The continuous reactive tabu search: Blending combinatorial optimization and stochastic search for global optimization

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.

[1]  Roberto Battiti,et al.  Parallel biased search for combinatorial optimization: genetic algorithms and TABU , 1992, Microprocess. Microsystems.

[2]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[3]  Harold J. Kushner,et al.  A New Method of Locating the Maximum Point of an Arbitrary Multipeak Curve in the Presence of Noise , 1964 .

[4]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[5]  J. F. Price,et al.  On descent from local minima , 1971 .

[6]  W. Price Global optimization by controlled random search , 1983 .

[7]  Roman G. Strongin,et al.  Global multidimensional optimization on parallel computer , 1992, Parallel Comput..

[8]  Dana H. Ballard,et al.  An Algorithm for the Solution of Constrained Generalised Polynomial Programming Problems , 1974, Comput. J..

[9]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[10]  Roberto Battiti,et al.  Learning with first, second, and no derivatives: A case study in high energy physics , 1994, Neurocomputing.

[11]  Roberto Brunelli,et al.  Training neural nets through stochastic minimization , 1994, Neural Networks.

[12]  H. Zimmermann Towards global optimization 2: L.C.W. DIXON and G.P. SZEGÖ (eds.) North-Holland, Amsterdam, 1978, viii + 364 pages, US $ 44.50, Dfl. 100,-. , 1979 .

[13]  Harold J. Kushner,et al.  A new method of locating the maximum point of an arbitrary multipeak curve in the presence of noise , 1963 .

[14]  Alexander H. G. Rinnooy Kan,et al.  Bayesian stopping rules for multistart global optimization methods , 1987, Math. Program..

[15]  R. Battiti,et al.  Simulated annealing and Tabu search in the long run: A comparison on QAP tasks☆ , 1994 .

[16]  R. Brunelli,et al.  Stochastic minimization with adaptive memory , 1995 .

[17]  Roberto Battiti,et al.  The Reactive Tabu Search , 1994, INFORMS J. Comput..

[18]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[19]  R. Battiti,et al.  Local search with memory: benchmarking RTS , 1995 .

[20]  Roger J.-B. Wets,et al.  Minimization by Random Search Techniques , 1981, Math. Oper. Res..

[21]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[22]  Bruce E. Stuckman,et al.  A global search method for optimizing nonlinear systems , 1988, IEEE Trans. Syst. Man Cybern..

[23]  Wesley E. Snyder,et al.  Optimization of functions with many minima , 1991, IEEE Trans. Syst. Man Cybern..

[24]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[25]  F. H. Branin Widely convergent method for finding multiple solutions of simultaneous nonlinear equations , 1972 .

[26]  Donald E. Knuth,et al.  The Art of Computer Programming: Volume 3: Sorting and Searching , 1998 .

[27]  W. Price Global optimization algorithms for a CAD workstation , 1987 .

[28]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[29]  Roberto Battiti,et al.  Training neural nets with the reactive tabu search , 1995, IEEE Trans. Neural Networks.