Professor Emeritus Reuven Rubinstein

General Information

Prof. Rubinstein joined the Faculty of Industrial Engineering and Management of the Technion in 1973. During his sabbatical years he was a visiting professor at many universities and research centers around the world, among them University of Illinois, Urbana, Harvard University, Stanford University, IBM Research Center, Bell Laboratories, NJ, NEC, and the Institute of Statistical Math., Japan.

He is a member of several societies including the Operations Research Society of Israel and the American Operations Research Society.

He is the founder of the well known score function (SF) method in simulation and the cross-entropy (CE) method for combinatorial optimization, which generated an entire new scientific community: (for details see the CE homepage ).

He holds a chair in Management Science at the Technion donated by Mr. Milford Bohm.

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Research Summary

Stochastic systems abound in real-world applications. Examples include traffic systems, flexible manufacturing systems, computer-communication systems, production lines, coherent lifetime systems, and flow networks. Most of these systems can be modeled in terms of discrete events whose occurrence causes the system to change from one state to another. In designing, analyzing and operating such complex systems, one is interested in performance evaluation, sensitivity analysis and optimization. Sensitivity analysis is concerned with evaluating sensitivities (gradients, Hessians, etc.) of performance measures with respect to parameters of interest. It provides guidance for design and operational decisions and plays a pivotal role in identifying the most significant system parameters, as well as bottleneck subsystems.

Our group carries out research in the fields of probability of rare events' estimation and stochastic optimization with emphasis on simulation-based optimization. Our research programs are dedicated to estimation of probabilities of rare events, like the probability of buffer overflow in a queueing network of ATM type, probability of breakdown in a highly reliable system and ruin probability in an insurance risk system. This is cased on a novel approach developed at the Technion which is called the cross-entropy (CE) method. Another research project is solving NP-hard combinatorial optimization problems using a randomized algorithm based on CE.

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Current Research Projects

Randomized and heuristic algorithms for combinatorial optimization

Estimation of probabilities of rare events of complex networks

Stochastic optimization in general

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Selected Publications

[1] Published

Rubinstein, R.Y., ``Sensitivity Analysis of Computer Simulation Models via the Score Efficient", Operations Research, Vol.37, pp.72--81, 1989.
Asmussen, S.and Rubinstein, R.Y., ``The Efficiency and Heavy Traffic Properties of the Score Function Method in Sensitivity Analysis of Queueing Models", Adv.Appl. Probab., Vol. 24, No.1, pp.172--201, 1992
Rubinstein, R..Y., ``Sensitivity Analysis of Discrete Event Systems by the `Push out' Method", Annals of Operations Research, Vol.39, pp.229--251, 1992.
Asmussen, S. and Rubinstein, R.Y., ``Performance Evaluation and Sensitivity Analysis via the Efficient Change of Measure", Stochastic Models, Vol.9, No.3, pp.313--339, 1993.
Rubinstein, R. Y. and Uryas'ev, S., ``On Relaxation Algorithm for the Computation of Noncooperative Equilibria", IEEE, Automatic Control, Vol.39, No.6, pp.1263--1268, 1994.
Rubinstein, R. Y., ``Optimization of Computer simulation Models with Rare Events", European Journal of Operations Research , 99, 89-112, 1997.
Lieber, D., Rubinstein, R.Y. and Elmakis, D., ``Quick Estimation of Rare Events in Stochastic Networks", IEEE Transactions on Reliability Systems , vol 46, No 2, 254-265, 1997.
Rubinstein, R. Y.``The Cross-Entropy Metod for Combinatorial and Continuous Optimization '' Methodology and Computing in Applied Probability, 1, 127-190. 1999
Lieber, D., Nemirovski, A and Rubinstein, R.Y., "A Fast Monte Carlo Method for Evaluation of Reliability Indices", IEEE Transactions on Reliability Systems vol. 48, No 3, 256-261, 1999.
Rubinstein R.Y.,"The cross-entropy method and rare-events for maximal cut and bipartition problems",ACM Transactions on Modelling and Computer Simulation Vol. 12, No. 1, 27-53, 2002.
Pflug, G and Rubinstein R.Y., "Inventory processes: Quasi-regenerative property, performance evaluation and sensitivity estimation via simulation",Stochastic Models, 2002.
Mannor Sh., Rubinstein, R.Y. and Y. Gat"The Cross Entropy method for Fast Policy Search",Proceedings of the ICML Conference, Washington DC, 2003.
de Boer, P. T., Kroese D. P., and R.Y. Rubinstein,"A Fast Cross-Entropy Method for Estimating Buffer Overflows in Queueing Networks", Management Science, Vol.50, No. 2, pp. 883-895, 2004.
Kroese, D. P. and R. Y. Rubinstein,"The Transform Likelihood Ratio Method for Rare Event Simulation with Heavy Tails", Queueing Systems, Vol. 46, No. 3/4, pp. 317-352, 2004.
R. Y. Rubinstein "The Stochastic Minimum Cross-Entropy Method for Combinatorial Optimization and Rare-event Estimation", Methodology and Computing in Applied Probability, 7, pp. 5-50, 2005
Alon, G., Kroese, D., Raviv, T. and Rubinstein R.Y."Application of the Cross Entropy Method for Optimal Buffer Allocation in a Simulation Based Environment",Annals of Operations Research, 134(1), pp. 137-151, 2005.
de Boer, P. T. Kroese, D. P, Mannor, S. and R.Y. Rubinstein,"A Tutorial on the Cross-Entropy Method",Annals of Operations Research, 134(1), pp. 19-67, 2005.
Asmussen, S., Kroese, D. P. and R. Y. Rubinstein, "Heavy Tails, Importance Sampling and the Cross-Entropy Method", Stochastic Models, Vol. 21, No. 1, pp. 57-76, 2005.
D. Peleg, S. Mannor and R. Y. Rubinstein "The Cross-Entropy Method for Classification", Proceeding of the 22-nd International Conference on Machine Learning, Bonn, Germany, 2005.
R. Y. Rubinstein "How Many Needles Are in a Hay Stack, or How to Solve Fast #P-Complete Counting Problems". Methodology and Computing in Applied Probability,11, pp 5-49, 2007.
D. Kroese, R. Y. Rubinstein and T. Taimre "Application of the Cross-Entropy Method to Clustering and Vector Quantization" Journal of Global Optimization37, pp.137-157, 2006
D. Kroese, S. Porotsky and R. Y. Rubinstein "The Cross-Entropy Method for Continuous Multiextremal Optimization" Methodology and Computing in Applied Probability, 8, pp.383-407, 2006.
Ridder A., and R. Y. Rubinstein “Minimum Cross-entropy Methods for Rare-event Simulation”. Simulation, Vol 83, 11, 2007.
R. Y. Rubinstein "The Gibbs Cloner for Combinatorial Optimization, Counting and Sampling", Methodology and Computing in Applied Probability, 11(2), 491-549, 2009
Rubinstein, R. Y. and Glynn P. W. "How to Deal with the Curse of Dimensionality of Likelihood Ratios in Monte Carlo Simulation", Stochastic Models, 2009
Rubinstein, R. Y. "Randomized Algorithms with Splitting: Why the Classic Randomized Algorithms do not Work and how to Make them Work”, Methodology and Computing in Applied Probability, 11(4), 2009

