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Simulation optimization: a review of algorithms and applications

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Abstract

Simulation optimization refers to the optimization of an objective function subject to constraints, both of which can be evaluated through a stochastic simulation. To address specific features of a particular simulation—discrete or continuous decisions, expensive or cheap simulations, single or multiple outputs, homogeneous or heterogeneous noise—various algorithms have been proposed in the literature. As one can imagine, there exist several competing algorithms for each of these classes of problems. This document emphasizes the difficulties in simulation optimization as compared to algebraic model-based mathematical programming makes reference to state-of-the-art algorithms in the field, examines and contrasts the different approaches used, reviews some of the diverse applications that have been tackled by these methods, and speculates on future directions in the field.

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References

  • Abramson MA (2007) NOMADm version 4.5 user’s guide. Air Force Institute of Technology, Wright-Patterson AFB, OH

  • Alkhamis TM, Ahmed MA, Tuan VK (1999) Simulated annealing for discrete optimization with estimation. Eur J Oper Res 116:530–544

  • Alrefaei MH, Andradóttir S (1999) A simulated annealing algorithm with constant temperature for discrete stochastic optimization. Manag Sci 45:748–764

    Google Scholar 

  • Ammeri A, Hachicha W, Chabchoub H, Masmoudi F (2011) A comprehensive literature review of mono-objective simulation optimization methods. Adv Prod Eng Manag 6(4):291–302

  • Anderson EJ, Ferris MC (2001) A direct search algorithm for optimization with noisy function evaluations. SIAM J Optim 11:837–857

    Google Scholar 

  • Andradóttir S (1998) Chapter 9: Simulation optimization. In: Banks J (ed) Handbook of simulation: principles, methodology, advances, applications, and practice. Wiley, New York

    Google Scholar 

  • Andradóttir S (2006a) An overview of simulation optimization via random search. In: Henderson SG, Nelson BL (eds) Handbooks in operations research and management science: simulation, vol 13, chap 20. Elsevier, Amsterdam, pp 617–631

  • Andradóttir S (2006b) Simulation optimization. In: Handbook of simulation: principles, methodology, advances, applications and practice. Wiley, New York, pp 307–333

  • Andradóttir S, Kim SH (2010) Fully sequential procedures for comparing constrained systems via simulation. Naval Res Logist 57(5):403–421

    Google Scholar 

  • Angün E (2004) Black box simulation optimization: generalized response surface methodology. Ph.D. thesis, Tilburg University

  • Angün E, Kleijnen JPC, Hertog DD, Gurkan G (2009) Response surface methodology with stochastic constraints for expensive simulation. J Oper Res Soc 60(6):735–746

    Google Scholar 

  • Ayvaz MT (2010) A linked simulation-optimization model for solving the unknown groundwater pollution source identification problems. J Contam Hydrol 117(1–4):46–59

    Google Scholar 

  • Azadivar F (1992) A tutorial on simulation optimization. In: Swain JJ, Goldsman D, Crain RC, Wilson JR (eds) Proceedings of the 1992 winter simulation conference, pp 198–204

  • Azadivar J (1999) Simulation optimization methodologies. In: Farrington PA, Nembhard HB, Sturrock DT, Evans GW (eds) Proceedings of the 1999 winter simulation conference, pp 93–100

  • Balakrishna R, Antoniou C, Ben-Akiva M, Koutsopoulos HN, Wen Y (2007) Calibration of microscopic traffic simulation models: methods and application. Transp Res Rec J Transp Res Board 1999(1):198–207

    Google Scholar 

  • Bangerth W, Klie H, Matossian V, Parashar M, Wheeler MF (2005) An autonomic reservoir framework for the stochastic optimization of well placement. Clust Comput 8(4):255–269

    Google Scholar 

  • Barton RR, Ivey JS Jr (1996) Nelder–Mead simplex modifications for simulation optimization. Manag Sci 42:954–973

    Google Scholar 

  • Barton RR, Meckesheimer M (2006) Metamodel-based simulation optimization. In: Henderson S, Nelson B (eds) Handbook in operations research and management science: simulation 13. Elsevier, Amsterdam, pp 535–574

    Google Scholar 

  • Bechhofer RE, Santner TJ, Goldsman DM (1995) Design and analysis of experiments for statistical selection, screening, and multiple comparisons. Wiley, New York

    Google Scholar 

  • Bertsimas D, Tsitsiklis J (1993) Simulated annealing. Stat Sci 8(1):10–15

    Google Scholar 

  • Bettonvil B, del Castillo E, Kleijnen JPC (2009) Statistical testing of optimality conditions in multiresponse simulation-based optimization. Eur J Oper Res 199:448–458

  • Bhatnagar S (2005) Adaptive multivariate three-timescale stochastic approximation algorithms for simulation based optimization. ACM Trans Model Comput Simul (TOMACS) 15(1):74–107

