article

A stochastic method for global optimization

Authors:

A. H. Rinnooy Kan,

L. StougieAuthors Info & Claims

Mathematical Programming: Series A and B, Volume 22, Issue 1

Pages 125 - 140

https://doi.org/10.1007/BF01581033

Published: 01 December 1982 Publication History

Abstract

A stochastic method for global optimization is described and evaluated. The method involves a combination of sampling, clustering and local search, and terminates with a range of confidence intervals on the value of the global optimum. Computational results on standard test functions are included as well.

References

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F. Archetti, B. Betro and S. Steffe, "A theoretical framework for global optimization via random sampling", Tech. Rept., University of Pisa (1975).

[2]

L. De Biase and F. Frontini, "A stochastic method for global optimization: its structure and numerical performance", in: L.C.W. Dixon and G.P. Szegö, eds., Towards global optimisation 2 (North-Holland, Amsterdam, 1978) pp. 85-102.

[3]

L.C.W. Dixon and G.P. Szegö, eds., Towards global optimisation (North-Holland, Amsterdam, 1975).

[4]

L.C.W. Dixon, J. Gomulka and G.P. Szegö, "Towards global optimisation", in: L.C.W. Dixon and G.P. Szegö, eds., Towards global optimisation (North-Holland, Amsterdam, 1975) pp. 29-54.

[5]

L.C.W. Dixon and G.P. Szegö, eds., Towards global optimisation 2 (North-Holland, Amsterdam, 1978).

[6]

L.C.W. Dixon and G.P. Szegö, "The global optimisation problem: an introduction", in: L.C.W. Dixon and G.P. Szegö, eds., Towards global optimisation 2 (North-Holland, Amsterdam, 1978) pp. 1-18.

[7]

W. Eberl and R. Hafner, "Die asymptotische Verteilung von Koinzidenzen", Zeitschrift für Wahrscheinlichkeitsrechnung 18 (1971) 322-332.

[8]

B. Everitt, Cluster analysis (Heinmann, London, 1974).

[9]

J. Gomulka, "Two implementations of Branin's method: Numerical experience", in: L.C.W. Dixon and G.P. Szegö, eds., Towards global optimisation 2 (North-Holland, Amsterdam, 1978) pp. 151-164.

[10]

L. De Haan, "Estimation of the minimum of a function using order statistics", Tech. Rept., Erasmus University, Rotterdam (1979).

[11]

G. van der Hoek and M.W. Dijkshoorn, "A numerical comparison of self scaling variable metric algorithms", Tech. Rept., Erasmus University, Rotterdam (1979).

[12]

A. Kester, "Asymptotic normality of the number of small distances between random points in a cube", Stochastic processes and their Applications 3 (1975) 45-54.

[13]

W.L. Price, "A controlled random search procedure for global optimisation", in: L.C.W. Dixon and G.P. Szegö, eds., Towards global optimisation 2 (North-Holland, Amsterdam, 1978) pp. 71-84.

[14]

A.A. Törn, "Cluster analysis using seed points and density-determined hyperspheres with an application to global optimization", Proceedings of 3rd International Joint Conference on Pattern Recognition (IEEE Computer Society, Silver Spring, MD, 1976) pp. 394-398.

[15]

A.A. Törn, "Optimality by means of confidence", Technical report, Åbo Swedish University School of Economics (1979).

Cited By

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A stochastic method for global optimization

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Published In

cover image Mathematical Programming: Series A and B

Mathematical Programming: Series A and B Volume 22, Issue 1

December 1982

356 pages

ISSN:0025-5610

Issue’s Table of Contents

Copyright © Copyright © 1982 The Mathematical Programming Society, Inc.

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 December 1982

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Cited By

Choudhury SGammell JBarfoot TSrinivasa SScherer S(2021)Regionally accelerated batch informed trees (RABIT*): A framework to integrate local information into optimal path planning2016 IEEE International Conference on Robotics and Automation (ICRA)10.1109/ICRA.2016.7487615(4207-4214)Online publication date: 10-Mar-2021
https://dl.acm.org/doi/10.1109/ICRA.2016.7487615
Beg AIslam M(2021)A novel genetic algorithm-based clustering technique and its suitability for knowledge discovery from a brain data set2016 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC.2016.7743892(948-956)Online publication date: 11-Mar-2021
https://dl.acm.org/doi/10.1109/CEC.2016.7743892
Beg AIslam MEstivill-Castro V(2020)HeMI ++: A Genetic Algorithm based Clustering Technique for Sensible Clusters2020 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC48606.2020.9185882(1-8)Online publication date: 19-Jul-2020
https://dl.acm.org/doi/10.1109/CEC48606.2020.9185882
Beg AIslam MEstivill-Castro V(2016)Genetic algorithm with healthy population and multiple streams sharing information for clusteringKnowledge-Based Systems10.1016/j.knosys.2016.09.030114:C(61-78)Online publication date: 15-Dec-2016
https://dl.acm.org/doi/10.1016/j.knosys.2016.09.030
Giddings ARardin RUzsoy R(2014)Statistical optimum estimation techniques for combinatorial optimization problemsJournal of Heuristics10.1007/s10732-014-9243-420:3(329-358)Online publication date: 1-Jun-2014
https://dl.acm.org/doi/10.1007/s10732-014-9243-4
Pál LAlba E(2013)Comparison of multistart global optimization algorithms on the BBOB noiseless testbedProceedings of the 15th annual conference companion on Genetic and evolutionary computation10.1145/2464576.2482693(1153-1160)Online publication date: 6-Jul-2013
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Pál LAlba E(2013)Benchmarking a hybrid multi level single linkagealgorithm on the bbob noiseless testbedProceedings of the 15th annual conference companion on Genetic and evolutionary computation10.1145/2464576.2482692(1145-1152)Online publication date: 6-Jul-2013
https://dl.acm.org/doi/10.1145/2464576.2482692
Regis RShoemaker C(2013)A quasi-multistart framework for global optimization of expensive functions using response surface modelsJournal of Global Optimization10.1007/s10898-012-9940-156:4(1719-1753)Online publication date: 1-Aug-2013
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Pál LCsendes TMarkót MNeumaier A(2012)Black box optimization benchmarking of the global methodEvolutionary Computation10.1162/EVCO_a_0008920:4(609-639)Online publication date: 1-Dec-2012
https://dl.acm.org/doi/10.1162/EVCO_a_00089
Pošík PHuyer WPál L(2012)A comparison of global search algorithms for continuous black box optimizationEvolutionary Computation10.1162/EVCO_a_0008420:4(509-541)Online publication date: 1-Dec-2012
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