S. A. Solla, G. B. Sorkin, and S. R. White. Configuration space analysis for optimization problems. In E. Bienenstock et. al., editor, Disordered Systems and Biological Organization, NATO ASI Series, volume F20, pages 283--293, Berlin, New York, 1986. Springer.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....[80] 49] In addition to Ref. 96] these metaphors have also been recently addressed by Hinton and Nowlan [65] and R. Belew and co workers [10] while an earlier reference is the work of W.A. Kornfeld [84] 85] The whole field can be viewed as cases of adaptation in rugged landscapes [82] [123] [81] 96] 92] 91] 124] 125] 99] These results on the TSP show that there is computational evidence which is consistent with the hypothesis that a group of competing and cooperating individual processes, which undergo periods of individual optimization can overcome the gap from local to ....

S.A. Solla, G.B. Sorkin and S.R. White, Configuration Space Analysis for Optimization Problems, in: E. Bienenstock ed., Disordered Systems and Biological Organization, NATO ASI Series Vol F20 (1985).

....that landscape. Note that an operator such as cross over induces large jumps across the fitness landscape because it causes many alleles to be simultaneously altered. More precisely, each set of genetic operators, in combination with each artificial gene interpreter, defines a configuration space[15, 11] in which adjacent points are related by a single move. Thus the ability of a GA to find maxima on a given fitness landscape is determined as much by the nature of its artificial genome interpreter as by its genetic operators. Work by Lister[12] using the stochastic simulated annealing technique ....

SA Solla, GB Sorkin, and SR White. Configuration space analysis for optimization problems. In Disordered systems and biological organisation, Bienstock E, (Ed.), Springer-Verlag, pages 283--293, 1986.

....the same type of poor structure that Wilson and Pawley observed in their study of Hopfield and Tank s analog network [9] B. Simulated Annealing can perform divide and conquer in a quasi fractal energy landscape. The above heading paraphrases a conjecture made by Solla, Sorkin and White [10], and which is illustrated in the energy landscape of Fig. 4. At very high temperatures, simulated annealing may wander across the entire landscape represented in the figure. At a lower temperature, the transition A B C is substantially more probable than the reverse transition. As the temperature ....

....the simpler segment reversal heuristic is sufficient for most real world applications. Kirkpatrick and Toulouse studied the distribution of minima in TSP landscapes defined by segment reversal, and found they exhibited a high degree of ultrametricity [12] which is a measure of self similarity [10]. Moving a single city at a time, as in McRotA, does not define a quasi fractal energy landscape. The number of moves required to reposition an entire cluster of cities is proportional to the size of the cluster. Furthermore, there is no substantial shortening of the path until all cities in the ....

S. Solla, G. Sorkin and S. White, "Configuration space analysis for optimization problems", in Disordered systems and biological organization, NATO ASI Series, vol. F20. E. Bienenstock et al., Eds, Berlin: Springer Verlag, pp. 283-293, 1986.

.... space must be either equilateral, or isosceles with a small base (third side shorter than the two equal ones) It is known that configuration spaces with ultrametrically distributed minima are quasi fractal, and empirical evidence suggests that simulated annealing can work well in such spaces [6] [9]. Other algorithms might also be developed to make use of this structural information. Given a sample of points in a configuration space, the degree of ultrametricity can be estimated using a correlation function of distances between sample points in the configuration space [9] which uses the two ....

....in such spaces [6] 9] Other algorithms might also be developed to make use of this structural information. Given a sample of points in a configuration space, the degree of ultrametricity can be estimated using a correlation function of distances between sample points in the configuration space [9], which uses the two longest sides of a sample of triangles randomly generated from the data points. Having no knowledge of the distribution of the data, we use the distribution free rank correlation coefficient S S = 1 Gamma 6 P k i=1 d 2 i k(k 2 Gamma 1) where k denotes the number of ....

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Sara A. Solla, Gregory B. Sorkin, and Steve R. White. Configuration space analysis for optimization problems. In E. Bienenstock et. al., editor, Disordered Systems and Biological Organization, NATO ASI Series, volume F20, pages 283--293, 1986.

....from the Department of Electrical and Computer Engineering, University of Queensland low lying regions. 2. Ultrametricity It is known that under certain conditions, the spin glass models of statistical physics, combinatorial optimization problems (e. g, traveling salesman [4] circuit placement [8] and graph colouring [2] 1] and other systems exhibit the phenomenon of ultrametricity (see [7] for a review) In general, a distance in a metric space obeys the triangular inequality: d(A; C) d(A; B) d(B; C) whereas an ultrametric space is endowed with an (ultrametric) distance measure ....

....along the diagonal q 1 = q 2 (though ultrametric sets may contain offdiagonal peaking with using this function) However, C 1 (q 1 ; q 2 ) is also positive for isosceles triangles with a long base. If the sides of triangles are labeled such that q 1 ; q 2 q 3 , a second correlation function [8] C 2 (q 1 ; q 2 ) e P (q 1 ; q 2 ) Gamma e P (q 1 ) e P (q 2 ) can be used, where e P (q 1 ; q 2 ) is the probability that a triangle will have its two longest sides of length q 1 and q 2 , and e P (q) is the probability that one of the two longest sides will have length q. C 2 (q 1 ....

[Article contains additional citation context not shown here]

Sara A. Solla, Gregory B. Sorkin, and Steve R. White. Configuration space analysis for optimization problems. In E. Bienenstock et. al., editor, Disordered Systems and Biological Organization, NATO ASI Series, volume F20, pages 283--293, 1986.

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S. A. Solla, G. B. Sorkin, and S. R. White. Configuration space analysis for optimization problems. In E. Bienenstock et. al., editor, Disordered Systems and Biological Organization, NATO ASI Series, volume F20, pages 283--293, Berlin, New York, 1986. Springer.

No context found.

S. Solla, G. Sorkin and S. White (1986), "Configuration space analysis for optimization problems", in Disordered Systems and Biological Organization, E. Bienenstock et al. (Eds.), NATO ASI Series, b F20/b, Berlin: Springer Verlag, pp. 283-293.

No context found.

S. A. Solla, G. B. Sorkin and S. R. White, "Configuration Space Analysis for Optimization Problems", in E. Bienenstock et al., eds., Disordered Systems and Biological Organization, Springer-Verlag, 1986, 283-292.

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