  • Bianchi L, Dorigo M, Gambardella LM, Gutjahr WJ (2009) A survey on metaheuristics for stochastic combinatorial optimization. Nat Comput 8(2):239–287

    Google Scholar 

  • Birge JR, Louveaux F (2011) Introduction to stochastic programming, 2nd edn. Springer, Berlin

    Google Scholar 

  • Box GEP, Wilson KB (1951) On the experimental attainment of optimum conditions. J R Stat Soc XII XIII(1):1–35

    Google Scholar 

  • Carson Y, Maria A (1997) Simulation optimization: Methods and applications. In: Andradóttir S, Healy KJ, Winters DH, Nelson BL (eds) Proceedings of the 1997 winter simulation conference, pp 118–126

  • Chang KH (2008) Stochastic trust region response surface convergent method for continuous simulation optimization. Ph.D. thesis, Purdue University

  • Chang KH (2012) Stochastic Nelder–Mead simplex method-A new globally convergent direct search method for simulation optimization. Eur J Oper Res 220:684–694

  • Chang KH, Hong LJ, Wan H (2013) Stochastic trust-region response-surface method (STRONG): a new response-surface framework for simulation optimization, vol 25(2), pp 230–243

  • Chen CH (1995) An effective approach to smartly allocate computing budget for discrete event simulation. In: Proceedings of the 34th IEEE conference on decision and control, pp 2598–2605

  • Chen CH (1996) A lower bound for the correct subset selection probability and its application to discrete event system simulations. IEEE Trans Autom Control 41:1227–1231

    Google Scholar 

  • Chen CH, Lee LH (2010) Stochastic simulation optimization: an optimal computing budget allocation. System engineering and operations research. World Scientific, Singapore

    Google Scholar 

  • Chen H, Schmeiser BW (1994) Retrospective optimization algorithms for stochastic root finding. In: Tew J, Manivannan S, Sadowski D, Seila A (eds) Proceedings of 1994 winter simulation conference, pp 255–261

  • Chen CH, Yücesan E, Dai L, Chen HC (2009) Optimal budget allocation for discrete-event simulation experiments. IIE Trans 42(1):60–70

    Google Scholar 

  • Chick SE (2006) Subjective probability and bayesian methodology. In: Henderson SG, Nelson BL (eds) Simulation, handbooks in operations research and management science, vol 13. Elsevier, Amsterdam, pp 225–257

    Google Scholar 

  • Cho J, Dorfman KD (2010) Brownian dynamics simulations of electrophoretic DNA separations in a sparse ordered post array. J Chromatog A 1217:5522–5528

    Google Scholar 

  • Cohn DA, Ghahramani Z, Jordan MI (1996) Active learning with statistical models. J Artif Intell Res 4:129–145

    Google Scholar 

  • Collins NE, Eglese RW, Golden BL (1988) Simulated annealing—an annotated bibliography. Am J Math Manag Sci 8:209–308

    Google Scholar 

  • Conn AR, Gould NIM, Toint PL (2000) Trust-region methods. MOS-SIAM series on optimization

  • Conn AR, Scheinberg K, Vicente LN (2009) Introduction to derivative-free optimization. SIAM, Philadelphia

    Google Scholar 

  • de Angelis V, Felici G, Impelluso P (2003) Integrating simulation and optimisation in health care centre management. Eur J Oper Res 150:101–114

  • de Boer PT, Kroese DP, Mannor S, Rubinstein RY (2005) A tutorial on the cross-entropy method. Ann Oper Res 134:19–67

  • Deng G (2007) Simulation-based optimization. Ph.D. thesis, University of Wisconsin-Madison

  • Deng G, Ferris MC (2006) Adaptation of the UOBYQA algorithm for noisy functions. In: Perrone LF, Wieland FP, Liu J, Lawson BG, Nicol DM, Fujimoto RM (eds) Proceedings of the 2006 winter simulation conference, pp 312–319

  • Deng G, Ferris MC (2007) Extension of the DIRECT optimization algorithm for noisy functions. In: Henderson SG, Biller B, Hsieh MH, Shortle J, Tew JD, Barton RR (eds) Proceedings of the 2007 winter simulation conference, pp 497–504

  • Dengiz B, Akbay KS (2000) Computer simulation of a PCB production line: metamodeling approach. Int J Prod Econ 63(2):195–205

    Google Scholar 

  • Dhivya M, Sundarambal M, Anand LN (2011) Energy efficient computation of data fusion in wireless sensor networks using cuckoo-based particle approach (cbpa). Int J Commun Netw Syst Sci 4(4):249–255

    Google Scholar 

  • Dolan ED, Moré JJ (2002) Benchmarking optimization software with performance profiles. Math Program 91:201–213

