Abstract
This chapter focusses on simulation-based techniques for solving stochastic problems of parametric optimization, also popularly called static optimization problems. Such problems have been defined in Chap. 3.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
M.H. Alrefaei, S. Andradóttir, A simulated annealing algorithm with constant temperature for discrete stochastic optimization. Manag. Sci. 45(5), 748–764 (1999)
M.H. Alrefaei, S. Andradóttir, A modification of the stochastic ruler method for discrete stochastic optimization. Eur. J. Oper. Res. 133, 160–182 (2001)
S. Andradóttir, Simulation optimization, in Handbook of Simulation, ed. by J. Banks, chapter 9 (Wiley, New York, 1998)
H. Arsham, A. Feurvergerd, D.L. McLeish, J. Kreimer, R.Y. Rubinstein, Sensitivity analysis and the what-if problem in simulation analysis. Math. Comput. Model. 12(2), 193–219 (1989)
R.R. Barton, J.S. Ivey, Nelder-Mead simplex modifications for simulation optimization. Manag. Sci. 42(7), 954–973 (1996)
R.E. Bechhofer, T.J. Santner, D.J. Goldsman, Design and Analysis of Experiments for Statistical Selection, Screening, and Multiple Comparisons (Wiley, New York, 1995)
D.P. Bertsekas, Non-linear Programming (Athena Scientific, Belmont, 1995)
S. Bhatnagar, Adaptive multivariate three-timescale stochastic approximation algorithms for simulation based optimization. ACM Trans. Model. Comput. Simul. 15(1), 74–107 (2005)
S. Bhatnagar, V.S. Borkar, A two time scale stochastic approximation scheme for simulation based parametric optimization. Probab. Eng. Inf. Sci. 12, 519–531 (1998)
S. Bhatnagar, V.S. Borkar, Multiscale chaotic SPSA and smoothed functional algorithms for simulation optimization. Simulation 79(10), 569–580 (2003)
S. Bhatnagar, H.J. Kowshik, A discrete parameter stochastic approximation algorithm for simulation optimization. Simulation 81(11), 757–772 (2005)
I. Bohachevsky, M. Johnson, M. Stein, Generalized simulated annealing for function approximation. Technometrics 28, 209–217 (1986)
S. Brooks, B. Morgan, Optimization using simulated annealing. The Statistician 44, 241–257 (1995)
Y. Carson, A. Maria, Simulation optimization: methods and applications, in Proceedings of the 1997 Winter Simulation Conference, Atlanta, 1997, pp. 118–126
A. Cauchy, Méthode génserale pour la résolution des systéms d’équations simultanées. C. R. Sci. Paris 25, 536–538 (1847)
H.S. Chang, M.C. Fu, J. Hu, S.I. Marcus, Simulation-Based Algorithms for Markov Decision Processes (Springer, London, 2007)
G. Deng, M.C. Ferris, Variable-number sample path optimization. Math. Program. Ser. B 117, 81–109 (2009)
M. Dorigo, T. Stützle, Ant Colony Optimization (MIT, Cambridge, MA, 2004)
T. Feo, M. Resende, Greedy randomized adaptive search procedures. J. Global Optim. 6, 108–133 (1995)
M.J. Fielding, Optimisation by simulated annealing, PhD thesis, Department of Mathematics, The University of Melbourne, 1999
B.L. Fox, G.W. Heine, Probabilistic search with overrides. Ann. Appl. Probab. 5, 1087–1094 (1995)
M.C. Fu, Optimization via simulation: theory vs. practice. INFORMS J. Comput. 14(3), 192–215 (2002)
M.C. Fu, Optimization via simulation: a review. Ann. Oper. Res. 53, 199–247 (1994)
M.C. Fu, J.Q. Hu, Conditional Monte Carlo-Gradient Estimation and Optimization Applications (Kluwer Academic, Boston, 1997)
S.B. Gelfand, S.K. Mitter, Simulated annealing with noisy or imprecise energy measurements. J. Optim. Theory Appl. 62(1), 49–62 (1989)
M. Gendreau, J.-Y. Potvin, Handbook of Metaheuristics (Springer, New York, 2010)
L. Gerencser, S.D. Hill, Z. Vago, Optimization over discrete sets by SPSA, in Proceedings of the Winter Simulation Conference, Phoenix, 1999, pp. 466–470
S. German, D. German, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. (PAMI) 6, 721–741 (1984)
F. Glover, Tabu search: a tutorial. Interfaces 20(4), 74–94 (1990)
F. Glover, J.P. Kelly, M. Laguna, New advances and applications of combining simulation and optimization, in Proceedings of the 1996 Winter Simulation Conference, Coronado, 1996, pp. 144–152
