Browsing by Author "Jafarian, Ahmad"

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Citation - WoS: 10
A Modified and Enhanced Ant Colony Optimization Algorithm for Traveling Salesman Problem
(Springer international Publishing Ag, 2019) Eskandari, Leila; Jafarian, Ahmad; Rahimloo, Parastoo; Baleanu, Dumitru; 56389; Matematik
Citation - WoS: 60
Citation - Scopus: 68
A New Hybrid Algorithm for Continuous Optimization Problem
(Elsevier Science inc, 2018) Farnad, Behnam; Jafarian, Ahmad; Baleanu, Dumitru; 56389; Matematik
This paper applies a new hybrid method by a combination of three population base algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Symbiotic Organisms Search (SOS). The proposed method has been inspired from natural selection process and it completes this process in GA by using the PSO and SOS. It tends to minimize the execution time and in addition to reduce the complexity. Symbiotic organisms search is a robust and powerful metaheuristic algorithm which has attracted increasing attention in recent decades. There are three alternative phases in the proposed algorithm: GA, which develops and selects best population for the next phases, PSO, which gets experiences for each appropriate solution and updates them as well and SOS, which benefits from previous phases and performs symbiotic interaction update phases in the real-world population. The proposed algorithm was tested on the set of best known unimodal and multimodal benchmark functions in various dimensions. It has further been evaluated in, the experiment on the clustering of benchmark datasets. The obtained results from basic and non-parametric statistical tests confirmed that this hybrid method dominates in terms of convergence, execution time, success rate. It optimizes the high dimensional and complex functions Rosenbrock and Griewank up to 10(-330) accuracy in less than 3 s, outperforming other known algorithms. It had also applied clustering datasets with minimum intra-cluster distance and error rate. (C) 2017 Elsevier Inc. All rights reserved.
Citation - WoS: 10
Citation - Scopus: 15
A novel computational approach to approximate fuzzy interpolation polynomials
(Springer international Publishing Ag, 2016) Jafarian, Ahmad; Jafari, Raheleh; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru; 56389; Matematik
This paper build a structure of fuzzy neural network, which is well sufficient to gain a fuzzy interpolation polynomial of the form y(p) = a(n)x(p)(n) +... + a(1)x(p) + a(0) where a(j) is crisp number (for j = 0,..., n), which interpolates the fuzzy data (x(j), y(j)) (for j = 0,..., n). Thus, a gradient descent algorithm is constructed to train the neural network in such a way that the unknown coefficients of fuzzy polynomial are estimated by the neural network. The numeral experimentations portray that the present interpolation methodology is reliable and efficient.
Citation - WoS: 6
Citation - Scopus: 8
Application of ANNs approach for wave-like and heat-like equations
(de Gruyter Poland Sp Zoo, 2017) Jafarian, Ahmad; Baleanu, Dumitru; Matematik
Artificial neural networks are data processing systems which originate from human brain tissue studies. The remarkable abilities of these networks help us to derive desired results from complicated raw data. In this study, we intend to duplicate an efficient iterative method to the numerical solution of two famous partial differential equations, namely the wave-like and heat-like problems. It should be noted that many physical phenomena such as coupling currents in a flat multi-strand two-layer super conducting cable, non-homogeneous elastic waves in soils and earthquake stresses, are described by initial-boundary value wave and heat partial differential equations with variable coefficients. To the numerical solution of these equations, a combination of the power series method and artificial neural networks approach, is used to seek an appropriate bivariate polynomial solution of the mentioned initial-boundary value problem. Finally, several computer simulations confirmed the theoretical results and demonstrating applicability of the method.
Citation - WoS: 57
Citation - Scopus: 73
Artificial neural network approach for a class of fractional ordinary differential equation
(Springer London Ltd, 2017) Jafarian, Ahmad; Mokhtarpour, Masoumeh; Baleanu, Dumitru; 56389; Matematik
The essential characteristic of artificial neural networks which against the logistic traditional systems is a data-based approach and has led a number of higher education scholars to investigate its efficacy, during the past few decades. The aim of this paper was concerned with the application of neural networks to approximate series solutions of a class of initial value ordinary differential equations of fractional orders, over a bounded domain. The proposed technique uses a suitable truncated power series of the solution function and transforms the original differential equation in a minimization problem. Then, the minimization problem is solved using an accurate neural network model to compute the parameters with high accuracy. Numerical results are given to validate the iterative method.
