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

The long nonlinear strain waves in a nanostructured rod are considered. The bulk strain solitons in a nanocomposite wave guide are obtained as solutions to a new mathematical model and found in experiments. It is shown that a small concentration of nanoparticles may dramatically change the strain soliton velocity, and this dependence is not monotonous. Evidently, robust measurements of macro- and micro-(nano-)elastic constants of new materials are much needed now for detailed study of strain solitons in nanocomposite wave guides.

Solitary strain waves in nanostructured rod

The differential evolution entirely parallel method has been developed to enable the identification of unknown parameters of mathematical models by minimization of the deviation of the solution from experimental data The method is implemented in a free open-source software that is downloadable from the Internet The results of processing of test functions showed that the accuracy of the method is comparable to that of the three best algorithms from CEC-2014 The method has been successfully used in a number of real biological problems

The differential evolution entirely parallel method for model adaptation in systems biology

We propose a mathematical model for propagation of the long nonlinearly elastic longitudinal strain waves in a bar, which contains nanoscale structural inclusions. The model is governed by a nonlinear doubly dispersive equation (DDE) with respect to the one unknown longitudinal strain function. We obtained the travelling wave solutions to DDE, and, in particular, the strain solitary wave solution, which was shown to be significantly affected by parameters of the inclusions. Moreover we found some critical inaccuracies, committed in papers by others in the derivation of a constitutive equation for the long strain waves in a microstructured medium, revised them, and showed an importance of improvements for correct estimation of wave parameters.

Bulk nonlinear elastic strain waves in a bar with nanosize inclusions

Publisher Summary This chapter discusses the ability of gene circuit method to interpret and predict regulatory mechanisms using (as an example) the segment determination system in fruit fly Drosophila. In modern genetics the regulatory interactions in multicellular organisms are inferred by a comparison of mutant and wild type phenotypes. An important example of use of this method is the deduction that virtually all of the pair-rule class of segmentation genes in the fruit fly Drosophila melanogaster is regulated by members of gap gene class. This conclusion follows directly from observations of segmentation gene expression patterns at gastrulation in a variety of gap and pair-rule mutants. The gene circuit is a data driven mathematical modeling method, whose main aim is to extract information about dynamical regulatory interactions between transcription factors from given gene expression patterns. This is achieved in four steps: (1) formulation of a mathematical modeling framework, (2) collection of gene expression data, (3) fitting of the model to expression data to obtain regulatory parameters, and (4) biological analysis of the resulting gene circuits.

Course 9 A survey of gene circuit approach applied to modelling of segment determination in fruit fly

Results are presented from theory and experiments carried out to excite and observe a localized nonlinear longitudinal strain wave (soliton) in different waveguides. The wave parameters are calculated. It is shown that such a wave conserves its profile during propagation in an elastic waveguide.

Alexander M. Samsonov

Papers

Solitary strain waves in nanostructured rod

The differential evolution entirely parallel method for model adaptation in systems biology

Bulk nonlinear elastic strain waves in a bar with nanosize inclusions

Course 9 A survey of gene circuit approach applied to modelling of segment determination in fruit fly

Holographic studies of strain soliton evolution in nonlinearly elastic solid waveguides