scholarly journals Soft Computing Paradigms to Find the Numerical Solutions of a Nonlinear Influenza Disease Model

2021 ◽  
Vol 11 (18) ◽  
pp. 8549
Author(s):  
Zulqurnain Sabir ◽  
Ag Asri Ag Ibrahim ◽  
Muhammad Asif Zahoor Raja ◽  
Kashif Nisar ◽  
Muhammad Umar ◽  
...  
Keyword(s):  
Nonlinear System ◽  
Local Search ◽  
Objective Function ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Disease Model ◽  
Numerical Results ◽  
Active Set ◽  
System Equations ◽  
Global And Local

The aim of this work is to present the numerical results of the influenza disease nonlinear system using the feed forward artificial neural networks (ANNs) along with the optimization of the combination of global and local search schemes. The genetic algorithm (GA) and active-set method (ASM), i.e., GA-ASM, are implemented as global and local search schemes. The mathematical nonlinear influenza disease system is dependent of four classes, susceptible S(u), infected I(u), recovered R(u) and cross-immune individuals C(u). For the solutions of these classes based on influenza disease system, the design of an objective function is presented using these differential system equations and its corresponding initial conditions. The optimization of this objective function is using the hybrid computing combination of GA-ASM for solving all classes of the influenza disease nonlinear system. The obtained numerical results will be compared by the Adams numerical results to check the authenticity of the designed ANN-GA-ASM. In addition, the designed approach through statistical based operators shows the consistency and stability for solving the influenza disease nonlinear system.

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

2022 ◽  
Vol 6 (1) ◽  
pp. 29
Author(s):  
Zulqurnain Sabir ◽  
Muhammad Asif Zahoor Raja ◽  
Thongchai Botmart ◽  
Wajaree Weera
Keyword(s):  
Numerical Solutions ◽  
Mean Squared Error ◽  
Merit Function ◽  
The Novel ◽  
Active Set ◽  
Shape Factors ◽  
Differential Model ◽  
Squared Error ◽  
Global And Local ◽  
Novel Design

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.

Stochastic numerical investigations for nonlinear three-species food chain system

2021 ◽  
Author(s):  
Zulqurnain Sabir
Keyword(s):  
Food Chain ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Interior Point Algorithm ◽  
Top Predator ◽  
Chain System ◽  
Comparison Of The Results ◽  
Global And Local ◽  
Algorithm Scheme

In this work, three-dimensional nonlinear food chain system is numerically treated using the computational heuristic framework of artificial neural networks (ANNs) together with the proficiencies of global and local search approaches based on genetic algorithm (GA) and interior-point algorithm scheme (IPAS), i.e. ANN–GA–IPAS. The three-dimensional food chain system consists of prey populations, specialist predator and top-predator. The formulation of an objective function using the differential system of three-species food chain and its initial conditions is presented and the optimization is performed by using the hybrid computing efficiency of GA–IPAS. The achieved numerical solutions through ANN–GA–IPAS to solve the nonlinear three-species food chain system are compared with the Adams method to validate the exactness of the designed ANN–GA–IPAS. The comparison of the results is presented to authenticate the correctness of the designed ANN–GA–IPAS for solving the nonlinear three-species food chain system. Moreover, statistical representations for 40 independent trials and 30 variables validate the efficacy, constancy and reliability of ANN–GA–IPAS.

scholarly journals Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model

2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
Juan L.G. Guirao ◽  
Zulqurnain Sabir ◽  
Tareq Saeed
Keyword(s):  
Numerical Solutions ◽  
Standard Form ◽  
Numerical Results ◽  
Third Order ◽  
Multiple Points ◽  
Shape Factors ◽  
Differential Model ◽  
Delay Differential ◽  
Global And Local ◽  
Novel Model

In this study, the design of a novel model based on nonlinear third-order Emden–Fowler delay differential (EF-DD) equations is presented along with two types using the sense of delay differential and standard form of the second-order EF equation. The singularity at ξ = 0 at single or multiple points of each type of the designed EF-DD model are discussed. The detail of shape factors and delayed points is provided for both types of the designed third-order EF-DD model. For the verification and validation of the model, two numerical examples are presented of each case and numerical results have been performed using the artificial neural network along with the hybrid of global and local capabilities. The comparison of the obtained numerical results with the exact solutions shows the perfection and correctness of the designed third-order EF-DD model.

