Differential evolution based computation intelligence solver for elliptic partial differential equations

A differential evolution based methodology is introduced for the solution of elliptic partial differential equations (PDEs) with Dirichlet and/or Neumann boundary conditions. The solutions evolve over bounded domains throughout the interior nodes by minimization of nodal deviations among the population. The elliptic PDEs are replaced by the corresponding system of finite difference approximation, yielding an expression for nodal residues. The global residue is declared as the root-mean-square value of the nodal residues and taken as the cost function. The standard differential evolution is then used for the solution of elliptic PDEs by conversion to a minimization problem of the global residue. A set of benchmark problems consisting of both linear and nonlinear elliptic PDEs has been considered for validation, proving the effectiveness of the proposed algorithm. To demonstrate its robustness, sensitivity analysis has been carried out for various differential evolution operators and parameters. Comparison of the differential evolution based computed nodal values with the corresponding data obtained using the exact analytical expressions shows the accuracy and convergence of the proposed methodology.

Bio-inspired heuristics hybrid with interior-point method for active noise control systems without identification of secondary path

In this study, hybrid computational frameworks are developed for active noise control（ANC） systems using an evolutionary computing technique based on genetic algorithms（GAs） and interior-point method（IPM）, following an integrated approach, GA-IPM. Standard ANC systems are usually implemented with the filtered extended least mean square algorithm for optimization of coefficients for the linear finite-impulse response filter, but are likely to become trapped in local minima（LM）. This issue is addressed with the proposed GA-IPM computing approach which is considerably less prone to the LM problem. Also, there is no requirement to identify a secondary path for the ANC system used in the scheme. The design method is evaluated using an ANC model of a headset with sinusoidal, random, and complex random noise interferences under several scenarios based on linear and nonlinear primary and secondary paths. The accuracy and convergence of the proposed scheme are validated based on the results of statistical analysis of a large number of independent runs of the algorithm.

Bio-inspired computational heuristics to study models of HIV infection of CD4＋ T-cell

In this work, biologically-inspired computing framework is developed for HIV infection of CD4＋ T-cell model using feed-forward artificial neural networks （ANNs）, genetic algorithms （GAs）, sequential quadratic programming （SQP） and hybrid approach based on GA-SQP. The mathematical model for HIV infection of CD4＋ T-cells is represented with the help of initial value problems （IVPs） based on the system of ordinary differential equations （ODEs）. The ANN model for the system is constructed by exploiting its strength of universal approximation. An objective function is developed for the system through unsupervised error using ANNs in the mean square sense. Training with weights of ANNs is carried out with GAs for effective global search supported with SQP for efficient local search. The proposed scheme is evaluated on a number of scenarios for the HIV infection model by taking the different levels for infected cells, natural substitution rates of uninfected cells, and virus particles. Comparisons of the approximate solutions are made with results of Adams numerical solver to establish the correctness of the proposed scheme. Accuracy and convergence of the approach are validated through the results of statistical analysis based on the sufficient large number of independent runs.