Abstract
Simulation optimization studies the problem of optimizing simulation-based objectives. This field has a strong history in engineering but often suffers from several difficulties including being time-consuming and NP-hardness. Simulation optimization is a new and hot topic in the field of system simulation and operational research. This paper presents a hybrid approach that combines Evolutionary Algorithms with neural networks (NNs) for solving simulation optimization problems. In this hybrid approach, we use NNs to replace the known simulation model for evaluating subsequent iterative solutions. Further, we apply the dynamic structure-based neural networks to learn and replace the known simulation model. The determination of dynamic structure-based neural networks is the kernel of this paper. The final experimental results demonstrated that the proposed approach can find optimal or close-to-optimal solutions and is superior to other recent algorithms in simulation optimization.










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Pierreval H, Paris JL (2000) Distributed evolutionary algorithms for simulation optimization. IEEE Trans Syst Man Cybern A Syst Hum 30(1):15–24
Kleijnen JPC (1993) Simulation and optimization production planning: a case study. Decis Support Syst 9(3):269–280
Rosenblatt MJ, Roll Y, Zyse V (1993) A combined optimization and simulation approach for designing automated storage/retrieval systems. IEE Trans 25(1):40–50
Shank JS, Tadikamalla PR (1993) Output maximization of a CIM system: simulation and statistical approach. Int J Prod Res 31(1):19–41
Brennan RW, Roger P (1995) Stochastic optimization applied to a manufacturing system operation problem. In: Winter simulation conference proceedings, IEEE Press, Arlington, pp 857–864
Hindi KS, Yang H, Fleszar K (2002) An evolutionary algorithm for resource-constrained project scheduling. IEEE Trans Evol Comput 6(5):512–518
Tsai HK, Yang JM, Tsai YF, Kao CY (2004) An evolutionary algorithm for large traveling salesman problems. IEEE Trans Syst Man Cybern B Cybern 34(4):1718–1729
Leung YW, Wang YP (2001) An orthogonal genetic algorithm with quantization for global numerical optimization. IEEE Trans Evol Comput 5(1):41–53
Ding HW, Benyoucef L, Xie XL (2005) A simulation optimization methodology for supplier selection problem. Int J Comput Integr Manuf 18(2–3):210–224
Fu MC, Glover FW, April J (2005) Simulation optimization: a review, new developments, and applications. In: The winter simulation conference proceedings, IEEE Press, Orlando, pp 83–95
Butler JC, Morrice DJ, Mullarkey PW (2001) A multiple attribute utility theory approach to ranking and selection. Manag Sci 47(6):800–816
Malone GJ, Kim SH, Goldsman D, Batur D (2005) Performance of variance updating ranking and selection procedures. In: The winter simulation conference proceedings, IEEE Press, Orlando, pp 825–832
Branke J, Chick SE, Schmidt C (2005) New developments in ranking and selection: an empirical comparison of the three main approaches. In: The winter simulation conference proceedings, IEEE Press, Orlando, pp 708–717
Ho YC, Sreenivas R, Vakili P (1992) Ordinal optimization of DEDS. Discret Event Dyn Syst Theory Appl 2(2):61–88
Ho YC, Cassandras CG, Chen CH, Dai LY (2000) Ordinal optimization and simulation. J Oper Res Soc 51(4):490–500
Kim SH, Nelson BL (2006) Selecting the best system. In: Henderson SG, Nelson BL (eds) Handbooks in operations research and management science, vol 1, handbooks in operations research and management science: simulation, 1st edn. Elsevier Science, Amsterdam
Chick SE, Inoue K (2001) New two-stage and sequential procedures for selecting the best simulated system. Oper Res 49(5):732–743
Chick SE, Inoue K (2001) New procedures to select the best simulated system using common random numbers. Manag Sci 47(8):1133–1149
Olafsson S (1999) Iterative ranking-and-selection for large-scale optimization. In: The winter simulation conference proceedings, IEEE Press, Phoenix, pp 479–485
Trailovic L, Pao LY (2004) Computing budget allocation for efficient ranking and selection of variances with application to target tracking algorithms. IEEE Trans Autom Control 49(1):58–67
Boesel J, Nelson BL, Kim S (2003) Using ranking and selection to ‘clean up’ after simulation optimization. Oper Res 51(5):814–825
