The simplex-simulated annealing approach to continuous non-linear optimization

Computers and Chemical Engineering

Volumn 20, Issue 9, 1996, Pages 1065-1080

  Cardoso, Margarida F ^a   Salcedo, R L ^a   Feyo De Azevedo, S ^a  

^a UNIVERSITY OF PORTO   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CHEMICAL ENGINEERING; OPTIMIZATION; PROBLEM SOLVING;

CONTINUOUS NONLINEAR OPTIMIZATION; GLOBAL OPTIMIZATION; NONLINEAR CONSTRAINED PROBLEMS;

SIMULATED ANNEALING;

EID: 0030243170     PISSN: 00981354     EISSN: None     Source Type: Journal    
DOI: 10.1016/0098-1354(95)00221-9     Document Type: Article

References (58)

1. Aarst E. and J. Korst, Simulated Annealing and Boltzmann Machines - a Stochastic Approach to Combinatorial Optimization and Neural Computers. Wiley, New York (1989).
2. Aarst E. H. L. and P. J. M. van Laarhoven, Statistical cooling: a general approach to combinatorial optimization problems. Philips J. Res. 40, 193 (1985).
3. Adelman A. and W. F. Stevens, Process optimization by the Complex method. A. I. Ch. E. J. 18(1), 20 (1972).
4. Barabino G. P., G. S. Barabino, B. Bianco and M. Marchesi, A study on the performance of simplex methods for function minimization. Proc. IEEE Int. Conf. Circuits Comput. ICCC 80, 150-1153. IEEE, New York (1980).
5. Bohachevsky I. O., M. E. Johnson and M. L. Stein, Generalized simulated annealing for function optimization. Technometrics 28(3), 209 (1986).
6. Box M. J., A new method of constrained optimization and a comparison with other methods. Computer J. 8, 42 (1965).
7. Campbell J. R. and J. L. Gaddy, Methodology for simultaneous optimization with reliability: nuclear PWR example. A. I. Ch. E. J. 22(6), 1050 (1976).
8. Cardoso M. F., R. L. Salcedo and S. F. de Azevedo, Non-equilibrium simulated annealing: a faster approach to combinatorial minimization. Ind. Engng Chem. Res. 33(8), 1908 (1994).
9. Colville A. R., A comparative study of non-linear programming codes. IBM N.Y. Scientific Center, T.R. 320-2925 (1968).
10. Corana A., M. Marchesi, C. Martini and S. Ridella, Minimizing multimodal functions of continuous variables with the simulated annealing algorithm. ACM Trans. Math. Software 13(3), 263 (1987).
11. Corey E. M. and D. A. Young, Optimization of physical data tables by simulated annealing. Comput. Phys. 3(3), 33 (1989).
12. Das H., P. T. Cummings and M. D. Levan, Scheduling of serial mutliproduct batch processes via simulated annealing. Computers chem. Engng 14(12), 1351 (1990).
13. Dolan W. B., P. T. Cummings and M. D. Levan, Process optimization via simulated annealing: application to network design. A. I. Ch. E. J. 35(5), 725 (1989).
14. Dolan W. B., P. T. Cummings and M. D. Levan, Algorithmic efficiency of simulated annealing for heat exchanger network design. Computers chem. Engng 14(10), 1039 (1990).
15. Dixon L. C. W., Conjugate directions without linear searches. J. Ins. Math. Appl. 11, 317 (1973).
16. Edgar T. F. and D. M. Himmelblau, Optimization of Chemical Processes. McGraw-Hill, New York (1988).
17. Floquet P., L. Pibouleau and S. Domenech, Separation sequence synthesis: how to use simulated annealing procedure. Computers chem. Engng 18(11/12), 1141 (1994).
18. Floudas C. A., A. Aggarwal and A. R. Ciric, Global optimum search for nonconvex NLP and MINLP problems. Computers chem. Engng 13(10), 1117 (1989).
19. Gaines L. D. and J. L. Gaddy, Process optimization by flow sheet optimization. Ind. Eng. Chem. Process Des. Dev. 15, 206 (1976).
20. Groisman G. and J. R. Parker, Computer-assisted photometry using simualted annealing. Comput. Phys. 7(1), 87 (1993).
21. Grossmann I. E. and R. W. H. Sargent, Optimal design of multipurpose chemical plants. Ind. Engng Chem. Process Des. Dev. 18, 343 (1979).
22. Heuckroth M. W., J. L. Gaddy and L. D. Gaines, An examination of the adaptive random search technique. A. I. Ch. E. J. 22, 744 (1976).
23. Ingber A. L., Simulated annealing: practice versus theory. J. Math. Comput. Modelling 18(11), 29 (1993).
24. Johnson D. S., C. R. Aragon, L. A. McGeoch and C. Schevon, Optimization by simulated annealing: an experimental evaluation; part I, graph partitioning. Op. Res. 37(6), 865 (1989).
25. Johnson D. S., C. R. Aragon, L. A. McGeoch and C. Schevon, Optimization by simulated annealing: an experimetnal evaluation; part II, graph coloring and number partitioning. Op. Res. 39(3), 378 (1991).
26. Kirkpatrick S., Optimization by simulated annealing: quantitative studies. J. Stat. Phys. 34(5/6), 975 (1984).