Citation - WoS: 21
Citation - Scopus: 22
Numerical Solution of Linear Integral Equations System Using the Bernstein Collocation Method
(Springer international Publishing Ag, 2013) Jafarian, Ahmad; Nia, Safa A. Measoomy; Golmankhaneh, Alireza K.; Baleanu, Dumitru; 56389; Matematik
Since in some application mathematical problems finding the analytical solution is too complicated, in recent years a lot of attention has been devoted by researchers to find the numerical solution of this equations. In this paper, an application of the Bernstein polynomials expansion method is applied to solve linear second kind Fredholm and Volterra integral equations systems. This work reduces the integral equations system to a linear system in generalized case such that the solution of the resulting system yields the unknown Bernstein coefficients of the solutions. Illustrative examples are provided to demonstrate the preciseness and effectiveness of the proposed technique. The results are compared with the exact solution by using computer simulations.
Citation - WoS: 36
Citation - Scopus: 41
On artificial neural networks approach with new cost functions
(Elsevier Science inc, 2018) Jafarian, Ahmad; Nia, Safa Measoomy; Golmankhaneh, Alireza Khalili; Baleanu, Dumitru; 56389; Matematik
In this manuscript, the artificial neural networks approach involving generalized sigmoid function as a cost function, and three-layered feed-forward architecture is considered as an iterative scheme for solving linear fractional order ordinary differential equations. The supervised back-propagation type learning algorithm based on the gradient descent method, is able to approximate this a problem on a given arbitrary interval to any desired degree of accuracy. To be more precise, some test problems are also given with the comparison to the simulation and numerical results given by another usual method. (C) 2018 Elsevier Inc. All rights reserved.
Citation - WoS: 13
Citation - Scopus: 10
On Fuzzy Fractional Laplace Transformation
(Hindawi Ltd, 2014) Jafarian, Ahmad; Golmankhaneh, Alireza Khalili; Baleanu, Dumitru; 56389; Matematik
Fuzzy and fractional differential equations are used to model problems with uncertainty and memory. Using the fractional fuzzy Laplace transformation we have solved the fuzzy fractional eigenvalue differential equation. By illustrative examples we have shown the results.
Citation - WoS: 21
Citation - Scopus: 25
Solving fully fuzzy polynomials using feed-back neural networks
(Taylor & Francis Ltd, 2015) Jafarian, Ahmad; Jafari, Raheleh; Golmankhaneh, Alireza Khalili; Baleanu, Dumitru; Matematik
Citation - WoS: 15
Citation - Scopus: 19
Using ANNs Approach for Solving Fractional Order Volterra Integro-differential Equations
(Springernature, 2017) Jafarian, Ahmad; Rostami, Fariba; Golmankhaneh, Alireza K.; Baleanu, Dumitru; 56389; Matematik
Indeed, interesting properties of artificial neural networks approach made this non-parametric model a powerful tool in solving various complicated mathematical problems. The current research attempts to produce an approximate polynomial solution for special type of fractional order Volterra integrodifferential equations. The present technique combines the neural networks approach with the power series method to introduce an efficient iterative technique. To do this, a multi-layer feed-forward neural architecture is depicted for constructing a power series of arbitrary degree. Combining the initial conditions with the resulted series gives us a suitable trial solution. Substituting this solution instead of the unknown function and employing the least mean square rule, converts the origin problem to an approximated unconstrained optimization problem. Subsequently, the resulting nonlinear minimization problem is solved iteratively using the neural networks approach. For this aim, a suitable three-layer feed-forward neural architecture is formed and trained using a back-propagation supervised learning algorithm which is based on the gradient descent rule. In other words, discretizing the differential domain with a classical rule produces some training rules. By importing these to designed architecture as input signals, the indicated learning algorithm can minimize the defined criterion function to achieve the solution series coefficients. Ultimately, the analysis is accompanied by two numerical examples to illustrate the ability of the method. Also, some comparisons are made between the present iterative approach and another traditional technique. The obtained results reveal that our method is very effective, and in these examples leads to the better approximations.