Abstract
In this paper, we report results of implementations of algorithms designed (i) to solve the global optimization problem (GOP) and (ii) to run on a parallel network of transputers. There have always been two alternative approaches to the solution of the GOP, probabilistic and deterministic. Interval methods can be implemented on our network of transputers using Concurrent ADA, and a secondary objective of the tests reported was to investigate the relative computer times required by parallel interval algorithms compared to probabilistic methods.
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References
Branin, F. H., Jr,A Widely Convergent Method for Finding Solutions of Simultaneous Nonlinear Equations, IBM New York Research Center, TR 21.466, 1972.
Price, W. L.,A Controlled Random Search Procedure for Global Optimization, Toward Global Optimisation 2, Edited by L. C. W. Dixon and G. P. Szego, North-Holland, Amsterdam, Holland, 1978.
Anderson, R. S., Jennings, L. S., andRyan, D. M., Editors,Optimization, University of Queensland Press, Queensland, Australia, 1972.
Rinnooy-Kan, A., andTimmer, G. T.,Stochastic Global Optimization Methods, Part 2: Multi-Level Methods, Mathematical Programming, Vol. 39, pp. 57–78, 1978.
Timmer, G. T.,Global Optimization: A Stochastic Approach, Erasmus University, Rotterdam, Holland, 1984.
Moore, R. E., andRatschek, H.,Inclusion Function and Global Optimization, Part 2, Mathematical Programming, Volume 41A, pp. 341–356, 1988.
Hansen, E. R.,Global Optimization Using Interval Analysis: The Multidimensional Case, Numerische Mathematik, Vol. 34, pp. 247–270, 1980.
Ratschek, H., andRokne, J.,New Computer Methods for Global Optimization, Ellis Horwood, Chichester, England, 1991.
Dixon, L. C. W., andJha, M.,The Parallel Truncated Newton Method Implemented on a Multitransputer Network, Parallel Computing-91, Edited by Evans, Joubert, and Liddell, Oxford University Press, Oxford, England, 1991.
Dixon, L. C. W., andSzego, G. P.,The Global Optimisation Problem: An Introduction, Toward Global Optimization 2, Edited by L. C. W. Dixon and G. P. Szego, North-Holland, Amsterdam, Holland, 1978.
Jha, M.,Optimization Algorithm for a Transputer Network, PhD Thesis, University of Hertfordshire, Hatfield, Herfordshire, England, 1992.
Bartholomew-Biggs, M. C.,Introduction to Nonlinear Equation Solving Using Interval Arithmetic and ADA Software, Technical Report 242, Numerical Optimisation Centre, University of Hertfordshire, Hatfield, Herfordshire, England, 1991.
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Dixon, L.C.W., Jha, M. Parallel algorithms for global optimization. J Optim Theory Appl 79, 385–395 (1993). https://doi.org/10.1007/BF00940587
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DOI: https://doi.org/10.1007/BF00940587