    Google Scholar 

  • Dorigo M, Blum C (2005) Ant colony optimization theory: a survey. Theor Comput Sci 344(2–3):243–278

    Google Scholar 

  • Dorigo M, Stützle T (2004) Ant colony optimization. MIT Press, Cambridge

    Google Scholar 

  • Driessen LT (2006) Simulation-based optimization for product and process design. Ph.D. thesis, Tilburg University

  • Ernst D, Glavic M, Stan GB, Mannor S, Wehenkel L (2007) The cross-entropy method for power system combinatorial optimization problems. In: Power tech, pp 1290–1295. IEEE

  • Ferris MC, Deng G, Fryback DG, Kuruchittham V (2005) Breast cancer epidemiology: calibrating simulations via optimization. Oberwolfach Rep 2:9023–9027

  • Figueira G, Almada-Lobo B (2014) Hybrid simulation-optimization methods: a taxonomy. Simul Model Pract Theory 46:118–134

    Google Scholar 

  • Frazier PI (2009) Knowledge-gradient methods for statistical learning. Ph.D. thesis, Princeton University

  • Frazier P, Powell W, Dayanik S (2009) The knowledge-gradient policy for correlated normal beliefs. INFORMS J Comput 21(4):599–613

  • Fu MC (1994) Optimization via simulation: a review. Ann Oper Res 53:199–247

  • Fu MC (2002) Optimization for simulation: theory vs practice. INFORMS J Comput 14(3):192–215

    Google Scholar 

  • Fu MC, Hill SD (1997) Optimization of discrete event systems via simulataneous perturbation stochastic approximation. IIE Trans 29(233-243)

  • Fu MC, Hu JQ (1997) Conditional Monte Carlo: gradient estimation and optimization applications. Kluwer, Dordrecht

    Google Scholar 

  • Fu MC, Hu J, Marcus SI (1996) Model-based randomized methods for global optimization. In: Proceedings of the 17th international symposium on mathematical theory of networks and systems, Kyoto, Japan, pp 355–363

  • Fu MC, Andradóttir S, Carson JS, Glover FW, Harrell CR, Ho YC, Kelly JP, Robinson SM (2000) Integrating optimization and simulation: research and practice. In: Joines JA, Barton RR, Kang K, Fishwick PA (eds) Proceedings of the 2000 winter simulation conference

  • Fu MC, Glover FW, April J (2005) Simulation Optimization: a review, new developments, and applications. In: Kuhl ME, Steiger NM, Armstrong FB, Joines JA (eds) Proceedings of the 2005 winter simulation conference, pp 83–95

  • Gendreau M, Potvin JY (2010) Tabu search. In: Handbook of metaheuristics, international series in operations research & management science, vol 146, 2nd ed. Springer, Berlin, pp 41–60

  • Gerencsér L, Kozmann G, Vágó Z, Haraszti K (2002) The use of the SPSA method in ECG analysis. IEEE Trans Biomed Eng 49(10):1094–1101

    Google Scholar 

  • Gittins JC (1989) Multi-armed bandit allocation indices. Wiley-interscience series in systems and optimization. Wiley, New York

    Google Scholar 

  • Glasserman P (1991) Gradient estimation via perturbation analysis. Kluwer, Dordrecht

    Google Scholar 

  • Glover F (1990) Tabu search: a tutorial. Interfaces 20(4):77–94

    Google Scholar 

  • Glover F, Hanafi S (2002) Tabu search and finite convergence. Discret Appl Math 119(1–2):3–36

    Google Scholar 

  • Glover F, Laguna M (1997) Tabu search. Kluwer, Boston

    Google Scholar 

  • Glover F, Laguna M (2000) Fundamentals of scatter search and path relinking. Control Cybern 29(3):653–684

    Google Scholar 

  • Goldsman D, Nelson BL (1998) Comparing systems via simulation. In: Banks J (ed) Handbook of simulation: principles, methodology, advances, applications, and practice, chap. 8. Wiley, New York

    Google Scholar 

  • Gong WB, Ho YC, Zhai W (2000) Stochastic comparison algorithm for discrete optimization with estimation. SIAM J Optim 10:384–404 (49)

  • Griewank A, Walther A (2008) Evaluating derivatives: principles and techniques of algorithmic differentiation, 2nd ed. No. 105 in other titles in applied mathematics. SIAM, Philadelphia, PA. http://www.ec-securehost.com/SIAM/OT105.html

  • Gürkan G, Ozge AY, Robinson SM (1994) Sample path optimization in simulation. In: Tew J, Manivannan S, Sadowski D, Seila A (eds) Proceedings of 1994 winter simulation conference, pp 247–254

  • Hajek B (1988) Cooling schedules for optimal annealing. Math Oper Res 13:311–329

    Google Scholar 

  • Hall JD, Bowden RO, Usher JM (1996) Using evolution strategies and simulation to optimize a pull production system. J Mater Process Technol 61(1–2):47–52

