Robust simulation optimization using φ-divergence

Article history: Received March 4 2016 Received in Revised Format April 27 2016 Accepted May 14 2016 Available online May 16 2016 We introduce a new robust simulation optimization method in which the probability of occurrence of uncertain parameters is considered. It is assumed that the probability distributions are unknown but historical data are on hand and using φ-divergence functionality the uncertainty region for the uncertain probability vector is defined. We propose two approaches to formulate the robust counterpart problem for the objective function estimated by Kriging. The first method is a minimax problem and the second method is based on the chance constraint definition. To illustrate the methods and assess their performance, numerical experiments are conducted. Results show that the second method obtains better robust solutions with less simulation runs. © 2016 Growing Science Ltd. All rights reserved

[1]  Hashem Mahlooji,et al.  An artificial neural network meta-model for constrained simulation optimization , 2014, J. Oper. Res. Soc..

[2]  R. Wets,et al.  Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse , 1986 .

[3]  Dimitris Bertsimas,et al.  Robust Optimization for Unconstrained Simulation-Based Problems , 2010, Oper. Res..

[4]  Jean-Philippe Vial,et al.  Deriving robust counterparts of nonlinear uncertain inequalities , 2012, Math. Program..

[5]  Julien Marzat,et al.  Worst-case global optimization of black-box functions through Kriging and relaxation , 2012, Journal of Global Optimization.

[6]  Jack P. C. Kleijnen,et al.  Constrained optimization in expensive simulation: Novel approach , 2010, Eur. J. Oper. Res..

[7]  Timothy W. Simpson,et al.  Metamodels for Computer-based Engineering Design: Survey and recommendations , 2001, Engineering with Computers.

[8]  Jack P. C. Kleijnen,et al.  Robust Optimization in Simulation: Taguchi and Krige Combined , 2009, INFORMS J. Comput..

[9]  R. H. Myers,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[10]  Mustafa Y. Sir,et al.  Multi-objective simulation optimization using data envelopment analysis and genetic algorithm: Specific application to determining optimal resource levels in surgical services , 2013 .

[11]  Z. Q. Lu.  Statistical Inference Based on Divergence Measures , 2007 .

[12]  Kwon-Hee Lee,et al.  A Global Robust Optimization Using Kriging Based Approximation Model , 2006 .

[13]  Barry L. Nelson,et al.  Recent advances in ranking and selection , 2007, 2007 Winter Simulation Conference.

[14]  Jack P. C. Kleijnen,et al.  Robust Optimization in Simulation: Taguchi and Response Surface Methodology , 2008 .

[15]  Jack P. C. Kleijnen,et al.  Parametric and distribution-free bootstrapping in robust simulation-optimization , 2010, Proceedings of the 2010 Winter Simulation Conference.

[16]  H. Luthi.  Algorithms for Worst-Case Design and Applications to Risk Management:Algorithms for Worst-Case Design and Applications to Risk Management , 2002 .

[17]  Kleijnen,et al.  Tilburg University Regression and Kriging Metamodels with Their Experimental Designs in Simulation , 2015 .

[18]  Saeed Maghsoodloo,et al.  Simulation optimization based on Taylor Kriging and evolutionary algorithm , 2011, Appl. Soft Comput..

[19]  Jack P. C. Kleijnen,et al.  Simulation-optimization via Kriging and bootstrapping: a survey , 2014, J. Simulation.

[20]  Carlo Meloni,et al.  Metamodel variability in robust simulation-optimization: a bootstrap analysis , 2012 .

[21]  Dumitru Dumitrescu,et al.  A new evolutionary approach to minimax problems , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[22]  Alexander Shapiro,et al.  Minimax analysis of stochastic problems , 2002, Optim. Methods Softw..

[23]  Jack P. C. Kleijnen,et al.  Robust simulation-optimization using metamodels , 2009, Proceedings of the 2009 Winter Simulation Conference (WSC).

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

[25]  Dick den Hertog,et al.  Robust optimization using computer experiments , 2008, Eur. J. Oper. Res..

[26]  Shalabh Bhatnagar,et al.  Stochastic Algorithms for Discrete Parameter Simulation Optimization , 2011, IEEE Transactions on Automation Science and Engineering.

[27]  Feng Yang,et al.  Neural network metamodeling for cycle time-throughput profiles in manufacturing , 2010, Eur. J. Oper. Res..

[28]  Jack P. C. Kleijnen,et al.  Convex and monotonic bootstrapped Kriging , 2012, Proceedings Title: Proceedings of the 2012 Winter Simulation Conference (WSC).

[29]  Jack P. C. Kleijnen,et al.  Regression and Kriging metamodels with their experimental designs in simulation: A review , 2017, Eur. J. Oper. Res..

[30]  Byung Rae Cho,et al.  A D-optimal design approach to constrained multiresponse robust design with prioritized mean and variance considerations , 2009, Comput. Ind. Eng..

[31]  Loo Hay Lee,et al.  Simulation optimization via kriging: a sequential search using expected improvement with computing budget constraints , 2013 .

[32]  L. Pardo.  Statistical Inference Based on Divergence Measures , 2005 .

[33]  Peter W. Glynn,et al.  Likelihood robust optimization for data-driven problems , 2013, Computational Management Science.

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

[35]  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 .

[36]  Scott D. Sudhoff,et al.  Evolutionary Algorithms for Minimax Problems in Robust Design , 2009, IEEE Transactions on Evolutionary Computation.

[37]  Dick den Hertog,et al.  Safe Approximations of Ambiguous Chance Constraints Using Historical Data , 2013, INFORMS J. Comput..

[38]  Alexander Shapiro,et al.  On a Class of Minimax Stochastic Programs , 2004, SIAM J. Optim..

[39]  Ali Ajdari,et al.  An Adaptive Exploration-Exploitation Algorithm for Constructing Metamodels in Random Simulation Using a Novel Sequential Experimental Design , 2014, Commun. Stat. Simul. Comput..

[40]  Giuseppe Carlo Calafiore,et al.  Ambiguous Risk Measures and Optimal Robust Portfolios , 2007, SIAM J. Optim..

[41]  Qingfu Zhang,et al.  A surrogate-assisted evolutionary algorithm for minimax optimization , 2010, IEEE Congress on Evolutionary Computation.

[42]  Diego Klabjan,et al.  Robust Stochastic Lot-Sizing by Means of Histograms , 2013 .

[43]  Anja De Waegenaere,et al.  Robust Solutions of Optimization Problems Affected by Uncertain Probabilities , 2011, Manag. Sci..

[44]  Cécile Murat,et al.  Recent advances in robust optimization: An overview , 2014, Eur. J. Oper. Res..

[45]  Kuo-Hao Chang,et al.  Stochastic Nelder-Mead simplex method - A new globally convergent direct search method for simulation optimization , 2012, Eur. J. Oper. Res..

[46]  Constantine Caramanis,et al.  Theory and Applications of Robust Optimization , 2010, SIAM Rev..