A New Version of the Price's Algorithm for Global Optimization

We present an algorithm for finding a global minimum of a multimodal,multivariate function whose evaluation is very expensive, affected by noise andwhose derivatives are not available. The proposed algorithm is a new version ofthe well known Price's algorithm and its distinguishing feature is that ittries to employ as much as possible the information about the objectivefunction obtained at previous iterates. The algorithm has been tested on alarge set of standard test problems and it has shown a satisfactorycomputational behaviour. The proposed algorithm has been used to solveefficiently some difficult optimization problems deriving from the study ofeclipsing binary star light curves.

[1]  L. Milano,et al.  Analysis of contact binary systems - AA Ursae Majoris, V752 Centauri, AO Camelopardalis, and V 677 Centauri , 1993 .

[2]  R. E. Wilson Eccentric orbit generalization and simultaneous solution of binary star light and velocity curves , 1979 .

[3]  P. Pardalos,et al.  Handbook of global optimization , 1995 .

[4]  M. Powell A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation , 1994 .

[5]  W. Murray Numerical Methods for Unconstrained Optimization , 1975 .

[6]  L. Milano,et al.  The optimization of the Wilson-Devinnet method: an application to CW Cas , 1988 .

[7]  M. Piccioni,et al.  Random tunneling by means of acceptance-rejection sampling for global optimization , 1989 .

[8]  D. J. Bell,et al.  Numerical Methods for Unconstrained Optimization , 1979 .

[9]  Jorge Nocedal,et al.  Theory of algorithms for unconstrained optimization , 1992, Acta Numerica.

[10]  Fabio Schoen,et al.  Stochastic techniques for global optimization: A survey of recent advances , 1991, J. Glob. Optim..

[11]  Francesco Archetti,et al.  A survey on the global optimization problem: General theory and computational approaches , 1984, Ann. Oper. Res..

[12]  J. Hammersley SIMULATION AND THE MONTE CARLO METHOD , 1982 .

[13]  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 .

[14]  Panos M. Pardalos,et al.  Recent Advances in Global Optimization. , 1993 .

[15]  L. Milano,et al.  An Optimization Method for solutions of Close Eclipsing Binaries , 1990 .

[16]  G. T. Timmer,et al.  Global Optimization , 1999, Science.

[17]  Christodoulos A. Floudas,et al.  Recent advances in global optimization for process synthesis, design and control: Enclosure of all solutions , 1999 .

[18]  Leo Breiman,et al.  A deterministic algorithm for global optimization , 1993, Math. Program..

[19]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[20]  Aimo A. Törn,et al.  Global Optimization , 1999, Science.

[21]  Wyn L. Price,et al.  A Controlled Random Search Procedure for Global Optimisation , 1977, Comput. J..