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1
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Phenotypic evolution with a mutation based on symmetric α-stable distributions

100%
Obuchowicz A., Prętki P.
International Journal of Applied Mathematics and Computer Science
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2004
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tom 14
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nr 3
289-316
EN
Multidimensional Symmetric α-Stable (SαS) mutations are applied to phenotypic evolutionary algorithms. Such mutations are characterized by non-spherical symmetry for α<2 and the fact that the most probable distance of mutated points is not in a close neighborhood of the origin, but at a certain distance from it. It is the so-called surrounding effect (Obuchowicz, 2001b; 2003b). For α=2, the SαS mutation reduces to the Gaussian one, and in the case of α=1, the Cauchy mutation is obtained. The exploration and exploitation abilities of evolutionary algorithms, using SαS mutations for different α, are analyzed by a set of simulation experiments. The obtained results prove the important influence of the surrounding effect of symmetric α-stable mutations on both the abilities considered.
2
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A neural-network controlled dynamic evolutionary scheme for global molecular geometry optimization

100%
Styrcz A., Mrozek J., Mazur G.
International Journal of Applied Mathematics and Computer Science
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2011
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tom 21
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nr 3
559-566
EN
A novel, neural network controlled, dynamic evolutionary algorithm is proposed for the purposes of molecular geometry optimization. The approach is tested for selected model molecules and some molecular systems of importance in biochemistry. The new algorithm is shown to compare favorably with the standard, statically parametrized memetic algorithm.
3
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A primal-dual integral method in global optimization

88%
Hichert J., Hoffmann A., Phú H., Reinhardt R.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2000
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tom 20
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nr 2
257-278
EN
Using the Fenchel conjugate $F^c$ of Phú's Volume function F of a given essentially bounded measurable function f defined on the bounded box D ⊂ Rⁿ, the integral method of Chew and Zheng for global optimization is modified to a superlinearly convergent method with respect to the level sequence. Numerical results are given for low dimensional functions with a strict global essential supremum.
4
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The island model as a Markov dynamic system

88%
Schaefer R., Byrski A., Smołka M.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
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nr 4
971-984
EN
Parallel multi-deme genetic algorithms are especially advantageous because they allow reducing the time of computations and can perform a much broader search than single-population ones. However, their formal analysis does not seem to have been studied exhaustively enough. In this paper we propose a mathematical framework describing a wide class of island-like strategies as a stationary Markov chain. Our approach uses extensively the modeling principles introduced by Vose, Rudolph and their collaborators. An original and crucial feature of the framework we propose is the mechanism of inter-deme agent operation synchronization. It is important from both a practical and a theoretical point of view. We show that under a mild assumption the resulting Markov chain is ergodic and the sequence of the related sampling measures converges to some invariant measure. The asymptotic guarantee of success is also obtained as a simple issue of ergodicity. Moreover, if the cardinality of each island population grows to infinity, then the sequence of the limit invariant measures contains a weakly convergent subsequence. The formal description of the island model obtained for the case of solving a single-objective problem can also be extended to the multi-objective case.
5
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Random perturbation of the projected variable metric method for nonsmooth nonconvex optimization problems with linear constraints

88%
El Mouatasim A., Ellaia R., Souza de Cursi E.
International Journal of Applied Mathematics and Computer Science
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2011
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tom 21
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nr 2
317-329
EN
We present a random perturbation of the projected variable metric method for solving linearly constrained nonsmooth (i.e., nondifferentiable) nonconvex optimization problems, and we establish the convergence to a global minimum for a locally Lipschitz continuous objective function which may be nondifferentiable on a countable set of points. Numerical results show the effectiveness of the proposed approach.
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