Abstract
A novel algorithm for the global optimization of functions (C-RTS) is presented, in which a combinatorial optimization method cooperates with a stochastic local minimizer. The combinatorial optimization component, based on the Reactive Tabu Search recently proposed by the authors, locates the most promising “boxes”, in which starting points for the local minimizer are generated. In order to cover a wide spectrum of possible applications without user intervention, the method is designed with adaptive mechanisms: the box size is adapted to the local structure of the function to be optimized, the search parameters are adapted to obtain a proper balance of diversification and intensification. The algorithm is compared with some existing algorithms, and the experimental results are presented for a variety of benchmark tasks.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D.H. Ballard, C.A. Jelinek and R. Schinzinger, An algorithm for the solution of constrained generalized polynomial programming problems, Comp. J. 17(1974)261–266.
R. Battiti and G. Tecchiolli, Parallel biased search for combinatorial optimization: genetic algorithms and TABU, Microproc. Microsyst. 16(1992)351–367.
R. Battiti and G. Tecchiolli, The reactive tabu search, ORSA J. Comp. 6(1994)126–140.
R. Battiti and G. Tecchiolli, Learning with first, second and no derivatives: A case study in high energy physics, Neurocomp. 6(1994)181–206.
R. Battiti and G. Tecchiolli, Training neural nets with the reactive tabu search, IEEE Trans. Neural Networks 6(1995)1185–1200.
R. Battiti, The reactive tabu search for machine learning, in:Proc. GAA '93, Giornate dei Gruppi di Lavoro AI*AI, Apprendimento Automatico, Milan (1993).
R. Battiti and G. Tecchiolli, Local search with memory: Benchmarking RTS, Preprint UTM, University of Trento, Italy (October, 1993), submitted.
R. Battiti and G. Tecchiolli, Simulated annealing and tabu search in the long run: A comparison on QAP tasks, Comp. Math. Appl. 28(6) (1994) 1–8.
G.L. Bilbro and W.E. Snyder, Optimization of functions with many minima, IEEE Trans. Syst., Man, Cybern. SMC-21(1991)840–849.
C.G.E. Boender and A.H.G. Rinnooy Kan, Bayesian stopping rules for multistart global optimization methods, Math. Progr. 37(1987)59–80.
F.H. Branin, Jr., Widely convergent method for finding multiple-solutions of simultaneous nonlinear equations, IBM J. Res. Develop. (September 1992) 504–522.
R. Brunelli and G. Tecchiolli, On random minimization of functions, Biol. Cybern. 65(1991)501–506.
R. Brunelli and G. Tecchiolli, Stochastic minimization with adaptive memory, J. Comp. Appl. Math. 57(1995)329–343.
R. Brunelli, On training neural nets through stochastic minimization, Neural Networks (1994).
L.C.W. Dixon and G.P. Szego (eds.),Towards Global Optimization 2 (North-Holland, 1978).
S. Fanelli and A. Ramponi, Computational experience with a multistart algorithm for global optimization based on new Bayesian stopping rules, in:Proc. 14th Symp. A.M.A.S.E.S., Pescara (September 1990).
M.R. Garey and D.S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, 1979).
F. Glover, Tabu search — Part I, ORSA J. Comp. 1(1989)190–206.
F. Glover, Tabu search — Part II, ORSA J. Comp. 2(1990)4–32.
A.A. Goldstein and I.F. Price, On descent from local minima, Math. Comp. 25 (July 1971).
G.H. Golub and C.F. Van Loan,Matrix Computations, 2nd ed. (The Johns Hopkins University Press, 1990).
E. Hansen,Global Optimization Using Interval Analysis (Marcel Dekker, 1992).
J.K. Hartman, Technical Report NP55HH72051A, Naval Postgraduate School, Monterey, CA (1972).
J.H. Holland,Adaptation in Natural and Artificial Systems. An Introductory Analysis with Applications to Biology, Control, Artificial Intelligence (University of Michigan Press, 1975).
A.V. Levy, A. Montalvo, S. Gomez and A. Galderon,Topics in Global Optimization, Lecture Notes in Mathematics No. 909 (Springer, 1981).
A.V. Levy and S. Gomez, The tunneling method applied to global optimization, in:Numerical Optimization 1984, ed. P.T. Boggs, R.H. Bryd and R.B. Schnabel (SIAM Publications, 1985) pp. 213–244.
S. Kirkpatrick, C.D. Gelatt and M.P. Vecchi, Optimization by simulated annealing, Science 220(1983)671–680.
D.E. Knuth,The Art of Computer Programming, Vol. 3:Sorting and Searching (Addison-Wesley, 1973).
H.J. Kushner, A new method of locating the maximum of an arbitrary multipeak curve in the presence of noise, in:Proc. Joint Automatic Control Conf. (1963).
W.L. Price, Global optimization by controlled random search, J. Optim. Theory Appl. 40(1983)333–348.
W.L. Price, Global optimization algorithms for a CAD workstation, J. Optim. Theory Appl. 55(1987)133–146.
F.J. Solis and R.J-B Wets, Minimization by random search techniques, Math. Oper. Res. 6(1981)19–30.
R.G. Strongin and Y.D. Sergeyev, Global multidimensional optimization on parallel computers, Parallel Comp. 18(1992)1259–1273.
B.E. Stuckman, A global search method for optimizing nonlinear systems, IEEE Trans. Syst., Man, Cybern., SMC-18(1988)965–977.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Battiti, R., Tecchiolli, G. The continuous reactive tabu search: Blending combinatorial optimization and stochastic search for global optimization. Ann Oper Res 63, 151–188 (1996). https://doi.org/10.1007/BF02125453
Issue Date:
DOI: https://doi.org/10.1007/BF02125453