The Shape of a Local Minimum and the Probability of its Detection in Random Search Export

@incollection{citeulike:3362796, abstract = {The problem of binary optimization is discussed. By analyzing the generalized Hopfield model we obtain expressions describing the relationship between the depth of a local minimum and the size of the basin of attraction. The shape of local minima landscape is described. Based on this, we present the probability of finding a local minimum as a function of the depth of the minimum. Such a relation can be used in optimization applications: it allows one, basing on a series of already found minima, to estimate the probability of finding a deeper minimum, and to decide in favor of or against further running the program. It is shown, that the deepest minimum is defined with the gratest probability in random search. The theory is in a good agreement with experimental results.}, author = {Kryzhanovsky, Boris and Kryzhanovsky, Vladimir and Mikaelian, Andrey}, citeulike-article-id = {3362796}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/978-3-540-85640-5_4}, doi = {10.1007/978-3-540-85640-5_4}, journal = {Informatics in Control, Automation and Robotics}, keywords = {attraction-basin, binary, fitness-landscape, hopfield, optimization, probability, probability-density, random}, pages = {51--61}, posted-at = {2008-10-01 14:38:13}, priority = {2}, title = {The Shape of a Local Minimum and the Probability of its Detection in Random Search}, url = {http://dx.doi.org/10.1007/978-3-540-85640-5_4}, year = {2009} }

TY - CHAP ID - citeulike:3362796 L3 - citeulike-article-id:3362796 N2 - The problem of binary optimization is discussed. By analyzing the generalized Hopfield model we obtain expressions describing the relationship between the depth of a local minimum and the size of the basin of attraction. The shape of local minima landscape is described. Based on this, we present the probability of finding a local minimum as a function of the depth of the minimum. Such a relation can be used in optimization applications: it allows one, basing on a series of already found minima, to estimate the probability of finding a deeper minimum, and to decide in favor of or against further running the program. It is shown, that the deepest minimum is defined with the gratest probability in random search. The theory is in a good agreement with experimental results. JF - Informatics in Control, Automation and Robotics EP - 61 TI - The Shape of a Local Minimum and the Probability of its Detection in Random Search SP - 51 KW - attraction-basin KW - binary KW - fitness-landscape KW - hopfield KW - optimization KW - probability KW - probability-density KW - random AU - Kryzhanovsky, Boris AU - Kryzhanovsky, Vladimir AU - Mikaelian, Andrey PY - 2009/// UR - http://dx.doi.org/10.1007/978-3-540-85640-5_4 ER -