Best possible probability distribution over extremal optimization ranksF. Heilmann1, K. H. Hoffmann1 and P. Salamon2
1 Institut für Physik, Technische Universität Chemnitz - D-09107 Chemnitz, Germany
2 Department of Mathematics and Statistics, San Diego State University San Diego, CA 92182, USA
(Received 9 January 2004; accepted in final form 2 March 2004)
We consider the problem of selecting the next degree of freedom (DoF) for update in an extremal optimization algorithm designed to find the ground state of a system with a complex energy landscape. We show that if we wish to minimize any linear function of the state probabilities, e.g. the final energy, then the best distribution for selecting the next DoF is a rectangular distribution with a cutoff for the fitness. We dub the family of algorithms using rectangular distributions in combination with extremal optimization Fitness Threshold Accepting .
02.50.Ga - Markov processes.
02.60.Pn - Numerical optimization.
05.10.-a - Computational methods in statistical physics and nonlinear dynamics.
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