

[34]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[35]  I. Grossmann.  Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques , 2002 .

[36]  Jack P. C. Kleijnen,et al.  Application-driven sequential designs for simulation experiments: Kriging metamodelling , 2004, J. Oper. Res. Soc..

[37]  M. Fu,et al.  Optimization of( s, S ) inventory systems with random lead times and a service level constraint , 1998 .

[38]  Randall P. Sadowski,et al.  Simulation with Arena , 1998 .

[39]  Jack P. C. Kleijnen,et al.  Validation of regression metamodels in simulation: Bootstrap approach , 2006, Eur. J. Oper. Res..

[40]  L.F.P. Etman,et al.  Simulation based optimization of stochastic systems with integer design variables by sequential multipoint linear approximation , 2001 .

[41]  Alireza Kabirian,et al.  Continuous optimization via simulation using Golden Region search , 2011, Eur. J. Oper. Res..

[42]  Søren Nymand Lophaven,et al.  DACE - A Matlab Kriging Toolbox , 2002 .

[43]  Søren Nymand Lophaven,et al.  DACE - A Matlab Kriging Toolbox, Version 2.0 , 2002 .

[44]  Ornella Pisacane.  Agent scheduling in a multiskill call center , 2009, 4OR.

[45]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[46]  Agus Sudjianto,et al.  Blind Kriging: A New Method for Developing Metamodels , 2008 .

[47]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

[48]  Julio R. Banga,et al.  Improved scatter search for the global optimization of computationally expensive dynamic models , 2009, J. Glob. Optim..

[49]  Barry L. Nelson,et al.  Stochastic kriging for simulation metamodeling , 2008, WSC 2008.

[50]  Rupert G. Miller.  Simultaneous Statistical Inference , 1966 .

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