    Google Scholar 

  • Hansen N (2006) The CMA evolution strategy: a comparing review. In: Lozano JA, Larrañaga P, Inza I, Bengoetxea E (eds) Towards a new evolutionary computation. Advances on estimation of distribution algorithms. Springer, Berlin, pp 75–102

    Google Scholar 

  • Hansen N (2011) The CMA Evolution strategy: a tutorial. http://www.lri.fr/hansen/cmaesintro.html

  • Healy K, Schruben LW (1991) Retrospective simulation response optimization. In: Nelson BL, Kelton DW, Clark GM (eds) Proceedings of the 1991 winter simulation conference, pp 954–957

  • Hill SD, Fu MC (1995) Transfer optimization via simultaneous perturbation stochastic approximation. In: Alexopoulos C, Kang K, Lilegdon WR, Goldsman D (eds) Proceedings of the 1995 winter simulation conference, pp 242–249

  • Ho YC (1999) An explanation of ordinal optimization: soft computing for hard problems. Inf Sci 113:169–192

    Google Scholar 

  • Ho YC, Cao XR (1991) Discrete event dynamic systems and perturbation analysis. Kluwer, Dordrecht

    Google Scholar 

  • Hochberg Y, Tamhane AC (1987) Multiple comparison procedures. Wiley, New York

    Google Scholar 

  • Hong LJ, Nelson BL (2006) Discrete optimization via simulation using COMPASS. Oper Res 54(1):115–129

  • Hong LJ, Nelson BL (2009) A brief introduction to optimization via simulation. In: Rossetti MD, Hill RR, Johansson B, Dunkin A, Ingalls RG (eds) Proceedings of the 2009 winter simulation conference

  • Hooke R, Jeeves TA (1961) Direct search solution of numerical and statistical problems. J Assoc Comput Mach 8:212–219

    Google Scholar 

  • Hsu JC (1996) Multiple comparisons: theory and methods. CRC Press, Boca Raton

    Google Scholar 

  • Hu J, Fu MC, Marcus SI (2005) Stochastic optimization using model reference adaptive search. In: Kuhl ME, Steiger NM, Armstrong FB, Joines JA (eds) Proceedings of the 2005 winter simulation conference, pp 811–818

  • Hu J, Fu MC, Marcus SI (2007) A model reference adaptive search method for global optimization. Oper Res 55(3):549–568

  • Huang D, Allen TT, Notz WI, Zeng N (2006) Global optimization of stochastic black-box systems via sequential kriging meta-models. J Glob Optim 34:441–466

    Google Scholar 

  • Humphrey DG, Wilson JR (2000) A revised simplex search procedure for stochastic simulation response-surface optimization. INFORMS J Comput 12(4):272–283

  • Hunter SR, Pasupathy R (2013) Optimal sampling laws for stochastically constrained simulation optimization on finite sets. INFORMS J Comput 25(3):527–542

  • Hutchison DW, Hill SD (2001) Simulation optimization of airline delay with constraints. In: Peters BA, Smith JS, Medeiros DJ, Rohrer MW (eds) Proceedings of the 2001 winter simulation conference, pp 1017–1022

  • Huyer W, Neumaier A (2008) SNOBFIT—stable noisy optimization by branch and fit. ACM Trans Math Softw 35:1–25

    Google Scholar 

  • Irizarry MDLA, Wilson JR, Trevino J (2001) A flexible simulation tool for manufacturing-cell design, II: response surface analysis and case study. IIE Trans 33(10):837–846

  • Jacobson SH, Schruben LW (1989) Techniques for simulation response optimization. Oper Res Lett 8:1–9

    Google Scholar 

  • Jia QS, Ho YC, Zhao QC (2006) Comparison of selection rules for ordinal optimization. Math Comput Model 43(9–10):1150–1171

    Google Scholar 

  • Jones DR, Perttunen CD, Stuckman BE (1993) Lipschitzian optimization without the Lipschitz constant. J Optim Theory Appl 79:157–181

    Google Scholar 

  • Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13:455–492

    Google Scholar 

  • Jung JY, Blau G, Pekny JF, Reklaitis GV, Eversdyk D (2004) A simulation based optimization approach to supply chain management under demand uncertainty. Comput Chem Eng 28:2087–2106

  • Kabirian A (2009) Continuous optimization via simulation using golden region search. Ph.D. thesis, Iowa State University

  • Kabirian A, Ólafsson S (2007) Allocation of simulation runs for simulation optimization. In: Henderson SG, Biller B, Hsieh MH, Shortle J, Tew JD, Barton RR (eds) Proceedings of the 2007 winter simulation conference, pp 363–371

  • Kabirian A, Ólafsson S (2011) Continuous optimization via simulation using golden region search