Intelligent Genetic Algorithm with a Gradient-Based Local Search Applied to Supersonic Wing Planform Optimization

2007 ◽  
Vol 23 (4) ◽  
pp. 285-294 ◽  
Author(s):  
J.-L. Liu ◽  
J.-L. Chen
Keyword(s):  
Genetic Algorithm ◽  
Local Search ◽  
Objective Function ◽  
Initial Conditions ◽  
Fractional Factorial ◽  
Optimization Approach ◽  
Design Variables ◽  
Gradient Based ◽  
Global Optima ◽  
Intelligent Genetic Algorithm

AbstractThis study proposes an efficiently evolutionary algorithm, termed IGA-LS, which combines an intelligent genetic algorithm (IGA) with a gradient-based local search (LS). The IGA performs a crossover operation and uses a fractional factorial design to determine the optimal combination of design variables. That is, in the proposed IGA, the chromosomes of children are generated via an intelligent crossover process with factorial experiments after the execution of the selection operation of the GA. This gene mating process differs from that of the traditional GA, in which each chromosome of child exchange genes randomly. The gradient-based optimization approach seeks feasible and usable directions in which to minimize a specified objective function. The initial conditions are provided by the IGA in each generation. Therefore, the IGA-LS offers fast convergence and high numerical accuracy. Several multi-modal test functions are introduced herein to examine the algorithmic capacity and efficiency of finding the global optima. Moreover, the proposed IGA-LS algorithm is applied to optimize the design of a supersonic wing planform for supersonic airplane. The objective function is to minimize the drag during supersonic cruising. From the numerical results, the presented algorithm outperforms the traditional GA, the micro-GA and the intelligent GA in terms of convergence rate and value of the optimal function.

A Study on the Characteristics of a Nonlinear Oscillatory System With Dry Friction

2003 ◽  
Author(s):  
Liming Dai ◽  
Liang Xu
Keyword(s):  
Nonlinear System ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Oscillatory System ◽  
Approximate Solutions ◽  
Weakly Nonlinear ◽  
System Parameters ◽  
Weakly Nonlinear System ◽  
Highly Nonlinear ◽  
Nonlinear Oscillatory System

Nonlinear oscillatory system involved with friction is very common in nonlinear dynamics of engineering fields. This paper is to investigate the motions a nonlinear oscillatory system with involvement of dry friction. The cases of weakly and highly nonlinearity of the system are considered. Approximate and numerical solutions for the system are developed via the author’s newly developed P-T method. As demonstrated in the present work, the properties of the weakly and highly nonlinear systems exhibit great differences, though the governing equations of the two systems employ identical system parameters. The approximate solutions developed for the system are continuous everywhere on the time range considered. Under the conditions of weakly nonlinearity, the approximate solutions developed can therefore be conveniently implemented for the purpose of an analytical studying the properties of the system with numerous system parameters and various initial conditions. Taking this advantage, the behavior of motion of the weakly nonlinear system is analyzed and compared with the corresponding solutions developed with Van der Pol’s method. It is found in the present work, the system may undergo a self-excited oscillation under certain conditions. The highly nonlinear system is a physically much involved one. Its behavior is thus much complex in comparing with that of the weakly nonlinear system. Based on the approximate solutions developed for the highly nonlinear system, recurrence relations are generated for numerical calculations. For the sake of comparison with the oscillation of the weakly nonlinear system, numerical simulations for the highly nonlinear system are performed under the same initial conditions and identical system parameters. The conditions of convergence and divergence of the weakly nonlinear system are also established for application. Behavior of the oscillatory motion of the highly nonlinear system is investigated on the basis of the corresponding numerical solutions developed.

Midcourse guidance law with neural networks

2005 ◽  
Vol 219 (2) ◽  
pp. 131-144 ◽  
Author(s):  
D Han ◽  
S N Balakrishnan ◽  
E J Ohlmeyer
Keyword(s):  
Optimal Control ◽  
Network Performance ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Numerical Results ◽  
Feedback Form ◽  
Lagrangian Multipliers ◽  
Adaptive Critic ◽  
Midcourse Guidance ◽  
Guidance Problem

A dual neural network ‘adaptive critic approach’ is used in this study to generate midcourse guidance commands for a missile to reach a predicted impact point while maximizing its final velocity. The adaptive critic approach is based on approximate dynamic programming. The first network, called a ‘critic’, network, outputs the Lagrangian multipliers arising in an optimal control formulation while the second network, called an ‘action’ network, outputs the optimal guidance/control. While a typical adaptive critic structure consists of a single critic and a single controller, the midcourse guidance problem needs indexing in terms of the independent variable and therefore there is a cascade of critics and controllers each set for a different index. Every controller learns from the critic at the previous stage. Though the networks are trained off-line, the resulting control is in a feedback form. A midcourse guidance problem is the first testbed for this approach where the input is vector-valued. The numerical results for a number of scenarios show that the network performance is excellent. Corroboration for optimality is provided by comparisons of the numerical solutions using a shooting method for a number of scenarios. Numerical results demonstrate some attractive features of the adaptive critic approach and show that this formulation works very well in guiding the missile to its final conditions from an envelope of initial conditions. This application also demonstrates the use of adaptive critics as a tool to solve a class of ‘free final time’ problems in optimal control, which are usually very difficult.

