A Neuro-Evolution Heuristic Using Active-Set Techniques to Solve a Novel Nonlinear Singular Prediction Differential Model

In this study, a novel design of a second kind of nonlinear Lane–Emden prediction differential singular model (NLE-PDSM) is presented. The numerical solutions of this model were investigated via a neuro-evolution computing intelligent solver using artificial neural networks (ANNs) optimized by global and local search genetic algorithms (GAs) and the active-set method (ASM), i.e., ANN-GAASM. The novel NLE-PDSM was derived from the standard LE and the PDSM along with the details of singular points, prediction terms and shape factors. The modeling strength of ANN was implemented to create a merit function based on the second kind of NLE-PDSM using the mean squared error, and optimization was performed through the GAASM. The corroboration, validation and excellence of the ANN-GAASM for three distinct problems were established through relative studies from exact solutions on the basis of stability, convergence and robustness. Furthermore, explanations through statistical investigations confirmed the worth of the proposed scheme.

Swarm Intelligence Procedures Using Meyer Wavelets as a Neural Network for the Novel Fractional Order Pantograph Singular System

The purpose of the current investigation is to find the numerical solutions of the novel fractional order pantograph singular system (FOPSS) using the applications of Meyer wavelets as a neural network. The FOPSS is presented using the standard form of the Lane–Emden equation and the detailed discussions of the singularity, shape factor terms along with the fractional order forms. The numerical discussions of the FOPSS are described based on the fractional Meyer wavelets (FMWs) as a neural network (NN) with the optimization procedures of global/local search procedures of particle swarm optimization (PSO) and interior-point algorithm (IPA), i.e., FMWs-NN-PSOIPA. The FMWs-NN strength is pragmatic and forms a merit function based on the differential system and the initial conditions of the FOPSS. The merit function is optimized, using the integrated capability of PSOIPA. The perfection, verification and substantiation of the FOPSS using the FMWs is pragmatic for three cases through relative investigations from the true results in terms of stability and convergence. Additionally, the statics’ descriptions further authorize the presentation of the FMWs-NN-PSOIPA in terms of reliability and accuracy.

Evolutionary heuristic with Gudermannian neural networks for the nonlinear singular models of third kind

The presented research work articulates a new design of heuristic computing platform with artificial intelligence algorithm by exploitation of modeling with feed-forward Gudermannian neural networks (FFGNN) trained with global search viability of genetic algorithms (GA) hybrid with speedy local convergence ability of sequential quadratic programing (SQP) approach, i.e., FFGNN-GASQP for solving the singular nonlinear third order Emden-Fowler (SNEF) models. The proposed FFGNN-GASQP intelligent computing solver Gudermannian kernel unified in the hidden layer structure of FFGNN systems of differential operators based on the SNEF that are arbitrary connected to represent the error-based merit function. The optimization objective function is performed with hybrid heuristics of GASQP. Three problems of the third order SNEF are used to evaluate the correctness, robustness and effectiveness of the designed FFGNN-GASQP scheme. Statistical assessments of the performance of FFGNN-GASQP are used to validate the consistent accuracy, convergence and stability.

Synthesis of highly efficient multilayer dielectric diffraction gratings for spectral combining of laser beams

Статья посвящена синтезу многослойных диэлектрических отражательных дифракционных решеток, с высокой эффективностью обеспечивающих спектральное сложение пучков с различной длиной волны в заданном дифракционном порядке. Приводятся результаты решения задачи синтеза многослойных диэлектрических дифракционных решеток, обеспечивающих спектральное сложение в первом или минус первом порядке дифракции. Кроме того, решается задача синтеза для таких решеток с учетом возможных технологических ограничений на высоту профиля (глубину травления). Решение задачи синтеза проводится путем минимизации зависящего от параметров решетки целевого функционала методом Нелдера-Мида. Решение прямой задачи на каждом шаге минимизации осуществляется при помощи комбинации неполного метода Галеркина и метода матриц рассеяния. The paper is devoted to the synthesis of multilayer dielectric reflection diffraction gratings providing high-efficiency spectral combining of the beams with different wavelengths in a given diffraction order. The results are presented for solving the synthesis problems for multilayer dielectric diffraction gratings providing spectral combining in the first or minus first diffraction order. Besides, the synthesis problem for such gratings is solved with account taken of possible technological constraints imposed by the height of the grating profile (etch depth). The solution of the synthesis problem is obtained by means of Nelder-Mead minimization of the merit function depending on the grating parameters. At each minimization step the direct problem is solved using a combination of the incomplete Galerkin method and scattering matrix method.