  • Kenne JP, Gharbi A (2001) A simulation optimization approach in production planning of failure prone manufacturing systems. J Intell Manuf 12:421–431

    Google Scholar 

  • Khan HA, Zhang Y, Ji C, Stevens CJ, Edwards DJ, O’Brien D (2006) Optimizing polyphase sequences for orthogonal netted radar. IEEE Signal Process Lett 13(10):589–592

    Google Scholar 

  • Kiefer J, Wolfowitz J (1952) Stochastic estimation of the maximum of a regression function. Ann Math Stat 23(3):462–466

    Google Scholar 

  • Kim SH (2005) Comparison with a standard via fully sequential procedures. ACM Trans Model Comput Simul (TOMACS) 15(2):155–174

  • Kim SH, Nelson BL (2006) Selecting the best system. In: Henderson SG, Nelson BL (eds) Handbooks in operations research and management science: simulation, chap 17. Elsevier, Amsterdam, pp 501–534

    Google Scholar 

  • Kim SH, Nelson BL (2007) Recent advances in ranking and simulation. In: Henderson SG, Biller B, Hsieh MH, Shortle J, Tew JD, Barton RR (eds) Proceedings of the 2007 winter simulation conference, pp 162–172

  • Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680

    Google Scholar 

  • Kleijnen JPC (1993) Simulation and optimization in production planning: a case study. Decis Support Syst 9:269–280

    Google Scholar 

  • Kleijnen JPC (2008) Design and analysis of simulation experiments. Springer, New York

    Google Scholar 

  • Kleijnen JPC (2009) Kriging metamodeling in simulation: a review. Eur J Oper Res 192(3):707–716

  • Kleijnen JPC, van Beers WCM (2005) Robustness of kriging when interpolating in random simulation with heterogeneous variances: some experiments. Euro J Oper Res 165:826–834

    Google Scholar 

  • Kleijnen JPC, Beers WCM, van Nieuwenhuyse I (2012) Expected improvement in efficient global optimization through bootstrapped kriging. J Glob Optim 54(1):59–73

  • Kleinman NL, Hill SD, Ilenda VA (1997) SPSA/SIMMOND optimization of air traffic delay cost. In: Proceedings of the 1997 American control conference, vol 2, pp 1121–1125

  • Köchel P, Nieländer U (2005) Simulation-based optimisation of multi-echelon inventory systems. Int J Prod Econ 93–94:505–513

    Google Scholar 

  • Kolda TG, Lewis RM, Torczon VJ (2003) Optimization by direct search: new perspectives on some classical and modern methods. SIAM Rev 45:385–482

    Google Scholar 

  • Kothandaraman G, Rotea MA (2005) Simultaneous-perturbation-stochastic-approximation algorithm for parachute parameter estimation. J Aircr 42(5):1229–1235

    Google Scholar 

  • Kroese DP, Porotsky S, Rubinstein RY (2006) The cross-entropy method for continuous multi-extremal optimization. Methodol Comput Appl Probab 8(3):383–407

    Google Scholar 

  • Kroese DP, Hui KP, Nariai S (2007) Network reliability optimization via the cross-entropy method. IEEE Trans Reliab 56(2):275–287

    Google Scholar 

  • Kulturel-Konak S, Konak A (2010) Simulation optimization embedded particle swarm optimization for reliable server assignment. In: Johansson B, Jain S, Montoya-Torres J, Hugan J, Yücesan E (eds) Proceedings of the 2010 winter simulation conference, pp 2897–2906

  • Larrañaga P, Lozano JA (2002) Estimation of distribution algorithms: a new tool for evolutionary computation. Kluwer, Dordrecht

    Google Scholar 

  • Lau TWE, Ho YC (1997) Universal alignment probabilities and subset selection for ordinal optimization. J Optim Theory Appl 93(3):455–489

    Google Scholar 

  • Law AM, Kelton WD (2000) Simulation modeling and analysis, 3rd edn. McGraw-Hill, Singapore

    Google Scholar 

  • Lee LH, Pujowidianto NA, Li LW, Chen CH, Yap CM (2012) Approximate simulation budget allocation for selecting the best design in the presence of stochastic constraints. IEEE Trans Autom Control 57(11):2940–2945

    Google Scholar 

  • Li Y (2009) A simulation-based evolutionary approach to LNA circuit design optimization. Appl Math Comput 209(1):57–67

    Google Scholar 

  • Lucidi S, Sciandrone M (2002) On the global convergence of derivative-free methods for unconstrained minimization. SIAM J Optim 13:97–116

    Google Scholar 

  • Lutz CM, Davis KR, Sun M (1998) Determining buffer location and size in production lines using tabu search. Eur J Oper Res 106:301–316

  • Martí R, Laguna M, Glover F (2006) Principles of scatter search. Eur J Oper Res 169(2):359–372

