Abstract
This paper proposes a novel metaheuristics approach to find the global optimum of continuous global optimization problems with box constraints. This approach combines the characteristics of modern metaheuristics such as scatter search (SS), genetic algorithms (GAs), and tabu search (TS) and named as hybrid scatter genetic tabu (HSGT) search. The development of the HSGT search, parameter settings, experimentation, and efficiency of the HSGT search are discussed. The HSGT has been tested against a simulated annealing algorithm, a GA under the name GENOCOP, and a modified version of a hybrid scatter genetic (HSG) search by using 19 well known test functions. Applications to Neural Network training are also examined. From the computational results, the HSGT search proved to be quite effective in identifying the global optimum solution which makes the HSGT search a promising approach to solve the general nonlinear optimization problem.
Similar content being viewed by others
References
Al-Sultan, K. S., and Al-Fawzan, M. A. (1997), A tabu search Hooke and Jeeves algorithm for unconstrained optimization, European Journal of Operational Research 103, 198–208.
Androulakis, I., and Venkatasubramanian, V. (1991), A genetic algorithm framework for process design and optimization, Computers and Chemical Engineering 15(4), 217–228.
Battiti, R., and Tecchiolli, G. (1994), The reactive tabu search, ORSA Journal on Computing 6(2), 126–140.
Battiti, R., and Tecchiolli, G. (1996), The continuous reactive tabu search: blending combinatorial optimization and stochastic search for global optimization, Annals of Operations Research-Metaheuristics in Combinatorial Optimization 63, 153–188.
Becker, R. W., and Lago, G. V. (1970), Global Optimization Algorithm, Proceedings of the 8th Allerton Conference on Circuits and Systems Theory.
Branin, F. H. (1972), Widely convergent methods for finding multiple solutions of simultaneous nonlinear equations, IBM Journal of Research Developments, 504–522.
Corana, A., Marchesi, M., Martini, C., and Ridella, S. (1987), Minimizing multimodal functions of continuous variables with the 'simulated annealing' algorithm, ACM Transaction on Mathematical Software 13(3), 262–280.
Cvijovic, D. and Klinowski, J. (1995), Taboo search: an approach to the multiple minima problem, Science 267, 664–666.
Davis, L. (1991), Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York.
Dixon, I. C.W. and Szegö, G. P. (1978a), Towards Global Optimization 1. North-Holland, New York.
Dixon, I. C. W., and Szegö, G. P. (1978b), Towards Global Optimization 2. North-Holland, New York.
Duan, Q. Y., Gupta, V. K., and Sorooshian, S. (1993), Shuffled complex evolution approach for effective and efficient global minimization, Journal of Optimization Theory and Applications 6(3), 501–521.
Fleurent, C., Glover, F., Michelon, P., and Valli, Z. (1995), A scatter search approach for unconstrained continuous optimization, Working paper, University of Colorado, Boulder, CO.
Floudas, C. A., and Pardalos, P. M. (1992), Recent Advances in Global Optimization, Princeton University Press, Princeton, NJ.
Garcia, C. G., and Gould, F. J. (1980), Relations between several path following algorithms and local global Newton methods, Siam Review 22, 263–274.
Glover, F. (1977), Heuristics for integer programming using surrogate constraints, Decision Sciences 8/1, 156–166.
Glover, F. (1994a), Tabu search nonlinear and parametric optimization (with links to Genetic Algorithms), Discrete Applied Mathematics 49, 231–255.
Glover, F. (1994b), Genetic algorithms and scatter search: unsuspected potentials, Statistics and Computing 4, 131–140.
Glover, F. (1995), Scatter search and start-paths: beyond the genetic metaphor, OR Spectrum 17, 125–137.
Glover, F. and Laguna, M. (1993), Tabu search. In C. R. Reeves (ed.), Modern Heuristic Techniques for Combinatorial Problems, 70–141. John Wiley & Sons, New York.
Goffe, W. Ferrier, G., and Rogers, J. (1994), Global optimization of statistical functions with simulated annealing, Journal of Econometrics 60, 65–99.
Goldberg, D. E. (1989), Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading, MA.
Goldstein, A. A., and Price, J. F. (1971), On descent from local minima, Mathematics of Computation 25, 569–574.