F. Glover, M. Laguna, Tabu Search (Kluwer Academic, Norwell, 1998)
F. Glover, M. Laguna, R. Marti, Fundamentals of scatter search and path relinking. Control Cybern. 29(3), 653–684 (2000)
D. Goldsman, B.L. Nelson, Comparing systems via simulation, in Handbook of Simulation, ed. by J. Banks, chapter 8 (Wiley, New York, 1998)
W.B. Gong, Y.C. Ho, W. Zhai, Stochastic comparison algorithm for discrete optimization with estimation, in Proceedings of the 31st Conference on Decision Control, Tucson, 1992, pp. 795–800
A. Gosavi, On step-sizes, stochastic paths, and survival probabilities in reinforcement learning, in Proceedings of the 2008 Winter Simulation Conference, Miami (IEEE, 2008)
A. Gosavi, Codes for neural networks, DP, and RL in the C language for this book (2014), http://web.mst.edu/~gosavia/bookcodes.html
B. Hajek, Cooling schedules for optimal annealing. Math. Oper. Res. 13, 311–329 (1988)
S.S. Heragu, Facilities Design, 3rd edn. (CRC, Boca Raton, 2008)
Y.C. Ho, X.R. Cao, Perturbation Analysis of Discrete Event Dynamic Systems (Springer, Boston, 1991)
Y.C. Ho, R. Sreenivas, P. Vakili, Ordinal optimization of discrete event dynamic systems. J. DEDS 2(2), 61–88 (1992)
Y. Hochberg, A.C. Tamhane, Multiple Comparison Procedures (Wiley, New York, 1987)
J.H. Holland, Adaptation in Natural and Artificial Systems (University of Michigan Press, Ann Arbor, 1975)
L.J. Hong, B.L. Nelson, Discrete optimization via simulation using COMPASS. Oper. Res. 54(1), 115–129 (2006)
R. Hooke, T.A. Jeeves, Direct search of numerical and statistical problems. ACM 8, 212–229 (1966)
J. Hu, M.C. Fu, S.I. Marcus, A model reference adaptive search method for global optimization. Oper. Res. 55, 549–568 (2007)
S.H. Jacobson, L.W. Schruben, A harmonic analysis approach to simulation sensitivity analysis. IIE Trans. 31(3), 231–243 (1999)
J.-S.R. Jang, C.-T. Sun, E. Mizutani, Neuro-Fuzzy and Soft Computing (Prentice Hall, Upper Saddle River, 1997)
J. Kennedy, R.C. Eberhart, Y. Shi, Swarm Intelligence (Morgan Kaufmann, San Francisco, 2001)
J. Kiefer, J. Wolfowitz, Stochastic estimation of the maximum of a regression function. Ann. Math. Stat. 23, 462–466 (1952)
S.-H. Kim, B.L. Nelson, A fully sequential procedure for indifference-zone selection in simulation. ACM Trans. Model. Comput. Simul. 11, 251–273 (2001)
S. Kirkpatrick, C.D. Gelatt, M.P. Vecchi, Optimization by simulated annealing. Science 220, 671–680 (1983)
J.P.C. Kleijnen, Sensitivity analysis and optimization in simulation: design of experiments and case studies, in Proceedings of the 1995 Winter Simulation Conference, Arlington, 1995, pp. 133–140
J.P.C. Kleijnen, Design and Analysis of Simulation Experiments (Springer, New York, 2007)
B. Kristinsdottir, Z.B. Zabinsky, G. Wood, Discrete backtracking adaptive search for global optimization, in Stochastic and Global Optimization, ed. by G. Dzemyda, V. Saltenis, A. Zilinskas (Kluwer Academic, Dordrecht/London, 2002), pp. 147–174
J.C. Lagarias, J.A. Reeds, M.H. Wright, P.E. Wright, Convergence properties of the Nelder–Mead simplex method in low dimensions. SIAM J. Optim. 9(1), 112–147 (1998)
A.M. Law, W.D. Kelton, Simulation Modeling and Analysis (McGraw Hill, New York, 1999)
M. Lundy, A. Mees, Convergence of the annealing algorithm. Math. Program. 34, 111–124 (1986)
N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, Equation of state calculations by fast computing machines. J. Chem. Phys 21, 1087–1092 (1953)
O. Molvalioglu, Z.B. Zabinsky, W. Kohn, The interacting particle algorithm with dynamic heating and cooling. J. Global Optim. 43, 329–356 (2019)
J.A. Nelder, R. Mead, A simplex method for function minimization. Comput. J. 7, 308–313 (1965)
R. Pasupathy, B.W. Schmeiser, Retrospective-approximation algorithms for multidimensional stochastic root-finding problems. ACM TOMACS 19(2), 5:1–5:36 (2009)