  • Maryak JL, Chin DC (2008) Global random optimization by simulataneous perturbation stochastic approximation. IEEE Trans Autom Control 53:780–783

    Google Scholar 

  • Meketon MS (1987) Optimization in simulation: a survey of recent results. In: Thesen A, Grant H, Kelton WD (eds) Proceedings of the 1987 winter simulation conference, pp 58–67

  • Merhof D, Soza G, Stadlbauer A, Greiner G, Nimsky C (2007) Correction of susceptibility artifacts in diffusion tensor data using non-linear registration. Med Image Anal 11(6):588–603

    Google Scholar 

  • Merton RC (1974) On the pricing of corporate debt: the risk structure of interest rates. J Financ 29(2):449–470

    Google Scholar 

  • Mishra V, Bhatnagar S, Hemachandra N (2007) Discrete parameter simulation optimization algorithms with applications to admission control with dependent service times. In: Proceedings of the 46th IEEE conference on decision and control, New Orleans, LA, pp 2986–2991

  • Mockus J (1989) Bayesian approach to global optimization. Kluwer, Dordrecht

    Google Scholar 

  • Mockus J, Tiesis V, Zilinskas A (1978) Towards global optimisation, vol. 2, chap. The application of Bayesian methods for seeking the extremum. North-Holland, Amsterdam

    Google Scholar 

  • Moré J, Wild S (2009) Benchmarking derivative-free optimization algorithms. SIAM J Optim 20:172–191

    Google Scholar 

  • Myers RH, Montgomery DC, Anderson-Cook CM (2009) Response surface methodology: process and product optimization using designed experiments. wiley series in probability and statistics. Wiley, New York

    Google Scholar 

  • Neddermeijer HG, Oortmarssen GJV, Piersma N, Dekker R (2000) A framework for response surface methodology for simulation optimization. In: Joines JA, Barton RR, Kang K, Fishwick PA (eds) Proceedings of the 2000 winter simulation conference, pp 129–136

  • Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7:308–313

    Google Scholar 

  • Nelson BL (2010) Optimization via simulation over discrete decision variables. Tutor Oper Res 7:193–207

    Google Scholar 

  • Nelson BL, Goldsman D (2001) Comparisons with a standard in simulation experiments. Manag Sci 47(3):449–463

    Google Scholar 

  • Nicolai R, Dekker R (2009) Automated response surface methodology for simulation optimization models with unknown variance. Qual Technol Qual Manag 6(3):325–352

  • Ólafsson S (2006) Metaheuristics. In: Henderson S, Nelson B (eds) Handbook in operations research and management science: simulation, vol 13. Elsevier, Amsterdam, pp 633–654

    Google Scholar 

  • Osorio C, Bierlaire M (2010) A simulation-based optimization approach to perform urban traffic control. In: Proceedings of the triennial symposium on transportation analysis

  • Pasupathy R, Ghosh S (2013) Simulation optimization: a concise overview and implementation guide. Tutor Oper Res 10:122–150

    Google Scholar 

  • Pasupathy R, Henderson SG (2011) SIMOPT: a library of simulation-optimization problems. In: Jain S, Creasey RR, Himmelspach J, White KP, Fu M (eds) Proceedings of the 2011 winter simulation conference

  • Pasupathy R, Kim S (2011) The stochastic root finding problem: overview, solutions, and open questions. ACM Trans Model Comput Simul (TOMACS) 21(3):19:1–19:23

  • Peters J, Vijayakumar S, Schaal S (2003) Reinforcement learning for humanoid robotics. In: Third IEEE-RAS international conference on humanoid robots, Karlsruhe, Germany, pp 1–20

  • Pflug GC (1996) Optimization of stochastic models: the interface between simulation and optimization. Kluwer, Dordrecht

    Google Scholar 

  • Plambeck EL, Fu BR, Robinson SM, Suri R (1996) Sample-path optimization of convex stochastic performance functions. Math Program 75(2):137–176

  • Powell WB (2013) http://www.castlelab.princeton.edu/cso.htm. Accessed 23 Oct 2013

  • Powell WB, Ryzhov IO (2012) Optimal learning. Wiley, New York

    Google Scholar 

  • Prakash P, Deng G, Converse MC, Webster JG, Mahvi DM, Ferris MC (2008) Design optimization of a robust sleeve antenna for hepatic microwave ablation. Phys Med Biol 53:1057–1069

    Google Scholar 

  • Radac MB, Precup RE, Petriu EM, Preitl S (2011) Application of ift and SPSA to servo system control. IEEE Trans Neural Netw 22(12):2363–2375

    Google Scholar 

  • Rall, LB (1981) Automatic differentiation: techniques and applications, lecture notes in computer science, vol 120. Springer, Berlin. doi:10.1007/3-540-10861-0

