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The present study aims to design stochastic intelligent computational heuristics for the numerical treatment of a nonlinear SITR system representing the dynamics of novel coronavirus disease 2019 (COVID-19). The mathematical SITR system using fractal parameters for COVID-19 dynamics is divided into four classes; that is, susceptible (S), infected (I), treatment (T), and recovered (R). The comprehensive details of each class along with the explanation of every parameter are provided, and the dynamics of novel COVID-19 are represented by calculating the solution of the mathematical SITR system using feed-forward artificial neural networks (FF-ANNs) trained with global search genetic algorithms (GAs) and speedy fine tuning by sequential quadratic programming (SQP)—that is, an FF-ANN-GASQP scheme. In the proposed FF-ANN-GASQP method, the objective function is formulated in the mean squared error sense using the approximate differential mapping of FF-ANNs for the SITR model, and learning of the networks is proficiently conducted with the integrated capabilities of GA and SQP. The correctness, stability, and potential of the proposed FF-ANN-GASQP scheme for the four different cases are established through comparative assessment study from the results of numerical computing with Adams solver for single as well as multiple autonomous trials. The results of statistical evaluations further authenticate the convergence and prospective accuracy of the FF-ANN-GASQP method.

Mixed integer programming (MIP) is commonly used to model indicator constraints, i.e., constraints that either hold or are relaxed depending on the value of a binary variable. Unfortunately, those models tend to lead to weak continuous relaxations and turn out to be unsolvable in practice; this is what happens, for e.g., in the case of Classification problems with Ramp Loss functions that represent an important application in this context. In this paper we show the computational evidence that a relevant class of these Classification instances can be solved far more efficiently if a nonlinear, nonconvex reformulation of the indicator constraints is used instead of the linear one. Inspired by this empirical and surprising observation, we show that aggressive bound tightening is the crucial ingredient for solving this class of instances, and we devise a pair of computationally effective algorithmic approaches that exploit it within MIP. One of these methods is currently part of the arsenal of IBM-Cplex  since version 12.6.1. More generally, we argue that aggressive bound tightening is often overlooked in MIP, while it represents a significant building block for enhancing MIP technology when indicator constraints and disjunctive terms are present.

We study the nonparametric least squares estimator (LSE) of a multivariate convex regression function. The LSE, given as the solution to a quadratic program with O(n 2 ) linear constraints (n being the sample size), is difficult to compute for large problems. Exploiting problem specific structure, we propose a scalable algorithmic framework based on the augmented Lagrangian method to compute the LSE. We develop a novel approach to obtain smooth convex approximations to the fitted (piecewise affine) convex LSE and provide formal bounds on the quality of approximation. When the number of samples is not too large compared to the dimension of the predictor, we propose a regularization scheme-Lipschitz convex regression-where we constrain the norm of the subgradients, and study the rates of convergence of the obtained LSE. Our algorithmic framework is simple and flexible and can be easily adapted to handle variants: estimation of a nondecreasing/nonincreasing convex/concave (with or without a Lipschitz bound) function. We perform numerical studies illustrating the scalability of the proposed algorithm-on some instances our proposal leads to more than a 10,000-fold improvement in runtime when compared to off-the-shelf interior point solvers for problems with n = 500.

A recent series of papers has examined the extension of disjunctive-programming techniques to mixed-integer second-order-cone programming. For example, it has been shown—by several authors using different techniques—that the convex hull of the intersection of an ellipsoid, E , and a split disjunction, ( l - x j ) ( x j - u ) ≤ 0 with l < u , equals the intersection of E with an additional second-order-cone representable (SOCr) set. In this paper, we study more general intersections of the form K ∩ Q and K ∩ Q ∩ H , where K is a SOCr cone, Q is a nonconvex cone defined by a single homogeneous quadratic, and H is an affine hyperplane. Under several easy-to-verify conditions, we derive simple, computable convex relaxations K ∩ S and K ∩ S ∩ H , where S is a SOCr cone. Under further conditions, we prove that these two sets capture precisely the corresponding conic/convex hulls. Our approach unifies and extends previous results, and we illustrate its applicability and generality with many examples.

This work introduces a rigorous framework for systematically determining fundamental performance bounds in the context of negative dielectrophoresis. To achieve this, we apply quadratically constrained quadratic programming, a powerful optimization approach particularly well-suited for quantifying theoretical performance limits under well-defined physical constraints. We generalize these results to experimentally relevant two-dimensional electrode geometries while explicitly partitioning the design domain into controllable and uncontrollable regions consistent with experimental constraints. Furthermore, we discuss the use of topology optimization techniques to identify electrode layouts that can experimentally achieve performance close to the derived theoretical limits, thus bridging the gap between theoretical analysis and practical experimental realization.

