Abstract
This work presents a novel optimization method capable of integrating ordinal optimization (OO) and simulated annealing (SA). A general regression neural network (GRNN) is trained using available data to generate a “rough” model that approximates the response surface in the feasible domain. A set of “good enough” candidates are generated by conducting a (SA) search on this “rough model”. Only candidates accepted by the SA search are actually tested by evaluating their true objective functions. The GRNN model is then updated using these new data. The procedure is repeated until a specified number of tests have been performed. The method (SAOO+GRNN) is tested the well-known paper trim loss problem. SAOO+GRNN approach can substantially reduce the number of function calls and the computing time far below those of simple ordinal optimization method with such as horse race selection rule, as well as straightforward simulated annealing.
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Collins, N. E., Eglese, R. W. and Golden, B. L. (1988) Simulated annealing—an annotated bibliography. American Journal of Mathematical and Management Sciences, 8(3), 209–307.
Davis, Mark E. (1999) Combinatorial methods: how will they integrate into chemical Engineering? AIChE Journal, 45(11), 2270–2272.
Edgar, T. F., Himmelblau, D. M. and Lasdon, L. S. (2001) Optimization of chemical processes. McGraw-Hill, New York.
Eglese, R. W. (1990) Simulated annealing: a tool for operational research. European Journal operational research, 46, 271–281.
Falcioni, M. and Deem, W. (2000) Library design in combinatorial chemistry by Monte Carlo methods. Physical Review E, 61(5), 5948–5952.
Floudas, C. A., Pardalos, P. M., Adjiman, C. S., Esposito, W. R., Gumus, Z., Harding, S. T., Klepeis, J. L., Meyer, C. A. and Schweiger, C. A. (1999) Handbook of Test Problems for Local and Global Optimization, Kluwer Academic Publishers, The Netherlands.
Foerster, H. and Wäscher, G. (1998) Simulated annealing for order spread minimization in sequencing cutting patterns. European Journal of Operational Research, 110(2), 272–281.
Goulimis, C. (1990) Optimal solution for the cutting stock problem. European Journal of Operational Research, 44, 197–208.
Harjunkoski, I., Westerlund, T., Isaksson, J. and Skrifvars, H. (1996) Different formula for solving trim loss problems in a paper-converting mill with ILP. Computers and Chemical Engineering, 20, s121–s126.
Harjunkoski, I., Westerlund, T., Pörn, R. and Skrifvars, H. (1998) Different transformations for solving non-convex trim-loss problems by MINLP. European Journal of Operational Research, 105, 594–603.
Ho, Y. C., Sreenivas, R. and Vakili, P. (1992) Ordinal optimization of discrete event dynamic systems. Journal of Discrete Event Dynamic Systems, 2(2), 61–88.
Holland, J. H. (1975) Adaptation in Natural and Artificial System, Ann Arbor, The University of Michigan Press.
Johnston, D. S., Aragon, C. R. and McGeoch, L. A. (1989) Optimization by simulated annealing: an experiment evaluation: Part 1, graph partitioning. Operational Research, 37, 865–892.
Kirkpatrick, S., Gelatt, C. D. Jr. and Vecchi, M. P. (1983) Optimization by Simulated Annealing. Science, 220, 671–680.
Koulamas, C., Anotony, S. R. and Jean, R. (1994) A survey of simulated annealing application to operations research problems. International Journal of Production Research, 30(1), 95–108.
Ku, H. M. and Karimi, I. (1991) An evaluation of simulated annealing for batch process scheduling. Industrial and Engineering Chemistry Research, 30, 163–169.
Lau, T. W. E. and Ho, Y. C. (1997) Universal alignment probability and subset selection for ordinal optimization. Journal of Optimization Theory and Applications, 93(3), 455–489.
Lee, J. T., Lau, E. and Ho, Y. C. (2001) The Witsenhausen counter example: a hierarchical search approach for non-convex optimization problems. IEEE Transactions Automatic Control, 46(3), 382–397.
Luo, Y. C., Guignard, M. and Chen, C. H. (2001) A hybrid approach for integer programming combing genetic algorithms, linear programming and ordinal optimization. Journal of Intelligent Manufacturing, 12(5), 509–519.
östermark, R. (1999) Solving a nonlinear non-convex trim loss problem with a genetic hybrid algorithm. Computers and Operations Research, 26(6), 623–635.
Painton, L. A. and Diwekar, U. M. (1994) Synthesizing optimal design configurations for a brayton cycle power plant. Computers and Chemical Engineering, 18(5), 369–381.
Specht, D. F. (1991) A general regression neural network. IEEE Transactions on Neural Network, 2(6), 568–576.
Tsujimura, Y. and Gen, M. (1998) Entropy-based genetic algorithm for solving TSP. Proceedings of Second International Conference on Knowledge Based Intelligent Electronic System, April, Adelaide, Australia.
Van Laarhoven, P. J. M. and Aarts, E. H. L. (1987) Simulated Annealing: Theory and Applications, Rediel, Dordrecht, The Netherlands.
Wäscher, G. (1990) An LP-based approach to cutting stock problems with multiple objectives. European Journal of Operational Research, 44, 175–184.
Westerlund, T. and Isaksson, J. (1998) Some efficient formulations for the simultaneous solution of trim-loss and scheduling problems in the paper-converting industry. Transactions of the Institute of Chemical Engineers, 76(A6), 677–684.
Westerlund, T., Pettersson, F. and Grossmann, I. E. (1994) Optimization of pump configurations as a MINLP problem. Computers and Chemical Engineering, 18, 845–858.
Zhang, L., Wang, L. and Tang, F. (2002), Order based genetic algorithm for flow shop scheduling. Proceedings of First International Conference on Machine Learning and Cybernetics, November, Bejing, China.
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Yen, C.H., Wong, D.S.H. & Jang, S.S. Solution of trim-loss problem by an integrated simulated annealing and ordinal optimization approach. Journal of Intelligent Manufacturing 15, 701–709 (2004). https://doi.org/10.1023/B:JIMS.0000037718.43289.62
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DOI: https://doi.org/10.1023/B:JIMS.0000037718.43289.62