  • Ramanathan SP, Mukherjee S, Dahule RK, Ghosh S, Rahman I, Tambe SS, Ravetkar DD, Kulkarni BD (2001) Optimization of continuous distillation columns using stochastic optimization approaches. Trans Inst Chem Eng 79:310–322

    Google Scholar 

  • Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. MIT Press, Cambridge

    Google Scholar 

  • Reeves CR (1997) Genetic algorithms for the operations researcher. INFORMS J Comput 9(3):231–250

  • Renotte C, Vande Wouwer A (2003) Stochastic approximation techniques applied to parameter estimation in a biological model. In: Proceedings of the second IEEE international workshop on Intelligent data acquisition and advanced computing systems: technology and applications, 2003, IEEE, pp 261–265

  • Rios LM, Sahinidis NV (2013) Derivative-free optimization: a review of algorithms and comparison of software implementations. J Glob Optim 56:1247–1293

    Google Scholar 

  • Robbins H, Monro S (1951) A stochastic approximation method. Ann Math Stat 22(3):400–407

    Google Scholar 

  • Robinson SM (1996) Analysis of sample-path optimization. Math Oper Res 21(3):513–528

  • Romero PA, Krause A, Arnold FH (2013) Navigating the protein fitness landscape with gaussian processes. Proc Natl Acad Sci (PNAS) 110(3). doi:10.1073/pnas.1215251110

  • Roustant O, Ginsbourger D, Deville Y (2012) Dicekriging, diceoptim: two r packages for the analysis of computer experiments by kriging-based metamodeling and optimization. J Stat Softw 51(1):1–55

    Google Scholar 

  • Rubinstein R (1999) The cross-entropy method for combinatorial and continuous optimization. Methodol Comput Appl Probab 1:127–190

    Google Scholar 

  • Rubinstein RY, Kroese DP (2004) The cross-entropy method: a unified approach to combinatorial optimization, Monte-Carlo simulation, and machine learning. Springer, New York

    Google Scholar 

  • Rubinstein RY, Shapiro A (1993) Discrete event systems: sensitivity analysis and stochastic optimization by the score function method. Wiley, New York

    Google Scholar 

  • Sacks J, Schiller SB, Welch WJ (1989) Designs for computer experiments. Technometrics 31:41–47

    Google Scholar 

  • Safizadeh MH (1990) Optimization in simulation: current issues and the future outlook. Naval Res Logist 37:807–825

    Google Scholar 

  • Sahinidis NV (2004) Optimization under uncertainty: State-of-the-art and opportunities. Comput Chem Eng 28(6–7):971–983

  • Schwartz JD, Wang W, Rivera DE (2006) Simulation-based optimization of process control policies for inventory management in supply chains. Automatica 42:1311–1320

    Google Scholar 

  • Scott W, Frazier PI, Powell W (2011) The correlated knowledge gradient for simulation optimization of continuous parameters using gaussian process regression. SIAM J Optim 21(3):996–1026

    Google Scholar 

  • Settles B (2010) Active learning literature survey. Tech. rep., University of Wisconsin-Madison

  • Shapiro A (1991) Asymptotic analysis of stochastic programs. Ann Oper Res 30:169–186

    Google Scholar 

  • Shapiro A (1996) Simulation based optimization. In: Charnes JM, Morrice DJ, Brunner DT, Swain JJ (eds) Proceedings of the 1996 winter simulation conference, pp 332–336

  • Shi L, Ólafsson S (2000) Nested partitions method for stochastic optimization. Methodol Comput Appl Probab 2:271–291

    Google Scholar 

  • Shi L, Ólafsson (2007) Nested partitions optimization: methodology and applications, international series in operations research & management science, vol 109. Springer, Berlin

    Google Scholar 

  • Song Y, Grizzle JW (1995) The extended kalman filter as a local asymptotic observer for discrete-time nonlinear systems. J Math Syst Estim Control 5(1):59–78

    Google Scholar 

  • Spall JC (1992) Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans Autom Control 37:332–341

    Google Scholar 

  • Spall JC (2003) Introduction to stochastic search and optimization: Estimation, simulation, and control. Wiley-Interscience

  • Spall JC (2009) Feedback and weighting mechanisms for improving Jacobian estimates in the adaptive simultaneous perturbation algorithm. IEEE Trans Autom Control 54(6):1216–1229

    Google Scholar 

  • Spall JC (2012) Stochastic optimization. In: Gentle JE, Härdle WK, Mori Y (eds) Handbook of computational statistics: concepts and methods, 2nd ed, chap 7. Springer, Berlin, pp 173–201

    Google Scholar 

  • Srinivas N, Krause A, Kakade SM, Seeger M (2012) Information-theoretic regret bounds for gaussian process optimization in the bandit setting. IEEE Trans Inf Theory 58(5):3250–3265

