On Convergence of Differential Evolution Over a Class of Continuous Functions With Unique Global Optimum

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. Since its inception in the mid 1990s, DE has been finding many successful applications in real-world optimization problems from diverse domains of science and engineering. This paper takes a first significant step toward the convergence analysis of a canonical DE (DE/rand/1/bin) algorithm. It first deduces a time-recursive relationship for the probability density function (PDF) of the trial solutions, taking into consideration the DE-type mutation, crossover, and selection mechanisms. Then, by applying the concepts of Lyapunov stability theorems, it shows that as time approaches infinity, the PDF of the trial solutions concentrates narrowly around the global optimum of the objective function, assuming the shape of a Dirac delta distribution. Asymptotic convergence behavior of the population PDF is established by constructing a Lyapunov functional based on the PDF and showing that it monotonically decreases with time. The analysis is applicable to a class of continuous and real-valued objective functions that possesses a unique global optimum (but may have multiple local optima). Theoretical results have been substantiated with relevant computer simulations.

Convergence problems in a class of model reference adaptive control systems

A class of model reference adaptive control system which make use of an augmented error signal has been introduced by Monopoli. Convergence problems in this attractive class of systems have been investigated in this paper using concepts from hyperstability theory. It is shown that the condition on the linear part of the system has to be stronger than the one given earlier. A boundedness condition on the input to the linear part of the system has been taken into account in the analysis - this condition appears to have been missed in the previous applications of hyperstability theory. Sufficient conditions for the convergence of the adaptive gain to the desired value are also given.

Class of linear time-varying discrete systems

A class of linear time-varying discrete systems is considered, and closed-form solutions are obtained in different cases. Some comments on stability are also included.

Solution of a class of surface water wave scattering problems involving non-reflecting vertical barriers

A large class of scattering problems of surface water waves by vertical barriers lead to mixed boundary value problems for Laplace equation. Specific attentions are paid, in the present article, to highlight an analytical method to handle this class of problems of surface water wave scattering, when the barriers in question are non-reflecting in nature. A new set of boundary conditions is proposed for such non-reflecting barriers and tile resulting boundary value problems are handled in the linearized theory of water waves. Three basic poblems of scattering by vertical barriers are solved. The present new theory of non-reflecting vertical barriers predict new transmission coefficients and tile solutions of tile mathematical problems turn out to be extremely simple and straight forward as compared to the solution for other types of barriers handled previously.

Synthesis of benzofuran based 1,3,5-substituted pyrazole derivatives: As a new class of potent antioxidants and antimicrobials-A novel accost to amend biocompatibility

In search for a new antioxidant and antimicrobial agent with improved potency, we synthesized a series of benzofuran based 1,3,5-substituted pyrazole analogues (5a-l) in five step reaction. Initially, o-alkyl derivative of salicyaldehyde readily furnish corresponding 2-acetyl benzofuran 2 in good yield, on treatment with 1,8-diaza bicyclo5.4.0]undec-7-ene (DBU) in the presence of molecular sieves. Further, aldol condensation with vanillin, Claisen-Schmidt condensation reaction with hydrazine hydrate followed by coupling of substituted anilines afforded target compounds. The structures of newly synthesized compounds were confirmed by IR, H-1 NMR, C-13 NMR, mass, elemental analysis and further screened for their antioxidant and antimicrobial activities. Among the tested compounds 5d and 5f exhibited good antioxidant property with 50% inhibitory concentration higher than that of reference while compounds 5h and 5l exhibited good antimicrobial activity at concentration 1.0 and 0.5 mg/mL compared with standard, streptomycin and fluconazole respectively. (C) 2012 Elsevier Ltd. All rights reserved.

Effect of length scale on mechanical properties of Al-Cu eutectic alloy

This paper attempts a quantitative understanding of the effect of length scale on two phase eutectic structure. We first develop a model that considers both the elastic and plastic properties of the interface. Using Al-Al2Cu lamellar eutectic as model system, the parameters of the model were experimentally determined using indentation technique. The model is further validated using the results of bulk compression testing of the eutectics having different length scales. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4761944]

Application of a Class of Nano fluids to improve the Loadability of Power Transformers

It is generally known that addition of conducting or insulating particles to mineral transformer oil, lowers its breakdown strength, E-d. However, if the particulates are of molecular dimensions, or nanoparticles, (NPs), as they are called, the breakdown strength is seen to increase considerably. Recent experiments by the authors on oil cooled power equipment such as transformers showed that, nanofluids comprising NPs of selected oxides of iron, such as Fe(3)o(4), called magnetite, added to transformer oil increased the breakdown voltage of the virgin oil and more importantly a remarkable enhancement in the thermal conductivity and the viscosity and hence an increased loadability of the transformer for a given top oil temperature (TOT).

Simulation of length-preserving motions of flexible one dimensional oObjects using optimization

During the motion of one dimensional flexible objects such as ropes, chains, etc., the assumption of constant length is realistic. Moreover,their motion appears to be naturally minimizing some abstract distance measure, wherein the disturbance at one end gradually dies down along the curve defining the object. This paper presents purely kinematic strategies for deriving length-preserving transformations of flexible objects that minimize appropriate ‘motion’. The strategies involve sequential and overall optimization of the motion derived using variational calculus. Numerical simulations are performed for the motion of a planar curve and results show stable converging behavior for single-step infinitesimal and finite perturbations 1 as well as multi-step perturbations. Additionally, our generalized approach provides different intuitive motions for various problem-specific measures of motion, one of which is shown to converge to the conventional tractrix-based solution. Simulation results for arbitrary shapes and excitations are also included.