Abstract
We consider the Nelder-Mead (NM) simplex algorithm for optimization of discrete-event stochastic simulation models. We propose new modifications of NM to reduce computational time and to improve the optimal solutions. Our means include utilizing past information of already seen solutions, expanding search space to their neighborhood, and using adaptive sample sizes. We compare performance of these extensions on two test functions with 3 levels of random variation. We find that using past information leads to reduction of computational effort. Comparing with the non-adaptive modification, the adaptive one needs more resources but gives better solution.
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References
Allon, G., Kroese, D., Raviv, T., Rubinstein, R.: Application of the Cross Entropy Method to the Buffer Allocation Problem in Simulation Based Environment. Annals of Operations Research 134, 137–151 (2005)
Andradóttir, S.: An Overview of Simulation Optimization Via Random Search. In: Handbooks in Operations Research and Management Science: Simulation, pp. 617–631. Elsevier, North-Holland (2006)
Barton, R.R., Ivey, J.S.: Nelder-Mead Simplex Modifications for Simulation Optimization. Management Science 42, 954–973 (1996)
Bonello, A.F., Mosca, R., Cotto, S.P.: Multi-Objective Optimisation of Food Refluent Treatment Plant Design Parameters through Designed Simulation with Significant Experimental Error. In: Proceedings of the 14th European Simulation Symposium, Dresden, Germany (2002)
Branco, D.M.: Nonlinear Optimization of a Stochastic Function in a Cell Migration Model. M.S. Thesis, Worcester Polytechnic Institute, MA, USA (2006)
Carson, Y., Maria, A.: Simulation Optimization: Methods and Applications. In: Proceedings of the 1997 Winter Simulation Conference, Atlanta, GA, USA, pp. 118–126 (1997)
Dennis, J.E., Woods, D.J.: Optimization on Microcomputers the Nelder-Mead Simplex Algorithm. In: New Computing Environments: Microcomputers in Large Scale Computing, pp. 116–122. The Society for Industrial and Applied Mathematics, Philadelphia (1987)
Ho, Y.C., Sreenivas, R.S., Vakili, P.: Ordinal Optimization of DEDS Discrete Event Dynamic Systems, vol. 2, pp. 61–88 (1992)
Holland, J.H.: Genetic Algorithms. Scientific American 267, 66–72 (1992)
Hong, L.J., Nelson, B.L.: An Indifference-Zone Selection Procedure with Minimum Switching and Sequential Sampling. In: Proceedings of the 2003 Winter Simulation Conference, New Orleans, LA, USA, pp. 474–480 (2003)
Hong, L.J., Nelson, B.L.: A Framework for Locally Convergent Random-Search Algorithms for Discrete Optimization Via Simulation. Association for Computing Machinery Transctions on Modeling and Computer Simulation 17, 1–22 (2007)
Hooke, R., Jeeves, T.A.: Direct Search Solution of Numerical and Statistical Problems. Association for Computing Machinery 8, 212–229 (1961)
Humphrey, D.G., Wilson, J.R.: A Revised Simplex Search Procedure for Stochastic Simulation Response Surface Optimization. Institute for Operations Research and the Management Sciences: Journal on Computing 12, 272–283 (2000)
Gosavi, A., Phatakwala, S.: A Finite-Differences Derivative-Descent Approach for Estimating Form Error in Precision-Manufactured Parts Manufacturing Science and Engineering, vol. 128, pp. 355–359 (2006)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by Simulated Annealing. Science 220, 671–680 (1983)
Kumral, M.: Solution of Ore Blending Problem by Stochastic Approach. In: Proceedings of the 10th International Mining Congress and Exhibition of Turkey, Antalya, Turkey, pp. 485–490 (2003)
Nelder, J.A., Mead, R.: A Simplex Method for Function Minimization. Computer Journal, 308–313 (1965)
Ólafsson, S., Kim, J.: Simulation Optimization: Simulation Optimization. In: Proceedings of the 2002 Winter Simulation Conference, Atlanta, GA, USA, pp. 79–84 (2002)
Pichitlamken, J., Nelson, B.L.: A Combined Procedure for Optimization Via Simulation. Association for Computing Machinery Transactions on Modeling and Computer Simulation 13, 155–179 (2003)
Pichitlamken, J., Nelson, B.L., Hong, J.L.: A Sequential Procedure for Neighborhood Selection-of-the-Best in Optimization Via Simulation. European Journal of Operational Research 173, 283–298 (2006)
Schwefel, H.-P.: Evolution and Optimum Seeking: The Sixth Generation. John Wiley & Sons, New York (1993)
Shi, L., Ólafsson, S.: An Integrated Framework for Deterministic and Stochastic Optimization. In: Proceedings of the 1997 Winter Simulation Conference, Atlanta, GA, USA, pp. 358–365 (1997)
Spendley, W., Hext, G.R., Himsworth, F.R.: Sequential Application of Simplex Designs in Optimisation and Evolutionary Operation. Technometrics 4, 441–461 (1962)
Swisher, J.R., Hyden, P.D., Jacobson, S.H., Schruben, L.W.: A Survey of Recent Advances in Discrete Input Parameter Discrete-Event Simulation Optimization. Institute of Industrial Engineers Transactions 36, 591–600 (2004)
Tippayawannakorn, N., Pichitlamken, J.: Global Search with Local Selection for Stochastic Problems with Finite Discrete Feasible Space. To appear, Ph.D. Thesis, Kasetsart, Bangkok, Thailand (2012)
Tomick, J.J.: On Convergence of the Nelder-Mead Simplex Algorithm for Unconstrained Stochastic Optimization. Ph.D. Thesis, The Pennsylvania State University, PA, USA (1995)
Yan, D., Mukai, H.: Stochastic Discrete Optimization. Society for Industrial and Applied Mathematics Journal on Control and Optimization 30, 594–612 (1992)
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Tippayawanakorn, N., Pichitlamken, J. (2012). Nelder-Mead Method with Local Selection Using Neighborhood and Memory for Optimization via Simulation. In: Kim, JH., Lee, K., Tanaka, S., Park, SH. (eds) Advanced Methods, Techniques, and Applications in Modeling and Simulation. Proceedings in Information and Communications Technology, vol 4. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54216-2_16
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DOI: https://doi.org/10.1007/978-4-431-54216-2_16
Publisher Name: Springer, Tokyo
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