Swisher JR, Jacobson SH, Sheldon H, Yucesan E (2003) Discrete-event simulation optimization using ranking, selection, and multiple comparison procedures: a survey. ACM Trans Model Comput Simul 13(2):1049–3301
Jivotovski G (2000) Gradient based heuristic algorithm and its application to discrete optimization of bar structures. Struct Multidiscip Optim 19(3):237–248
Soliman EA, Bakr MH, Nikolova NK (2005) Accelerated gradient-based optimization of planar circuits. IEEE Trans Antennas Propag 53(2):880–883
Liao LZ, Qi LQ, Tam HW (2005) A gradient-based continuous method for large-scale optimization problems. J Glob Optim 31(2):271–286
Dwight RP, Brezillon J (2006) Effect of approximations of the discrete adjoint on gradient-based optimization. AIAA J 44(12):3022–3031
Fu MC (2006) Gradient estimation. In: Henderson SG, Nelson BL (eds) Handbooks in operations research and management science, vol 1, handbooks in operations research and management science: simulation, 1st edn. Elsevier Science, Amsterdam
Mahnken R, Johansson M, Runesson K (1998) Parameter estimation for a viscoplastic damage model using a gradient-based optimization algorithm. Eng Comput 15(6–7):925–954
Norgren M, He S (1999) Gradient-based optimization approach to the inverse problem for multi-layered structures sailing. Int J Appl Electromagn Mech 10(4):315–335
Kegl M, Butinar BJ, Kegl B (2002) An efficient gradient-based optimization algorithm for mechanical systems. Commun Numer Methods Eng 18(5):363–371
Wilson E, Rock SM (2002) Gradient-based parameter optimization for systems containing discrete-valued functions. Int J Robust Nonlinear Control 12(11):1009–1028
Bhatnagar S (2005) Adaptive multivariate three-timescale stochastic approximation algorithms for simulation based optimization. ACM Trans Model Comput Simul 15(1):74–107
Bhatnagar S, Kowshik HJ (2005) A discrete parameter stochastic approximation algorithm for simulation optimization. Simulation 81(11):757–772
Yin G, Krishnamurthy V, Ion C (2004) Regime switching stochastic approximation algorithms with application to adaptive discrete stochastic optimization. SIAM J Optim 14(4):1187–1215
Ravi R, Sinha A (2006) Hedging uncertainty: approximation algorithms for stochastic optimization problems. Math Program 108(1):97–114
Hong LJ, Nelson BL (2006) Discrete optimization via simulation using COMPASS. Oper Res 54(1):115–129
Sadegn P, Spall JC (1998) Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans Autom Control 43(10):1480–1484
Kleinman NL, Nathan L, Spall JC, Naiman DQ (1999) Simulation-based optimization with stochastic approximation using common random numbers. Manag Sci 45(11):1570–1578
Hutchison DW, Hill SD (2000) Simulation optimization of airline delay using simultaneous perturbation stochastic approximation. In: The IEEE annual simulation symposium proceedings, IEEE Press, Washington DC, pp 253–258
He Y, Fu MC, Marcus SI (2003) Convergence of simultaneous perturbation stochastic approximation for nondifferentiable optimization. IEEE Trans Autom Control 48(8):1459–1463
Andradottir S (2006) An overview of simulation optimization via random search. In: Henderson SG, Nelson BL (eds) Handbooks in operations research and management science, vol 1, handbooks in operations research and management science: simulation, 1st edn. Elsevier Science, Amsterdam
Swisher JR, Hyden PD, Jacobson SH, Schruben LW (2004) A survey of recent advances in discrete input parameter discrete-event simulation optimization. IIE Trans 36(6):591–600
Myers RH, Montgomery DC, Geoffrey VG et al (2004) Response surface methodology: a retrospective and literature survey. J Qual Technol 36(1):53–78
Yeun YS, Yang YS, Ruy WS, Kim BJ (2005) Polynomial genetic programming for response surface modeling part 1: a methodology. Struct Multidiscip Optim 29(1):19–34
Youn BD, Choi KK (2004) A new response surface methodology for reliability-based design optimization. Comput Struct 82(2–3):241–256
Barton R (2006) Response surface methodology. In: Henderson SG, Nelson BL (eds) Handbooks in operations research and management science, vol 1, handbooks in operations research and management science: simulation, 1st edn. Elsevier Science, Amsterdam
Hunt FY (2005) Sample path optimality for a Markov optimization problem. Stoch Process Appl 115(5):769–779
Palmer K, Asiabanpour B, Khoshnevis B (2006) Development of a rapid prototyping system using response surface methodology. Qual Reliab Eng Int 22(8):919–937