Haykin, S. (1994), Neural Networks: A Comprehensive Foundation. Macmillian College, New York.
Holland, J. H. (1992), Adaptation in Natural and Artificial Systems. MIT Press, Cambridge, MA.
Horst, R., Pardalos, P. M. and Thoai, N. V. (1995). Introduction to Global Optimization, Kluwer Academic Publishers, New York
Kirkpatrick, S., Gellat, D. and Vecci, M. (1983), Optimization by simulated annealing, Science 220/4598, 671–680.
Koon, G. and Sebald, A. (1995), Some interesting test functions for evaluating evolutionary programming strategies. In J. R. McDonnell, R. G. Reynolds, and D. B. Fogel (eds.), Proceedings of the Fourth Annual Conference on Evolutionary Programming. MIT Press, Cambridge, MA.
Michalewicz, Z. (1996a), Genetic Algorithms + Data Structure = Evolution Programs (3d ed.). Springer, New York.
Michalewicz, Z. and Janikow, C.Z. (1996b), GENOCOP: A genetic algorithm for numerical optimization problems with linear constraints. Communications of the ACM 39(12), 175–201.
Press, W. H., Teukosky, S. A., Vetterling, W. T. and Flannery, B. P. (1992). Numerical Recipes in FORTRAN: The art of Scientific Computing.Cambridge University Press, New York.
Price, W. L. (1978). A controlled random search procedure for global optimization. In I. C.W. Dixon, and G. P. Szegö (eds.), Towards Global Optimization 1, 71–84. North-Holland, New York.
Reeves, C. R. (1993), Modern Heuristic Techniques for Combinatorial Problems, John Wiley & Sons, New York.
Reklaitis, G. V., Ravindran, A. and Ragsdell, K. M. (1983), Engineering Optimization Methods and Applications. John Wiley and Sons, New York.
Rinnooy Kan, A. H. G. and Timmer, G. T.. (1989), Global Optimization. In G. L. Nemhauser, A. H. G Rinnooy Kan, and M. J. Todd (eds.), Handbooks in OR@MS, 631–662. North-Holland, New York.
Shubert, B. O. (1972), A sequential method seeking the global maximum of a function, SIAMJournal on Numerical Analysis 9, 379–388.
Smith, S., Eskow, E. and Schanbel, R. (1991), Large adaptive, asynchronous stochastic global optimization algorithms for sequential and parallel computation. In T. F. Coleman, and Y. Li (eds), Large-Scale Numerical Optimization. SIAM, Philadelphia.
Srinivas, M. and Patnaik, L. M. (1994). Genetic algorithms: a survey, Computer 27(1), 17–26.
Törn, A. L. (1978), A search clustering approach to global optimization. In I. C.W. Dixon, and G. P. Szegö (eds), Towards Global Optimization 2, 71–84. North-Holland, New York.
Törn, A. L and Zilinskas, A. (1989), Global Optimization Lecture Notes. In Computer Science 350. Springel, Berlin.
Trafalis, T. B. and Al-Harkan, I. (1995), A continuous scatter search approach for global optimization, Extended Abstract. In Conference in Applied Mathematical Programming and Modeling (APMOD'95). London, UK.
Trafalis, T. B. and Al-Harkan, I. A hybrid scatter genetic tabu approach for continuous global optimization. In P.M. Pardalos, A. Migdalas and R. Burkard, (eds.), Combinatorial and Global Optimization. World Scientific Publishing Co., forthcoming.
Trafalis, T. B. and Kasap, S. (1996), An affine scaling scatter search approach for continuous global optimization problems, Intelligent Engineering Systems Through Artificial Neural Networks, (Ed. C. H. Dagli et al.), 6, ASME Press, 1027–1032.
Trafalis, T. B. and Kasap, S. (1998), An affine scaling genetic scatter tabu (ASGST) search: a hybrid of modern heuristics and interior point methods, Proceedings of the 2nd International Symposium on Intelligent Manufacturing Systems IMS'98, Volume I, Sakarya, Turkey, 283–292.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Trafalis, T.B., Kasap, S. A novel metaheuristics approach for continuous global optimization. Journal of Global Optimization 23, 171–190 (2002). https://doi.org/10.1023/A:1015564423757
Issue Date:
DOI: https://doi.org/10.1023/A:1015564423757