Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use. DE operates through similar computational steps as employed by a standard evolutionary algorithm (EA). However, unlike traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world resulting in a lot of variants of the basic algorithm with improved performance. This paper presents a detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far. Also, it provides an overview of the significant engineering applications that have benefited from the powerful nature of DE.

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Differential Evolution: A Survey of the State-of-the-Art

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Twenty-four articles by biologists, ecologists, and other scientists represent a year's progress in the field. Among the topics addressed: the effects of introduced species, paleobiogeography, genetics and geographic structure, marine fisheries management, time as an ecological resource, genetic var

Annual Review of Ecology, Evolution and Systematics

http://llama.mshri.on.ca/courses/Biophysics205/Papers/Albert_2003.pdf

The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster.

Expression of the Drosophila segment polarity genes is initiated by a prepattern of pair-rule gene products and maintained by a network of regulatory interactions throughout several stages of embryonic development. Analysis of a model of gene interactions based on differential equations showed that wild-type expression patterns of these genes can be obtained for a wide range of kinetic parameters, which suggests that the steady states are determined by the topology of the network and the type of regulatory interactions between components, not the detailed form of the rate laws. To investigate this, we propose and analyze a Boolean model of this network which is based on a binary ON/OFF representation of transcription and protein levels, and in which the interactions are formulated as logical functions. In this model the spatial and temporal patterns of gene expression are determined by the topology of the network and whether components are present or absent, rather than the absolute levels of the mRNAs and proteins and the functional details of their interactions. The model is able to reproduce the wild type gene expression patterns, as well as the ectopic expression patterns observed in over-expression experiments and various mutants. Furthermore, we compute explicitly all steady states of the network and identify the basin of attraction of each steady state. The model gives important insights into the functioning of the segment polarity gene network, such as the crucial role of the wingless and sloppy paired genes, and the network's ability to correct errors in the prepattern.

The topology of the regulatory interactions predics the expression pattern of the segment polarity genes in Drosophila melanogaster

We report first experimental registration of the splitting induced generation of a soliton train from a single incident strain soliton in two- and three-layered elastic waveguides. The origin is in the nonlinear response of the wave to an abrupt change of physical properties of the waveguide. We show a good agreement between our experimental results and theoretical estimates, based on a weakly nonlinear solution for the doubly dispersive (Boussinesq type) equation with piecewise constant coefficients for the waveguide made of a piecewise isotropic nonlinearly elastic material.

Splitting induced generation of soliton trains in layered waveguides

We report the registration of delamination induced variations in the dynamics of bulk strain solitary waves in layered polymeric bars with the glassy and rubber-like adhesives, for the layers made of the same material. The key phenomenon in a layered structure with the glassy bonding is the delamination caused fission of a single incident soliton into a wave train of solitons, with the detectable increase in the amplitude of the leading solitary wave. The significant feature of bulk strain solitons in structures bonded with the rubber-like adhesive is the generation of radiating solitary waves, whilst co-propagating ripples disappear in the delaminated area. The observed variations may be used for the detection of delamination in lengthy layered structures.

Bulk strain solitary waves in bonded layered polymeric bars with delamination

*SUMMARY Motivation: Modern molecular biology has massive amounts of quantitative data already at its disposal. The crucially important problem for getting closer insights into mechanisms of development is to reduce the complexity of finding the parameters of mathematical models by fitting to experimental data. Parallel Differential Evolution is the modern optimization technique that posses natural parallelization. Results: The new migration scheme for Parallel Differential Evolution has been developed that showed high speed of convergence on the test problem. The dependency of the accuracy of the final result on the period of communication between branches was analyzed. Availability: available on request from the authors.

http://www.bionet.nsc.ru/meeting/bgrs_proceedings/papers/2006/BGRS_2006_V2_027.pdf

New migration scheme for parallel differential evolution

Elastic strain wave propagation in a thin non-linearly elastic layer superimposed on non-linearly elastic half-space is studied. Two layer-half-space contact models are considered. It is found that the Benjamin-Ono equation can be derived for description of longitudinal non-linear strain waves, when the contact between the layer and the half-space is provided only by means of the normal stresses and displacements. When the full contact problem is considered the more complicated integro-differential equation is derived. It is found that long non-linear periodical and solitary strain waves as well as envelope waves may exist in the first case, while only envelope wave solutions are found to the full contact problem. Linear wave analysis shows that the Korteveg-de Vries equation, often usable, is unlikely to be an adequate model for longitudinal surface strain waves. Application of the results obtained to experiments devoted to superconductivity threshold control in thin metal films as well as to generation of acoustic solitons in layered half-space is discussed.

Long non-linear strain waves in layered elastic half-space

The propagation of nonlinear elastic longitudinal strain solitary waves ~i.e., strain solitons ! in a cylindrical rod being in sliding contact with an external elastic medium is considered. The waves have phase velocity in an interval, determined by the elastic properties of the external medium. Furthermore, it is shown that relative to the free rod case the external medium may alter the type of strain soliton. The theory developed can formally be used to estimate the surface-tension-like effects resulting from imperfections of the rod’s lateral surface. Finally, from the results obtained an approach is suggested for the possible experimental determination of the Murnaghan third-order isotropic elastic moduli. @S1063-651X~98!04309-8#

Alexander M. Samsonov

Papers

Splitting induced generation of soliton trains in layered waveguides

Bulk strain solitary waves in bonded layered polymeric bars with delamination

New migration scheme for parallel differential evolution

Long non-linear strain waves in layered elastic half-space

Strain solitary waves in an elastic rod embedded in another elastic external medium with sliding