Kemper P, Muller D, Thummler A (2006) Combining response surface methodology with numerical methods for optimization of Markovian models. IEEE Trans Dependable Secur Comput 3(3):259–269
Vadde KK, Syrotiuk VR, Montgomery DC (2006) Optimizing protocol interaction using response surface methodology. IEEE Trans Mob Comput 5(6):627–638
Beers V, Kleijnen JPC (2003) Kriging for interpolation in random simulation. J Oper Res Soc 54(3):255–262
Robinson SM (1996) Analysis of sample-path optimization. Math Oper Res 21(3):513–528
Plambeck EL, Fu B-R, Robinson SM, Suri R (1996) Sample-path optimization of convex stochastic performance functions. Math Program (Series B) 75(2):137–176
Meng FW, Xu HF (2006) Exponential convergence of sample average approximation methods for a class of stochastic mathematical programs with complementarity constraints. J Comput Math 24(6):733–748
Wei J, Realff MJ (2004) Sample average approximation methods for stochastic MINLPs. Comput Chem Eng 28(3):333–346
Blomvall J, Shapiro A (2007) Solving multistage asset investment problems by the sample average approximation method. Math Program 108(2–3):571–595
Verweij B, Ahmed S, Kleywegt AJ et al (2003) The sample average approximation method applied to stochastic routing problems: a computational study. Comput Optim Appl 24(2–3):289–333
Royset JO, Polak E (2004) Reliability-based optimal design using sample average approximations. Probab Eng Mech 19(4):331–343
Lasserre JB (1999) Sample-path average optimality for Markov control processes. IEEE Trans Autom Control 44(10):1966–1971
Charon I, Hudry O (2001) A generalization of some metaheuristics. Eur J Oper Res 135(1):86–101
Yagiura M, Ibaraki T (1996) Metaheuristics as robust and simple optimization tools. In: The international conference of evolutionary computation proceedings, IEEE Press, Nagoya, pp 541–546
Fortemps P, Ost C, Pirlot M et al (1996) Using metaheuristics for solving a production scheduling problem in a chemical firm, a case study. Int J Prod Econ 46–47(1):13–26
Talbi E-G (2002) A taxonomy of hybrid metaheuristics. J Heuristics 8(5):541–564
Fanni A, Manunza A, Marchesi M, Pilo F (1999) Tabu search metaheuristics for electromagnetic problems optimization in continuous domains. IEEE Trans Magn 35(3):1694–1697
Sousa SHG, Maschio C, Schiozer DJ (2006) Scatter search metaheuristic applied to the history-matching problem. In: The SPE annual technical conference and exhibition proceedings, vol 5, IEEE Press, San Antonio, pp 3544–3553
Greistorfer P (2003) A tabu scatter search metaheuristic for the arc routing problem. Comput Ind Eng 44(2):249–266
Olaffson S (2006) Metaheuristics. In: Henderson SG, Nelson BL (eds) Handbooks in operations research and management science, vol 1, handbooks in operations research and management science: simulation, 1st edn. Elsevier Science, Amsterdam
Shi L, Olafsson S (2000) Nested partitioned method for global optimization. Oper Res 48(3):390–407
Tekin E, Sabuncuoglu I (2004) Simulation optimization: a comprehensive review on theory and applications. IIE Trans (Institute of Industrial Engineers) 36(11):1067–1081
Zhao JH, Dao TM, Liu ZH (2005) Optimization of mechanical systems reliability using ant colony based simulation approach. In: The IASTED international conference on modelling and simulation proceedings, Acta Press, Cancun, pp 182–187
Jalali MR, Afshar A, Marino MA (2005) Ant colony optimization algorithm (ACO), a new heuristic approach for engineering optimization. WSEAS Trans Inf Sci Appl 2(5):606–610
Dorigo M, Stutzle T (2004) Ant colony optimization, vol 1, 1st edn. MIT Press, Cambridge
Larranaga P, Lozano JA (2001) Estimation of distribution algorithms: a new tool for evolutionary computation, vol 1, 1st edn. Kluwer, Boston
Zhang QF, Sun JY, Tsang E, Ford J (2004) Hybrid estimation of distribution algorithm for global optimization. Eng Comput 21(1):91–107
Simionescu PA, Beale DG, Dozier GV (2004) Constrained optimization problem solving using estimation of distribution algorithms. In: The congress on evolutionary computation proceedings, vol 1, IEEE Press, Portland, pp 296–302
D’Acquisto G, Naldi M (2005) Cross-entropy-based adaptive optimization of simulation parameters for Markovian-driven service systems. Simul Model Pract Theory 13(7):619–645
Boer P-TD, Kroese DP, Mannor S, Rubinstein RY (2005) A tutorial on the cross-entropy method. Ann Oper Res 134(1):19–67
