Nature-inspired computational intelligence integration with Nelder–Mead method to solve nonlinear benchmark models

Raja, Muhammad Asif Zahoor; Zameer, Aneela; Kiani, Adiqa Kausar; Shehzad, Azam; Khan, Muhammad Abdul Rehman

doi:10.1007/s00521-016-2523-1

Cited by 30 publications

(13 citation statements)

References 59 publications

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“…Kennedy and Eberhart suggested PSO, i.e., a famous global search easy implementation algorithm introduced at the last of the previous century and required short requirements of the memory [47]. Few recent applications of the PSO are fuel ignition model [48], balancing stochastic U-lines problems [49], nonlinear physical systems [50], feature classification [51] and operation scheduling of microgrids [52].…”

Section: Optimization Procedure: Pso-ip Algorithmmentioning

confidence: 99%

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

Sabir

Raja

et al. 2021

Complex Intell. Syst.

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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.

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Section: Optimization Procedure: Pso-ip Algorithmmentioning

confidence: 99%

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

Sabir

Raja

et al. 2021

Complex Intell. Syst.

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“…This optimization algorithm exploits mathematical modeling inspired bythe swarm pattern of birds flocking as well as fish schooling. Recently, this global optimization procedure is used in different applications, like the fuel ignition model [46], non-linear physical models [47], parameter approximation systems of control auto regressive moving average models [48], balancing stochastic U-lines problems [49], operation scheduling of microgrids [50], and features classification [51].…”

Section: Optimization Process: Pso-ipsmentioning

confidence: 99%

A Neuro-Swarming Intelligence-Based Computing for Second Order Singular Periodic Non-linear Boundary Value Problems

et al. 2020

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In the present investigation, a novel neuro-swarming intelligence-based numerical computing solver is developed for solving second order non-linear singular periodic (NSP) boundary value problems (BVPs), i.e., NSP-BVPs, using the modeling strength of artificial neural networks (ANN) optimized with global search efficacy of particle swarm optimization (PSO) supported with the methodology of rapid local search by interior-point scheme (IPS), i.e., ANN-PSO-IPS. In order to check the proficiency, robustness, and stability of the designed ANN-PSO-IPS, two numerical problems of the NSP-BVPs have been presented for different numbers of neurons. The outcomes of the proposed ANN-PSO-IPS are compared with the available exact solutions to establish the worth of the solver in terms of accuracy and convergence, which is further endorsed through results of statistical performance metrics based on multiple implementations.

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“…In NNDEM given in (6) generally developed using log-sigmoid, ( ) 1 (1 ) z f z e   as an activation function and its derivatives, therefore, the updated NNDEMs for the nonlinear RL circuits solutions is as follows: The generic architecture of the NNDEMs for nonlinear RL circuit for DC and AC excitation can be formulated using set of equations (8).…”

Section: Neural Network Based Differential Equations Modelsmentioning

confidence: 99%

“…The universal function approximation strength of artificial neural networks (ANNs) has been utilized immensely by the researchers in diverse domain of engineering and technology [1][2][3][4][5]. For example, estimation of STATCOM voltages and reactive powers [6], optimization of heat conduction model of human head [7], optimization of an irreversible thermal engine [8], estimation of underwater inherent optical characteristics [9], prediction of attendance demand in games [10], nonlinear system based on elliptic partial differential equations [11] and optimization of credit classification analysis problems [12].…”

Section: Introductionmentioning

confidence: 99%

Integrated computational intelligent paradigm for nonlinear electric circuit models using neural networks, genetic algorithms and sequential quadratic programming

Mehmood

Zameer

Ling

et al. 2019

Neural Comput & Applic

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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 Adams 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.

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Nature-inspired computational intelligence integration with Nelder–Mead method to solve nonlinear benchmark models

Cited by 30 publications

References 59 publications

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

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

A Neuro-Swarming Intelligence-Based Computing for Second Order Singular Periodic Non-linear Boundary Value Problems

Integrated computational intelligent paradigm for nonlinear electric circuit models using neural networks, genetic algorithms and sequential quadratic programming

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