Double descent and intermittent color diffusion for landscape exploration

In this work, we present a method to explore the landscape of a smooth potential in the search of global minimizers, combining a double-descent technique and a basin-escaping technique based on intermittent colored diffusion. Numerical results illustrate the performance of the method.

[1]  Shui-Nee Chow,et al.  Global Optimizations by Intermittent Diffusion , 2013 .

[2]  Y. Jabri The Mountain Pass Theorem: Variants, Generalizations and Some Applications , 2003 .

[3]  F. Aluffi-Pentini,et al.  Global optimization and stochastic differential equations , 1985 .

[4]  C. Kelley Iterative Methods for Linear and Nonlinear Equations , 1987 .

[5]  Fabio Schoen,et al.  Global Optimization of Morse Clusters by Potential Energy Transformations , 2004, INFORMS J. Comput..

[6]  Fabio Schoen,et al.  Global Optimization: Theory, Algorithms, and Applications , 2013 .

[7]  James Bisgard,et al.  Mountain Passes and Saddle Points , 2015, SIAM Rev..

[8]  Guanrong Chen,et al.  Chaos, CNN, Memristors and Beyond: A Festschrift for Leon Chua , 2013 .

[9]  Peter Rossmanith,et al.  Simulated Annealing , 2008, Taschenbuch der Algorithmen.

[10]  J. J. Moré,et al.  Computing Mountain Passes , 2002 .

[11]  J. Doye,et al.  Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms , 1997, cond-mat/9803344.

[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]  Philip E. Gill,et al.  Practical optimization , 1981 .

[14]  Qiang Du,et al.  Shrinking Dimer Dynamics and Its Applications to Saddle Point Search , 2012, SIAM J. Numer. Anal..

[15]  Helena Ramalhinho Dias Lourenço,et al.  Iterated Local Search , 2001, Handbook of Metaheuristics.

[16]  Kathryn A. Dowsland,et al.  Simulated Annealing , 1989, Encyclopedia of GIS.

[17]  Isaac Siwale ON GLOBAL OPTIMIZATION , 2015 .

[18]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[19]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[20]  Francesco Zirilli,et al.  A global optimization algorithm using stochastic differential equations , 1988, TOMS.