Opinion Dynamics Optimization by Varying Susceptibility to Persuasion via Non-Convex Local Search

2021 ◽  
Vol 16 (2) ◽  
pp. 1-34
Author(s):  
Rediet Abebe ◽  
T.-H. HUBERT Chan ◽  
Jon Kleinberg ◽  
Zhibin Liang ◽  
David Parkes ◽  
...  
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Iterative Process ◽  
Large Scale ◽  
Opinion Dynamics ◽  
Theoretical Models ◽  
Global Optimum ◽  
Local Optimum ◽  
Opinion Formation ◽  
Long Line

A long line of work in social psychology has studied variations in people’s susceptibility to persuasion—the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people’s intrinsic opinions, it is also natural to consider interventions that modify people’s susceptibility to persuasion. In this work, motivated by this fact, we propose an influence optimization problem. Specifically, we adopt a popular model for social opinion dynamics, where each agent has some fixed innate opinion, and a resistance that measures the importance it places on its innate opinion; agents influence one another’s opinions through an iterative process. Under certain conditions, this iterative process converges to some equilibrium opinion vector. For the unbudgeted variant of the problem, the goal is to modify the resistance of any number of agents (within some given range) such that the sum of the equilibrium opinions is minimized; for the budgeted variant, in addition the algorithm is given upfront a restriction on the number of agents whose resistance may be modified. We prove that the objective function is in general non-convex. Hence, formulating the problem as a convex program as in an early version of this work (Abebe et al., KDD’18) might have potential correctness issues. We instead analyze the structure of the objective function, and show that any local optimum is also a global optimum, which is somehow surprising as the objective function might not be convex. Furthermore, we combine the iterative process and the local search paradigm to design very efficient algorithms that can solve the unbudgeted variant of the problem optimally on large-scale graphs containing millions of nodes. Finally, we propose and evaluate experimentally a family of heuristics for the budgeted variant of the problem.

scholarly journals Design and Automated Optimization of an Internal Turret Mooring System in the Frequency and Time Domain

2021 ◽  
Vol 9 (6) ◽  
pp. 581
Author(s):  
Hongrae Park ◽  
Sungjun Jung
Keyword(s):  
System Design ◽  
Time Domain ◽  
Initial Conditions ◽  
Minimum Weight ◽  
Optimization Algorithms ◽  
Local Optimization ◽  
Mooring System ◽  
Floating Offshore Wind Turbines ◽  
Global And Local Optimization ◽  
Global And Local

A cost-effective mooring system design has been emphasized for traditional offshore industry applications and in the design of floating offshore wind turbines. The industry consensus regarding mooring system design is mainly inhibited by previous project experience. The design of the mooring system also requires a significant number of design cycles. To take aim at these challenges, this paper studies the application of an optimization algorithm to the Floating Production Storage and Offloading (FPSO) mooring system design with an internal turret system at deep-water locations. The goal is to minimize mooring system costs by satisfying constraints, and an objective function is defined as the minimum weight of the mooring system. Anchor loads, a floating body offset and mooring line tensions are defined as constraints. In the process of optimization, the mooring system is analyzed in terms of the frequency domain and time domain, and global and local optimization algorithms are also deployed towards reaching the optimum solution. Three cases are studied with the same initial conditions. The global and local optimization algorithms successfully find a feasible mooring system by reducing the mooring system cost by up to 52%.

Observations Regarding Numerical Results Obtained by the Floquet-Method

2013 ◽  
Author(s):  
Till J. Kniffka ◽  
Horst Ecker
Keyword(s):  
Numerical Methods ◽  
Monodromy Matrix ◽  
Mathieu Equation ◽  
Numerical Results ◽  
The Other ◽  
Benchmark Problem ◽  
Stability Studies ◽  
Floquet Method ◽  
System Equations ◽  
Time Periodic

Stability studies of parametrically excited systems are frequently carried out by numerical methods. Especially for LTP-systems, several such methods are known and in practical use. This study investigates and compares two methods that are both based on Floquet’s theorem. As an introductary benchmark problem a 1-dof system is employed, which is basically a mechanical representation of the damped Mathieu-equation. The second problem to be studied in this contribution is a time-periodic 2-dof vibrational system. The system equations are transformed into a modal representation to facilitate the application and interpretation of the results obtained by different methods. Both numerical methods are similar in the sense that a monodromy matrix for the LTP-system is calculated numerically. However, one method uses the period of the parametric excitation as the interval for establishing that matrix. The other method is based on the period of the solution, which is not known exactly. Numerical results are computed by both methods and compared in order to work out how they can be applied efficiently.

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