G.C. Pflug, Optimization of Stochastic Models: The Interface Between Simulation and Optimization (Kluwer Academic, Boston, 1996)
D.T. Pham, D. Karaboga, Intelligent Optimisation Techniques: Genetic Algorithms, Tabu Search, Simulated Annealing, Neural Networks (Springer, New York, 1998)
E.L. Plambeck, B.R. Fu, S.M. Robinson, R. Suri, Sample path optimization of convex stochastic performance functions. Math. Program. 75, 137–176 (1996)
W.H. Press, S.A. Tuekolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, Cambridge, 1992)
A.A. Prudius, S. Andradóttir, Balanced explorative and exploitative search with estimation for simulation optimization. INFORMS J. Comput. 21, 193–208 (2009)
Y. Rinott, On two-stage selection procedures and related probability-inequalities. Commun. Stat. Theory Methods A7, 799–811 (1978)
H.E. Romeijn, R.L. Smith, Simulated annealing and adaptive search in Global optimization. Probab. Eng. Inf. Sci 8, 571–590 (1994)
H.E. Romeijn, R.L. Smith, Simulated annealing for constrained global optimization. J. Global Optim. 5, 101–126 (1994)
R.Y. Rubinstein, A. Shapiro, Sensitivity Analysis and Stochastic Optimization by the Score Function Method (Wiley, New York, 1983)
G. Rudolph, Convergence of canonical genetic algorithms. IEEE Trans. Neural Netw. 5, 96–101 (1994)
S. Sarkar, S. Chavali, Modeling parameter space behavior of vision systems using Bayesian networks. Comput. Vis. Image Underst. 79, 185–223 (2000)
L. Shi, S. Olafsson, Nested partitions method for Global optimization. Oper. Res. 48(3), 390–407 (2000)
L. Shi, S. Olafsson, Nested partitions method for stochastic optimization. Methodol. Comput. Appl. Probab. 2(3), 271–291 (2000)
L. Shi, S. Olafsson, Nested Partitions Method, Theory and Applications (Springer, New York, 2008)
R.L. Smith, Efficient Monte Carlo procedures for generating points uniformly distributed over bounded regions. Oper. Res. 32, 1296–1308 (1984)
J.C. Spall, Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Autom. Control 37, 332–341 (1992)
J.C. Spall, Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control (Wiley, New York, 2003)
H. Szu, R. Hartley, Fast simulated annealing. Phys. Lett. A 122, 157–162 (1987)
T. Tezcan, A. Gosavi, Optimal buffer allocation in production lines using an automata search, in Proceedings of the 2001 Institute of Industrial Engineering Research Conference, Dallas, 2001
M.A.L. Thathachar, P.S. Sastry, Learning optimal discriminant functions through a cooperative game of automata. IEEE Trans. Syst. Man Cybern. 17, 73–85 (1987)
P. van Laarhoven, E. Aarts, Simulated Annealing: Theory and Applications (Kluwer Academic, Dordrecht, 1987)
I.-J. Wang, J.C. Spall, Stochastic optimization with inequality constraints using simultaneous perturbations and penalty functions, in Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, 2003
R.R. Wilcox, A table for Rinott’s selection procedure. J. Qual. Technol. 16, 97–100 (1984)
D. Yan, H. Mukai, Stochastic discrete optimization. SIAM J. Control Optim. 30, 594–612 (1992)
Z.B. Zabinsky, Stochastic Adaptive Search for Global Optimization (Springer, New York, 2003)
Z. Zabinsky, Random search algorithms for simulation optimization, in Handbook of Simulation Optimization (forthcoming), ed. by M. Fu (Springer, New York, 2014)
Z.B. Zabinsky, D. Bulger, C. Khompatraporn, Stopping and restarting strategy for stochastic sequential search in global optimization. J. Global Optim. 46, 273–286 (2010)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media New York
About this chapter
Cite this chapter
Gosavi, A. (2015). Parametric Optimization: Stochastic Gradients and Adaptive Search. In: Simulation-Based Optimization. Operations Research/Computer Science Interfaces Series, vol 55. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7491-4_5
Download citation
DOI: https://doi.org/10.1007/978-1-4899-7491-4_5
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-7490-7
Online ISBN: 978-1-4899-7491-4
eBook Packages: Business and EconomicsBusiness and Management (R0)