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Öğe Mathematical Treatment of Nonlinear Pine Wilt Disease Model: An Evolutionary Approach(Univ Punjab, Dept Mathematics, 2022) Tabassum, Muhammad Farhan; Farman, Muhammad; Akgul, Ali; Akram, SanaIn human life, the forest plays an important role in safeguard-ing trees against disease infection. The pine wilt disease is one of the big threats for the forest and the environment. Optimum control the-ory is about discovering a complex system control rule over a period of time. In this paper Evolutionary Pade acute accent Approximation (EPA) scheme has been implemented for the treatment of non-linear pine wilt disease model. Evolutionary Pade acute accent Approximation scheme transforms the nonlinear pine wilt disease model into optimization problem. Initial conditions are con-verted into problem constraints and then constraint problem is converted into unconstraint problem by using penalty function. Sufficient parameter settings for EPA have been implemented. The simulations are numerical solutions of the model of pine wilt disease by solving the proven problem of optimization. It is also determined the threshold value for the fun-damental reproductive number and the endemic disease balance point of the model. Evolutionary Pade acute accent Approximation has provided convergence solution regarding relationship among the different population compart-ments for diseases equilibrium, it has been observed that the results EPA scheme are more reliable and significant when a comparison is drawn with Non-Standard Finite Difference (NSFD) numerical scheme. Finally, EPA scheme reduces the infected rates very fast. Further, in a strong contrast to NFSD, this technique has eliminated the need to provide step size.Öğe Optimal solution of engineering design problems through differential gradient evolution plus algorithm: a hybrid approach(Iop Publishing Ltd, 2022) Tabassum, Muhammad Farhan; Akgul, Ali; Akram, Sana; Hassan, Saadia; Saman; Qudus, Ayesha; Karim, RabiaIt is very necessary and applicable to optimize all disciplines. In practical engineering problems the optimization has been a significant component. This article presents the hybrid approach named as differential gradient evolution plus (DGE+) algorithm which is the combination of differential evolution gorithm and gradient evolution (GE) algorithm. DE was used to diversify and GE was used for intensification with a perfect equilibrium between exploration and exploitation with an improvised distribution of dynamic probability and offers a new shake-off approach to prevent premature convergence to local optimum. To describe the success, the proposed algorithm is compared to modern meta-heuristics. To see the accuracy, robustness, and reliability of DGE+ it has been implemented on eight complex practical engineering problems named as: pressure vessel, belleville spring, tension/compression spring, three-bar truss, welded beam, speed reducer, gear train and rolling element bearing design problem, the results revealed that DGE+ algorithm can deliver highly efficient, competitive and promising results.Öğe Solution of chemical dynamic optimization systems using novel differential gradient evolution algorithm(Iop Publishing Ltd, 2021) Tabassum, Muhammad Farhan; Saeed, Muhammad; Akgul, Ali; Farman, Muhammad; Akram, SanatOptimization for all disciplines is essential and relevant. Optimization has played a vital role in industrial reactors' design and operation, separation processes, heat exchangers, and complete plants in Chemical Engineering. In this paper, a novel hybrid meta-heuristic optimization algorithm which is based on Differential Evolution (DE), Gradient Evolution (GE), and Jumping Technique (+) named Differential Gradient Evolution Plus (DGE+) is presented. The main concept of this hybrid algorithm is to enhance its exploration and exploitation ability. The proposed algorithm hybridizes the above-mentioned algorithms with the help of an improvised dynamic probability distribution, additionally provides a new shake off method to avoid premature convergence towards local minima. The performance of DGE+ is investigated in thirteen benchmark unconstraint functions, and the results are compared to the other state-of-the-art meta-heuristics. The comparison shows that the proposed algorithm can outperform the other state-of-the-art meta-heuristics in almost all benchmark functions. To evaluate the precision and robustness of the DGE+ it has also been applied to complex chemical dynamic optimization systems such as optimization of a multimodal continuous stirred tank reactor, Lee-Ramirez bioreactor, Six-plate gas absorption tower, and optimal operation of alkylation unit, the results of comparison revealed that the proposed algorithm can provide very compact, competitive and promising performance overall complex non-linear chemical design problems.Öğe Solution of Non-Linear Chemical Processes using Novel Differential Gradient Evolution Algorithm(L and H Scientific Publishing, LLC, 2022) Tabassum, Muhammad Farhan; Chaudhry, Nazir Ahmad; Akgül, Ali; Farman, Muhammad; Akram, SanaOptimization for all disciplines is very important and relevant. Optimization has played a key role in the design and operation of industrial reactors, separation processes, heat exchangers and complete plants in Chemical Engineering. In this paper, a novel hybrid meta-heuristic optimization algorithm which is based on Differential Evolution (DE), Gradient Evolution (GE) and Jumping Technique (+) named as Differential Gradient Evolution Plus (DGE+) is presented. The main concept of this hybrid algorithm is to enhance its exploration and exploitation ability. The proposed algorithm hybridizes the above-mentioned algorithms with the help of an improvised dynamic probability distribution, additionally provides a new shake off method to avoid premature convergence towards local minima. The performance of DGE+ is investigated in thirteen benchmark unconstraint functions and the results are compared to the other state-of-the-art metaheuristics. The comparison shows that the proposed algorithm is able to outperform the other state-of-the-art meta-heuristics in almost all benchmark functions. To evaluate the efficiency of the DGE+ it has also been applied to complex constrained non-linear chemical design problems such as optimal operation of alkylation unit, reactor network design, optimal design of heat exchanger network, optimization of an isothermal continuous stirred tank reactor, the results of comparison revealed that the proposed algorithm is able to provide very compact, competitive and promising performance. © 2022. L&H Scientific Publishing, LLC. All Rights Reserved.Öğe Treatment of dynamical nonlinear Measles model: An evolutionary approach(Semnan Univ, 2022) Tabassum, Muhammad Farhan; Akgul, Ali; Akram, Sana; Farman, Muhammad; Karim, Rabia; ul Hassan, Saadia MahmoodMeasles is a respiratory system infection caused by a Morbillivirus genus virus. The disease spreads directly or indirectly through respiration from the infected person's nose and mouth after contact with fluids. The vast population of infects in developing countries is yet at risk. Generally, the mathematical model of Measles virus propagation is nonlinear and therefore changeable to solve by traditional analytical and finite difference schemes by processing all properties of the model like boundedness, positivity feasibility. In this paper, an unconditionally convergent semi-analytical approach based on modern Evolutionary computational technique and Pade-Approximation (EPA) has been implemented for the treatment of non-linear Measles model. The convergence solution of EPA scheme on population: susceptible people, infective people, and recovered people have been studied and found to be significant. Eventually, EPA reduces contaminated levels very rapidly and no need to supply step size. A robust and durable solution has been established with the EPA in terms of the relationship between disease-free equilibrium in the population. When comparing the Non-Standard Finite Difference (NSFD) approach, the findings of EPA have shown themselves to be far superior.