27. Kirkpatrick S., C. D. Gelatt and M. P. Vechi, Optimization by simulated annealing. Science 220, 671 (1983).
28. Kocis G. R. and I. E. Grossmann, Global optimization of nonconvex mixed-integer nonlinear programming (MINLP) problems in process synthesis. Ind. Engng Chem. Res., 27, 1407 (1988).
29. Ku H. and I. Karimi, An evaluation of simulated annealing for batch process scheduling. Ind. Engng Chem. Res. 30(1), 163 (1991).
30. Luus R. R., Optimal control by direct search on feed back gain matrix. Chem. Engng Sci. 29, 1013 (1974).
31. Luus R. R., Optimization of multistage recycle systems by direct-search. Can. J. Chem. Engng 53, 217 (1975).
32. Luus R. and T. H. I. Jaakola, Optimization by direct search and systematic reduction of the size of search region. A. I. Ch. E. J. 19, 760 (1973).
33. Maria G., An adaptive strategy for solving kinetic model concomitant estimation-reduction problems. Can. J. Chem. Engng 67, 825 (1989).
34. Martin D. L. and J. L. Gaddy, Process optimization with the adaptive randomly directed search. A. I. Ch. E. Symp. Ser. 78(214), 99 (1982).
35. Masri S. F., G. A. Bekey and F. B. Safford, A global optimization algorithm using adaptive random search. Appl. Math. Comput. 7, 353 (1980).
36. Metropolis N., A. Rosenbluth, M. Rosenbluth, A. Teller and E. Teller, Equation of state calculations by fast computing machines. J. Chem. Phys. 21, 1087 (1953).
37. Meyer R. R. and P. M. Roth, Modified damped least squares - an algorithm for non-linear estimation. J. Instrum. Math. App. 9, 218 (1972).
38. Mihail R. and G. Maria, A modified Matyas algorithm (MMA) for random process optimization. Computers chem. Engng 10, 539 (1986).
39. Nash J. C. and M. Walker-Smith, Nonlinear Parameter Estimation, Ch. 14. Marcel Dekker, New York (1987).
40. Neider J. A. and R. Mead, A simplex method for function minimization. Comput. J. 7, 308 (1965).
41. Olson D. M. and L. S. Nelson, The Nelder-Mead simplex procedure for function minimization. Technometrics 17, 45 (1975).
42. Patel A. N., R. S. H. Mah and I. A. Karimi, Preliminary design of multiproduct noncontinuous plants using simulated annealing. Computers chem. Engng 15(7), 451 (1991).
43. Press W. H., B. P. Flannery, S. A. Teukolsky and W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing. Cambridge University Press, UK (1986).
44. Press W. H. and S. A. Teukolsky, Simulated annealing optimization over continuous spaces. Comput. Phys. 5(4), 426 (1991).
45. Price W. L., A controlled random search procedure for global optimization. In L. C. W. Dixon and G. P. Szego, eds, Towards Global Optimization 2, p. 71. North-Holland, Amsterdam (1978).
46. Pronzato L., E. Walter, A. Venot and J. F. Lebruche, A general purpose global optimizer: implementations and applications. Math. Comput. Sim. 25, 412 (1984).
47. Rosenbrock H. H., An automatic method for finding the greatest or least value of a function. Comput. J. 3, 175 (1960).
48. Salcedo R. L., Solving nonconvex nonlinear programming and mixed-integer nonlinear programming problems with adaptive random search. Ind. Engng Chem. Res. 31(1), 262 (1992).
49. Salcedo R. L., M. F. Cardoso and S. Feyo de Azevedo, A fast simulated annealing algorithm for combinatorial minimization. Proc. Escape 3, Graz (Austria), Suppl. Vol., F. Moser, H. Schnitzer and H. J. Bart, eds, pp. 12-17 (1993).
50. Salcedo R., M. J. Goncalves and S. Feyo de Azevedo, An improved random-search algorithm for nonlinear optimization. Computers chem. Engng 14(10), 1111-1126 (1990).
51. Shedler G. S., Generation methods for discrete event simulation. In Computer Performance Modeling Hndbook, pp. 227-251. Academic Press, New York (1983).
52. Silverman A. and J. Adler, Animated simulated annealing. Comput. Phys. 6(3), 277-281 (1992).
53. Tao B. Y., Optimization via the simplex method. Chem. Engng ??, 85-89 (1988).
54. Törn A. A., A search-clustering approach to global optimization. In L. C. W. Dixon and G. P. Szego eds, Towards Global Optimization 2, pp. 49-62. North-Holland, Amsterdam (1978).
55. Umeda T. and A. Ichikawa, A modified complex method for optimization. Ind. Engng Chem. Process Des. Dev. 10(2), 229 (1971).
56. Vanderbilt D. and S. G. Louie, A Monte Carlo simulated annealing approach to optimization over continuous variables. J. Comput. Phys. 56, 259 (1984).
57. Wang B. C. and R. Luus, Optimization of nonunimodal systems. Int. J. Num. Meth. Engng 11, 1235 (1977).
58. Wang B. C. and R. Luus, Reliability of optimization procedures for obtaining global optimum. A. I. Ch. E. J. 24, 619 (1978).