Ho, Y.C., Sreenivas, R., Vakili, P.,"Ordinal Optimization of Discrete Event Dynamic Systems", J. of DEDS 2(2), 61-88, (1992).
This is the first paper on ordinal optimization. It introduces the idea and demonstrates via a series of simulation experiments that considerable saving in computation is possible if one is willing to ask a softer question, namely, "not is this the best but is this good enough"?
Patsis, N., Chen, C.H., & Larson, M.,"Parallel Simulation of DEDS", Proceeding of Optimization Days , Montreal, Canada (1993) to appear in IEEE Trans. on Control Technology (1996)
This paper won the runner up award on the 1992 MasPar Challenge for Massively Parallel Computation as having the highest speedup and scalability
Deng, M., Ho, Y.C., and Hu, J.Q. "Effect of Correlated Estimation Error in Ordinal Optimization", Proceedings of the Winter Simulation Conference , December (1992), pp 466-475.
This paper studies the effect of correlated estimation errors (vs. i.i.d. errors) in ordinal optimization and concludes that the effects of correlation is minimal and generally only help rather than hinder the conclusion.
Y. C. Ho, "A New Paradigm for Stochastic Optimization and Parallel Simulation" Proc. of 1993 DES Workshop in IMA/U.Minn Lecture Notes Series, Springer-Verlag, (1994) Prsented at the IMA workshop 5/23/93 in Minneapolis and the ORSA/TIMS/INRIA Conference on Applied Probability in Paris 6/18/93
This paper outlines the vision of using ordinal optimization and massively parallel simulation concurrently to improve simulation efficiency by orders of magnitude.
Y. C. Ho,"Heuristics, Rules of Thumb, and the 80/20 Proposition" to appear IEEE Trans. on Automatic Control , Vol 39, #5, 1025-1027, May 1994
This is probable the quickest introduction to the idea of ordinal optimization.
Y. C. Ho and M. Larson, "Ordinal Optimization and Rare Event Probability Simulation" J. Discrete Event Dynamic Systems, Vol 5, #2-3, 1995
This paper shows the idea of a surrogate problem in ordinal optimization and ordinal equivalence. Rare event probabilities can be compared using not so rare event probabilities resulting in massive computational saving.
Wieseltheir, J.E., Barnhart, C.M., and Ephremides, A., "Ordinal Optimization of Admission control in Wireless Multihop Voice/Data Nework via Standard Clock Simulation", J.DEDS, Vol.5, #2-3, 1995.
This is the first application of OO by an outside group.
A. Ganz and X. Wang, "Efficient algorithm for virtual topology design in multihop lightwave networks," IEEE/ACM Transactions on Networking, vol. 2, June 1994.
Xie, Xiaohan , "An Ordinal Optimization Approach to a Token Partition Problem for Stochastic Timed Event Graphs" m/s INRIA, Technopole Metz 2000, 57070 Metz, France
Two more applications: Using parallel simulation, OO, and Chen's optimal budget to solve the choice of initial marking.
Dai, Li-Yi, "Convergence Properties of Ordinal Comparison in the Simulation of Discrete Event Dynamic Systems", J. of Opt. Th. & App., Vol.91, No.2. pp.363-388, 1996.
Xie, Xiaolan "Dynamics and Convergence Rate of Ordinal Comparison of Stochastic Discrete Event Systems", IEEE Trans. on Auto. Control, Vol.42, No.4, pp.586-590, April 1997.
First Proofs of the fact "order converges faster than value".
Lau, T.W.E. and Ho, Y.C., "Universal Alignment Probabilities and Subset Selection for Ordinal Optimization", JOTA , Vol.39, #3 June 1997, 455-490.
Deng, M. And Ho, Y.C., "An Ordinal Optimization Approach to Optimal Control Problems", AUTOMATICA, Vol.35, pp. 331-338, 1999.
Lee, L.H, Lau, T.W.E., Ho, Y.C., "Explanation of Goal Softening in Ordinal Optimization", IEEE Trans. on Auto. Control, Vol.44, #1, pp.94-99, 1999.
Recent foundational works on OO
Z. B. Tang and Ho, Y.C., "Modification of Adaptive Partitioned Random Search", Proc. 1995 Conference on Decision and Control
L. Dai and C.-H. Chen, "Rates of convergence of ordinal comparison for dependent discrete event dynamic systems", J. Optimization Theory and Applications, Vol. 94, No. 1, July, 1997
Y.C. Ho, "On the Numerical Solution of Stochastic Optimization Problems", IEEE Tran. on Automatic Control, 42, #5, 1997.
