Abstract
The unconstrained global programming problem is addressed using an efficient multi-start algorithm, in which parallel local searches contribute towards a Bayesian global stopping criterion.
The stopping criterion, denoted the unified Bayesian global stopping criterion, is based on the mild assumption that the probability of convergence to the global optimum x* is comparable to the probability of convergence to any local minimum \( \tilde x_j \) .
The combination of the simple multi-start local search strategy and the unified Bayesian global stopping criterion outperforms a number of leading global optimization algorithms, for both serial and parallel implementations. Results for parallel clusters of up to 128 machines are presented.
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References
Schoen, F. Stochastic techniques for global optimization: A survey of recent advances, J. Global Optim., 1 (1991) 207–228
Snyman, J.A. and Fatti, L.P. A multi-start global minimization algorithm with dynamic search trajectories, J. Optim. Theory Appl., 54 (1987) 121–141
Boender, C.G.E., Rinnooy Kan, A.H.G. A Bayesian analysis of the number of cells of a multinomial distribution, Statistician, 32 (1983) 240–248
Byrd, R.H., Lu, P., Nocedal, J. and Zhu, C. A limited memory algorithm for bound constrained optimization, SIAM J. Scient. Comput., 16 (1995) 1190–1208
Zhu, C., Byrd, R.H., Lu, P. and Nocedal, J. L-BFGS-B: FORTRAN subroutines for large scale bound constrained optimization, Tech. Report, NAM-11, EECS Department, Northwestern University (1994)
Gilbert, J.C. and Nocedal, J. Global convergence properties of conjugate gradient methods, SIAM Journal on Optimization, 2 (1992) 21–42
Groenwold, A.A. and Snyman, J.A. Global optimization using dynamic search trajectories, Proc., Conf. of Discrete and Global Optimization, Chania, Crete (1998)
Geist, A., Beguelin, A, Dongarra, J., Jiang, W., Manchek, R. and Sunderam, V. Pvm: Parallel Virtual Machine system, ftp://netlib2.cs.utk.edu/pvm3/,ver. 3.4 (1997)
Törn, A. and Zilinskas, A. Global optimization: Lecture notes in computer science, No. 350, Springer-Verlag, Berlin Heidelberg (1989)
Boender, C.G.E., Rinnooy Kan, A.H.G., Timmer, G.T. and Stougie, L. A stochastic method for global optimization, Math. Program., 22 (1982) 125–140
Rinnoy Kan, A.H.G. and Timmer, G.T. Stochastic global optimization methods, Part I: Clustering methods, Mathemat. Program., 39 (1987) 27–56
Aluffi-Pentini, F., Parisi, V. and Zirilli, F. Global optimization and stochastic differential equations, J. Optim. Theory Appl., 47 (1985) 1–16
Aluffi-Pentini, F., Parisi, V. and Zirilli, F. SIGMA-A stochastic-integration global minimization algorithm, ACM Trans. Math. Softw., 14 (1988) 366–380
Mockus, J. Bayesian approach to global optimization, Kluwer Academic Publishers, Dordrecht (1989)
Griewank, A.O. Generalized descent for global optimization, J. Optim. Theory Appl., 34 (1981) 11–39
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Bolton, H.P.J., Schutte, J.F., Groenwold, A.A. (2000). Multiple Parallel Local Searches in Global Optimization. In: Dongarra, J., Kacsuk, P., Podhorszki, N. (eds) Recent Advances in Parallel Virtual Machine and Message Passing Interface. EuroPVM/MPI 2000. Lecture Notes in Computer Science, vol 1908. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45255-9_15
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DOI: https://doi.org/10.1007/3-540-45255-9_15
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