    Google Scholar 

  • Stephens CP, Baritompa W (1998) Global optimization requires global information. J Optim Theory Appl 96:575–588

    Google Scholar 

  • Swisher JR, Hyden PD, Jacobson SH, Schruben LW (2000) A survey of simulation optimization techniques and procedures. In: Joines JA, Barton RR, Kang K, Fishwick PA (eds) Proceedings of the 2000 winter simulation conference

  • Syberfeldt A, Lidberg S (2012) Real-world simulation-based manufacturing optimization using cuckoo search. In: Laroque C, Himmelspach J, Pasupathy R, Rose O, Uhrmacher A (eds) Proceedings of the 2012 winter simulation conference

  • Tein LH, Ramli R (2010) Recent advancements of nurse scheduling models and a potential path. In: Proceedings of the 6th IMT-GT conference on mathematics, statistics and its applications, pp 395–409

  • Tekin E, Sabuncuoglu I (2004) Simulation optimization: a comprehensive review on theory and applications. IIE Trans 36:1067–1081

    Google Scholar 

  • Teng S, Lee LH, Chew EP (2007) Multi-objective ordinal optimization for simulation optimization problems. Automatica 43(11):1884–1895

    Google Scholar 

  • Trosset MW (2000) On the use of direct search methods for stochastic optimization. Tech. rep., Rice University, Houston, TX

  • van Beers AC, Kleijnen JPC (2004) Kriging interpolation in simulation: a survey. In: Proceedings of the 2004 winter simulation conference, vol 1, pp 121–129

  • Vande Wouwer A, Renotte, Bogaerts P, Remy M (2001) Application of SPSA techniques in nonlinear system identification. In: Proceedings of the European control conference, p 2835

  • Wang Q, Spall JC (2011) Discrete simultaneous perturbation stochastic approximation on loss functions with noisy measurements. In: Proceedings of the American control conference. IEEE, San Francisco, pp 4520–4525

  • Wang H, Pasupathy R, Schmeiser BW (2012) Integer-ordered simulation optimization using R-SPLINE: retrospective search with piecewise-linear interpolation and neighborhood enumeration. ACM Trans Model Comput Simul (TOMACS) 23:17:1–17:24

  • Whitley D (1994) A genetic algorithm tutorial. Stat Comput 4:65–85

    Google Scholar 

  • Xie J, Frazier PI (2013) Sequential bayes-optimal policies for multiple comparisons with a known standard. Oper Res 61(5):1174–1189

    Google Scholar 

  • Xie J, Frazier PI, Sankaran S, Marsden A, Elmohamed S (2012) Optimization of computationally expensive simulations with gaussian processes and parameter uncertainty: application to cardiovascular surgery. In: 50th Annual allerton conference on communication, control, and computing

  • Xing XQ, Damodaran M (2002) Assessment of simultaneous perturbation stochastic approximation method for wing design optimization. J Aircr 39:379–381

    Google Scholar 

  • Xing XQ, Damodaran M (2005a) Application of simultaneous perturbation stochastic approximation method for aerodynamic shape design optimization. AIAA J 43(2):284–294

  • Xing XQ, Damodaran M (2005b) Inverse design of transonic airfoils using parallel simultaneous perturbation stochastic approximation. J Aircr 42(2):568–570

  • Xu J, Nelson BL, Hong LJ (2010) Industrial strength COMPASS: a comprehensive algorithm and software for optimization via simulation. ACM Trans Model Comput Simul (TOMACS) 20(1):1–29

  • Xu J, Nelson BL, Hong LJ (2013) An adaptive hypberbox algorithm for high-dimensional discrete optimization via simulation problems. INFORMS J Comput 25(1):133–146

  • Yalçinkaya Ö, Mirac Bayhan G (2009) Modelling and optimization of average travel time for a metro line by simulation and response surface methodology. Eur J Oper Res 196:225–233

  • Yan D, Mukai H (1992) Stochastic discrete optimization. SIAM J Control Optim 30:594–612

  • Yang XS, Deb S (2010) Engineering optimisation by cuckoo search. Int J Math Model Numer Optim 1(4):330–343

    Google Scholar 

  • Yeomans JS (2007) Solid waste planning under uncertainty using evolutionary simulation–optimization. Socio-Econ Plan Sci 41:38–60

    Google Scholar 

  • Yun I, Park B (2010) Application of stochastic optimization method for an urban corridor. In: Perrone LF, Wieland FP, Liu J, Lawson BG, Nicol DM, Fujimoto RM (eds) Proceedings of the 2010 winter simulation conference, pp 1493–1499

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Amaran, S., Sahinidis, N.V., Sharda, B. et al. Simulation optimization: a review of algorithms and applications. 4OR-Q J Oper Res 12, 301–333 (2014). https://doi.org/10.1007/s10288-014-0275-2

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