Rubinstein RY, Kroese DP (2004) The cross-entropy method: a unified approach to combinatorial optimization, Monte-Carlo simulation, and machine learning, vol 1, 1st edn. Springer, New York
Hu J, Fu MC, Marcus SI (2005) A model reference adaptive search algorithm for global optimization. The Institute for Systems Research, Maryland, Technical Research Report, TR 2005-81, March 2005
Hu JQ, Fu MC, Marcus SI (2005) Stochastic optimization using model reference adaptive search. In: The winter simulation conference proceedings, IEEE Press, Orlando, pp 811–818
Jones MH, White KP (2004) Stochastic approximation with simulated annealing as an approach to global discrete-event simulation optimization. In: The winter simulation conference proceedings, IEEE Press, Washington DC, pp 500–507
Buchholz P, Thummler A (2005) Enhancing evolutionary algorithms with statistical selection procedures for simulation optimization. In: The winter simulation conference proceedings, IEEE Press, Orlando, pp 842–852
Sriver TA, Chrissis JW (2004) Combined pattern search and ranking and selection for simulation optimization. In: The winter simulation conference proceedings, IEEE Press, Washington DC, pp 645–653
Hedlund HE, Mollaghasemi M (2001) A genetic algorithm and an indifference-zone ranking and selection framework for simulation optimization. In: The winter simulation conference proceedings, IEEE Press, Arlington, pp 417–421
Li QY, Gong YB, Yang DG, Liang JS (2003) Study on simulation-based optimization for flip chip package parameters by using RSM analysis and ant algorithm. In: The fifth international conference on electronic packaging technology proceedings, IEEE Press, Shanghai, pp 86–90
Persson A, Grimm H, Ng A (2006) Simulation-based optimization using local search and neural network metamodels. In: The artificial intelligence and soft computing proceeding, ACTA Press, Palma de Mallorca, pp 149–156
Neelakantan TR, Pundarikanthan NV (2000) Neural network-based simulation-optimization model for reservoir operation. J Water Resour Plan Manag 126(2):57–64
Wang L (2005) A hybrid genetic algorithm-neural network strategy for simulation optimization. Appl Math Comput 170(2):1329–1343
Pan QK, Wang WH, Zhu JY (2006) Effective hybrid heuristics based on particle swarm optimization and simulated annealing algorithm for job shop scheduling. China Mech Eng 17(10):1044–1046
Wah BW, Chen Y (2001) Hybrid constrained simulated annealing and genetic algorithms for nonlinear constrained optimization. In: The IEEE conference on evolutionary computation proceedings, vol 2, IEEE Press, Seoul, pp 925–932
Heitzinger C, Selberherr S (2002) An extensible TCAD optimization framework combining gradient based and genetic optimizers. Microelectron J 33(1–2):61–68
Montastruc L, Azzaro-Pantel C, Pibouleau L, Domenech S (2004) Use of genetic algorithms and gradient based optimization techniques for calcium phosphate precipitation. Chem Eng Process 43(10):1289–1298
Ahmed MA, Alkhamis TM (2002) Simulation-based optimization using simulated annealing with ranking and selection. Comput Oper Res 29(2):387–402
Wong BK, Bodnovich TA, Selvi Y (1997) Neural network applications in business: a review and analysis of the literature. Decis Support Syst 19(4):301–320
Wong BK, Selvi Y (1998) Neural network applications in finance: a review and analysis of literature. Inf Manag 34(3):129–139
Avi-Itzhak HI, Diep TA, Garland H (1995) High accuracy optical character recognition using neural networks with centroid dithering. IEEE Trans Pattern Anal Mach Intell 17(2):218–224
Leung HF, Lam HK, Ling SH, Tam PKS (2003) Tuning of the structure and parameters of neural network using an improved genetic algorithm. IEEE Trans Neural Netw 14(1):79–88
Wang WJ, Tang XC, Li WC (1993) Variable structure neural network model and its applications. In: The IEEE region 10 conference on computer, communication, control and power engineering, IEEE Press, Beijing, pp 799–802
Chang MP, Chang DS, Yu CC (1999) Nonlinear state estimation using variable-structure neural network. J Chin Inst Chem Eng 30(4):289–296
Luan DN, Chang DS, Chang MP, Yu CC (2000) Diagnosis of abrupt faults using variable-structure neural network. J Chin Inst Eng 23(5):567–574
Mekki H, Chtourou M, Derbel N (2006) Variable structure neural networks for adaptive control of nonlinear systems using the stochastic approximation. Simul Model Pract Theory 14(7):1000–1009