Yang, M.S., Lee, L.H., and Ho, Y.C., "On Stochastic Optimization and Its Applications to Manufacturing" Proc. of AMS Conference on Stochastic Problems in Manufacturing, Springer-Verlag Lecture Notes in Applied Mathematics Vol. 33, 317-331, 1997
Successful applications of OO to two real life manufacturing problems involving turbine blade and tailoredclothing manufacturing.
Ho, Y.C., "Explanation of ordinal optimization: Soft computing for hard problems", Information Sciences, Vol.113, No.3-4, pp.169-192, Feb, 1999.
Lee, J.T., Lau, E., and Ho, Y.C., "The Witsenhausen Counterexample: A Hierarchical Search Approach for Nonconvex Optimization Problems", IEEE Transactions on Automatic Control, Vol.46, No.3, pp.382-397, March 2001.
Li, D., Lee, L.H., and Ho, Y.C., "Constraint ordinal optimization", Information Sciences, Vol.148, pp.201-220, 2002.
Lin, S.Y., and Ho, Y.C., "Universal Alignment Probability Revisited", Journal of Optimization Theory and Applications, Vol.113, No.2, pp.399-407, May 2002.
Zhao, Q.C., Ho, Y.C., and Jia, Q.S., "Vector Ordinal Optimization", submitted to Automatica, 2003.
Related Literature in Statistics
Gibbons, J.D., Olkin, I., and Sobel, M.,Selecting and Ordering of Populations, Wiley, (1977).
Santner, T.J., and Tamhane, A.C.,Design of Experiments: Ranking and Selection, M. Dekker, (1984).
Bechhofer, R.E.,"A single Sample Multiple Choice Procedure for Ranking Means of Normal Population with known Variance", Annals of Mathematical Statistics 25, 16-39, (1954).
M. Sobel "On Selecting a Subset Containing at Least One of the t Best Population" in Multivariate Analysis - II (P.R. Krishnaiah, Ed.) Academic Press, 1969, 515-540
Goldman, D., and Nelson, B.L., "Ranking, Selection, and Multiple Comparisons in Computer Simulation" 1994 Winter Simulation Conferecne Prioceedings
Other Related Literature
Serhat Yesilyurt & Anthony Patera, "Surrogate for Numerical Simulation; Optimization of Eddy-Promotor Heat Exchanger" Submitted to Computer Method in Applied Mechanics and Engineering, July 1993
Serhat Yesilyurt, C. Ghaddar, M. Cruz, A. T. Patera " Bayesian -Validaterd Surrogate for Noisy Computer Simulation: Application to Randon Media" Submitted to SIAM Journal on Scientific Computing, Nov. 1993
Glasserman, P. and Vakili, P. "Correlation of Uniformized Markov Chains Simulated in Parallel", Proceedings of the Winter Simulation Conference , December (1992), pp 412-419
Glasserman, P. and Yao, David "Some Guidelines and Guarantees for Common Random Numbers", Management Science, (1994)
Vakili, P.,"A Standard Clock Technique for Efficient Simulation", Operations Research Letters 10, 445-452, (1991).
Vakili, P. Mollamustafaoglu, L., Ho, Y.C.,"Massively Parallel Simulation of a Class of Discrete Event Systems", Proc. of the 4th IEEE Massively Parallel Computation Conference , (1992).
Vakili, P., "Massively Parallel and Distributed Simulation of a class of Discrete Event Systems : a different perspective", ACM Transactions on Modeling and Computer Simulation , July 1993.
C.H. Chen and Y. C. Ho, "Extensions of the Standard Clock Method for Discrete Event Simulation", to appear IEEE Trans. on Control Technology,1995
Hu, J.Q., "Parallel Simulation via Event Synchronization", to appear J. of Discrete Event Dynamic Systems, Vol.5, #2-3, 1995.
Cassandras, C.G., Discrete Event Systems: Modeling and Performance Analysis, Irwin Publ., 1993.
Chen, C-H, and Ho, Y.C. "An Approximation Approach of the Standard Clock Method for General Discrete Event Simulation" , IEEE Trans. on Control System Technology, v.3, #3, Sept. 1995 309-317