In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that employs variance reduction in the gradient approximations. Under reasonable assumptions, we prove that a measure of first-order stationarity evaluated at the iterates generated by our proposed algorithm converges to zero in expectation from arbitrary starting points, for both constant and adaptive step size strategies. Finally, we demonstrate the practical performance of our proposed algorithm on constrained binary classification problems that arise in machine learning.

In this paper, we propose a method for stress-constrained topology optimization of continuum structure sustaining harmonic load excitation using the reciprocal variables. In the optimization formulation, the total volume is minimized with a given stress amplitude constraint. The p -norm aggregation function is adopted to treat the vast number of local constraints imposed on all elements. In contrast to previous studies, the optimization problem is well posed as a quadratic program with second-order sensitivities, which can be solved efficiently by sequential quadratic programming. Several numerical examples demonstrate the validity of the presented method, in which the stress constrained designs are compared with traditional stiffness-based designs to illustrate the merit of considering stress constraints. It is observed that the proposed approach produces solutions that reduce stress concentration at the critical stress areas. The influences of varying excitation frequencies, damping coefficient and force amplitude on the optimized results are investigated, and also demonstrate that the consideration of stress-amplitude constraints in resonant structures is indispensable.

In this paper, a novel application of biologically inspired computing paradigm is presented for solving initial value problem (IVP) of electric circuits based on nonlinear RL model by exploiting the competency of accurate modeling with feed forward artificial neural network (FF-ANN), global search efficacy of genetic algorithms (GA) and rapid local search with sequential quadratic programming (SQP). The fitness function for IVP of associated nonlinear RL circuit is developed by exploiting the approximation theory in mean squared error sense using an approximate FF-ANN model. Training of the networks is conducted by integrated computational heuristic based on GA-aided with SQP, i.e., GA-SQP. The designed methodology is evaluated to variants of nonlinear RL systems based on both AC and DC excitations for number of scenarios with different voltages, resistances and inductance parameters. The comparative studies of the proposed results with Adam’s numerical solutions in terms of various performance measures verify the accuracy of the scheme. Results of statistics based on Monte-Carlo simulations validate the accuracy, convergence, stability and robustness of the designed scheme for solving problem in nonlinear circuit theory.

Model Predictive Control (MPC) has emerged as a promising approach for energy management in hybrid electric vehicles, enabling predictive optimization of powertrain operation. The energy management problem in parallel hybrid powertrains constitutes a Mixed-Integer Nonlinear Programming (MINLP) problem, combining continuous decision variables such as torque distribution with discrete decisions including engine on/off states and clutch engagement. This problem structure presents distinct challenges for different optimization approaches. Gradient-based methods such as Sequential Quadratic Programming (SQP) solve continuous, differentiable optimization problems and require auxiliary methods to handle integer variables, while metaheuristic approaches such as Genetic Algorithms (GA) can handle the mixed-integer structure directly at the cost of increased computational effort. This study presents a systematic comparison between GA and SQP as optimization solvers within an MPC framework for a P1P3 parallel hybrid powertrain. A multi-objective cost function is formulated to simultaneously optimize system efficiency, battery state of charge management, and noise emissions. Both approaches are evaluated across the WLTC as well as a real-world RDE scenario. On the WLTC, both MPC approaches reduce fuel consumption by 0.5–1.0% and improve system efficiency by 3.7–4.6% compared to a state-of-the-art deterministic reference strategy optimized for fuel consumption. At the same time, both approaches additionally achieve substantial reductions in noise emissions compared to the deterministic reference, which was not optimized for acoustic behavior. On both cycles, the GA-based MPC achieves favorable performance compared to SQP, with the performance gap widening from the WLTC to the RDE cycle. Both methods achieve real-time capability, yet SQP reduces computational time by a factor of four compared to GA. As long as computational resources in automotive ECUs remain constrained, this efficiency advantage positions gradient-based optimization for series production applications, whereas metaheuristic methods offer greater flexibility for concept development stages with relaxed real-time requirements. The findings contribute to the understanding of optimization algorithm selection for MINLP energy management problems in hybrid electric vehicles.

In this paper, a bio-inspired computational intelligence technique is presented for solving nonlinear doubly singular system using artificial neural networks (ANNs), genetic algorithms (GAs), sequential quadratic programming (SQP) and their hybrid GA–SQP. The power of ANN models is utilized to develop a fitness function for a doubly singular nonlinear system based on approximation theory in the mean square sense. Global search for the parameters of networks is performed with the competency of GAs and later on fine-tuning is conducted through efficient local search by SQP algorithm. The design methodology is evaluated on number of variants for two point doubly singular systems. Comparative studies with standard results validate the correctness of proposed schemes. The consistent correctness of the proposed technique is proven through statistics using different performance indices.