[2] Accepted for publication

Glynn P., Dolgin A., Rubinstein R. Y., and Vaisman "How to Generate Uniform Samples on Discrete Sets Using the Splitting Method", Prob. in Eng. and Inf. Sciences

[3] Submitted for publication

Awad H. P., Glynn P. W., and R. Y. Rubinstein "Importance Sampling for Markov Process Expectations", Mathematics of OR .
Rubinstein R. Y., Dolgin A. and Vaisman R. "The Splitting Method for Decision Making"
Garvels M.J.J. and R.Y. Rubinstein "A Combined Splitting - Cross Entropy Method for Rare Event Probability Estimation of Single Queues and ATM Networks".

[4] Recent Slides

Why Classic Randomized Algorithms do not Work, and How to Make them Work

[5] Books

Rubinstein, R.Y., Simulation and the Monte Carlo Methods, John Wiley and Sons, Inc., 1981, 278 pp.
Rubinstein, R.Y., Monte Carlo Optimization, Simulation and Sensitivity of Queueing Networks, John Wiley and Sons, Inc., 1986, 267 pp.
Rubinstein, R..Y. and Shapiro, A., Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization, John Wiley and Sons Inc, 1993, 353 pp
Melamed, B.and Rubinstein, R..Y., Modern Simulation and Modeling. John Wiley and Sons Inc, 1998, 350 pp
Rubinstein, R.Y. and Kroese D. P. The Cross-Entropy Method Springer, 2004.
Rubinstein, R.Y. and Kroese D. P. Simulation and the Monte Carlo Methods: 2nd Edition, John Wiley and Sons Inc., 2007. (Series, Probability and Statistics)

[6] Chapters in Books

Asmussen, S. and R.Y. Rubinstein, ``Complexity properties of steady-state rare events simulation in queueing models" . Advances in Queueing: Theory, Methods and Open Problems, (J.Dshalalow, editor), CRC Press,429-462,1995.
Rubinstein, R, Y., `` Combinatorial Optimization via the Simulated Cross-Entropy Method, Encyclopedia of Management Sciences, Gass S. and C.Harris eds, Kluwer, 2001.
Nemirovski, A.and Rubinstein R.Y., ``An Efficient Stochastic Approximation Algorithm for Stochastic Saddle Point Problems ", Issues on Uncertainty, Kluwer, 2001.
R.Y. Rubinstein, ``Combinatorial Optimization, Cross-Entropy, Ants and Rare Events'', Stochastic Optimization: Algorithms and Applications, S. Uryasev and P. M. Pardalos Editors, Kluwer Academic Publishers, 2001.
R. Y. Rubinstein "Entropy and Cloning Methods for Combinatorial Optimization, Sampling and Counting Using the Gibbs Sampler" Information Theory and Statistical Learning, Editors Frank Emmeret-Streib and Matthias Dehmer, Springer, 2009.

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