Ling SH, Lam HK, Leung FHF, Lee YS (2003) A genetic algorithm based variable structure neural network. In: IECON proceedings (industrial electronics conference), IEEE Press, Roanoke, pp 436–441
Hsiao YT, Chuang CL, Jiang JA (2005) A novel dynamic structural neural network with neuro-regeneration and neuro-degeneration. In: The ninth international workshop on cellular neural networks and their applications, IEEE Press, Hsinchu, pp 9–14
Bhat NV, Minderman PA, Mcavoy T, Wang NS (1990) Modeling chemical process systems via neural computation. IEEE Control Syst Mag 10(3):24–30
Fukuda T, Shibata T (1992) Theory and applications of neural networks for industrial control systems. IEEE Trans Ind Electron 39(6):472–490
Xia YS (2004) An extended projection neural network for constrained optimization. Neural Comput 16(4):863–883
Xia YS, Wang J (2004) A recurrent neural network for solving nonlinear optimization subject to nonlinear inequality constraints. IEEE Trans Circuits Syst 51(7):1385–1394
Kitano H (1994) Neurogenetic learning: an integrated method of designing and training neural networks using genetic algorithms. Phys D 75(1–3):225–238
Boozarjomehry RB, Svrcek WY (2001) Automatic design of neural network structures. Comput Chem Eng 25(1):1075–1088
Xu L, Jordan MI, Hinton GE (1995) An alternative model for mixtures of experts. In: Tesauro G, Touretzky D, Leen T (eds) Advances in neural information processing systems, vol 7. MIT Press, Cambridge, pp 633–640
Amari S, Murata N, Muller KR et al (1997) Asymptotic statistical theory of overtraining and cross-validation. IEEE Trans Neural Netw 8(5):985–996
Moody J, Utans J (1994) Architecture selection strategies for neural networks: application to corporate bond rating prediction in neural networks in the capital markets. Wiley, New York
Kottathra K, Attikiouzel Y (1996) A novel multicriteria optimization algorithm for the structure determination of multilayer feedforward neural networks. J Netw Comput Appl 19(2):135–147
Lindenmayer A (1968) Mathematical models for cellular interactions in development I. Filaments with one-sided inputs. J Theor Biol 18(3):280–300
Lindenmayer A (1968) Mathematical models for cellular interactions in development II. Simple and branching filaments with two-sided inputs. J Theor Biol 18(3):300–316
Rovithakis A, Chalkiadakis I, Zervakis ME (2004) High-order neural network structure selection for function approximation applications using genetic algorithms. IEEE Trans Syst Man Cybern B Cybern 34(1):150–158
Henrique M, Lima EL, Seborg DE (2000) Model structure determination in neural network models. Chem Eng Sci 55(22):5457–5469
Mao KZ, Tan KC, Ser W (2000) Probabilistic neural-network structure determination for pattern classification. IEEE Trans Neural Netw 11(4):1009–1016
Na MG, Sim YR, Park KH, Lee SM (2003) Sensor monitoring using a fuzzy neural network with an automatic structure constructor. IEEE Trans Nucl Sci 50(2):241–250
Tsai JT, Chou JH, Liu TK (2006) Tuning the structure and parameters of a neural network by using hybrid Taguchi-genetic algorithm. IEEE Trans Neural Netw 17(1):69–70
Mao KZ, Huang CB (2005) Neuron selection for RBF neural network classifier based on data structure preserving criterion. IEEE Trans Neural Netw 16(6):1531–1540
Zhong WC, Liu J, Xue MZ et al (2004) A multiagent genetic algorithm for global numerical optimization. IEEE Trans Syst Man Cybern B Cybern 34(2):1128–1141
Tsai JT, Liu TK, Chou JH (2004) Hybrid Taguchi-genetic algorithm for global numerical optimization. IEEE Trans Evol Comput 8(4):365–377
Tu Z, Lu Y (2004) A robust stochastic genetic algorithm (StGA) for global numerical optimization. IEEE Trans Evol Comput 8(5):456–470
Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716–723
Rissanen J (1983) A universal prior for integers and estimation by minimum description length. Ann Stat 11(2):416–431
Arribas JI, Cid-Sueiro J (2005) A model selection algorithm for posteriori probability estimation with neural networks. IEEE Trans Neural Netw 16(4):799–809
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Jun, Z., Yu-An, T., Xue-Lan, Z. et al. An improved dynamic structure-based neural networks determination approaches to simulation optimization problems. Neural Comput & Applic 19, 883–901 (2010). https://doi.org/10.1007/s00521-010-0348-x
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DOI: https://doi.org/10.1007/s00521-010-0348-x