Monte Carlo Sampling Method for a Class of Box-Constrained Stochastic Variational Inequality Problems

This paper uses a merit function derived from the Fishcher–Burmeister function and formulates box-constrained stochastic variational inequality problems as an optimization problem that minimizes this merit function. A sufficient condition for the existence of a solution to the optimization problem is suggested. Finally, this paper proposes a Monte Carlo sampling method for solving the problem. Under some moderate conditions, comprehensive convergence analysis is included as well.

Merit-Based Motion Planning for Autonomous Vehicles in Urban Scenarios

Safe and adaptable motion planning for autonomous vehicles remains an open problem in urban environments, where the variability of situations and behaviors may become intractable using rule-based approaches. This work proposes a use-case-independent motion planning algorithm that generates a set of possible trajectories and selects the best of them according to a merit function that combines longitudinal comfort, lateral comfort, safety and utility criteria. The system was tested in urban scenarios on simulated and real environments, and the results show that different driving styles can be achieved according to the priorities set in the merit function, always meeting safety and comfort parameters imposed by design.

A neuro-swarming intelligent heuristic for second-order nonlinear Lane–Emden multi-pantograph delay differential system

The current study is related to present a novel neuro-swarming intelligent heuristic for nonlinear second-order Lane–Emden multi-pantograph delay differential (NSO-LE-MPDD) model by applying the approximation proficiency of artificial neural networks (ANNs) and local/global search capabilities of particle swarm optimization (PSO) together with efficient/quick interior-point (IP) approach, i.e., ANN-PSOIP scheme. In the designed ANN-PSOIP scheme, a merit function is proposed by using the mean square error sense along with continuous mapping of ANNs for the NSO-LE-MPDD model. The training of these nets is capable of using the integrated competence of PSO and IP scheme. The inspiration of the ANN-PSOIP approach instigates to present a reliable, steadfast, and consistent arrangement relates the ANNs strength for the soft computing optimization to handle with such inspiring classifications. Furthermore, the statistical soundings using the different operators certify the convergence, accurateness, and precision of the ANN-PSOIP scheme.

Maximum Relevance Minimum Redundancy Dropout with Informative Kernel Determinantal Point Process

In recent years, deep neural networks have shown significant progress in computer vision due to their large generalization capacity; however, the overfitting problem ubiquitously threatens the learning process of these highly nonlinear architectures. Dropout is a recent solution to mitigate overfitting that has witnessed significant success in various classification applications. Recently, many efforts have been made to improve the Standard dropout using an unsupervised merit-based semantic selection of neurons in the latent space. However, these studies do not consider the task-relevant information quality and quantity and the diversity of the latent kernels. To solve the challenge of dropping less informative neurons in deep learning, we propose an efficient end-to-end dropout algorithm that selects the most informative neurons with the highest correlation with the target output considering the sparsity in its selection procedure. First, to promote activation diversity, we devise an approach to select the most diverse set of neurons by making use of determinantal point process (DPP) sampling. Furthermore, to incorporate task specificity into deep latent features, a mutual information (MI)-based merit function is developed. Leveraging the proposed MI with DPP sampling, we introduce the novel DPPMI dropout that adaptively adjusts the retention rate of neurons based on their contribution to the neural network task. Empirical studies on real-world classification benchmarks including, MNIST, SVHN, CIFAR10, CIFAR100, demonstrate the superiority of our proposed method over recent state-of-the-art dropout algorithms in the literature.