A novel population initialization strategy for accelerating Levy flights based multi-verse optimizer

Ahmad, Sohail; Sulaiman, Muhammad; Kumam, Poom; Hussain, Zawar; Jan, Muhammad Asif; Mashwani, Wali Khan; Ullah, M. Irshad

doi:10.3233/jifs-190112

Cited by 41 publications

(6 citation statements)

References 31 publications

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“…Results obtained by our technique are presented for homogeneous and heterogeneous porous media. The mathematical model for heterogeneous porous media is presented in Eq (29)(30)(31), and for homogeneous porous media, the ordinary differential equation together with its conditions is given in Eq (40)(41)(42). It is obvious from both models (for homogeneous and heterogenous media) that saturation depends on time T and distance X.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…h and h is a step size. Similarly, fitness function for the ODE in Eq (40) and boundary conditions in Eqs (41)(42) representing the secondary oil recovery process through homogenous porous media, is given as,…”

Section: Fitness Function Formulationmentioning

confidence: 99%

“…Fractional order DPSO algorithm is used to solve the corneal model for eye surgery [40]. A novel initialization strategy is introduced in a multi-verse optimization technique, and different design engineering problems are solved in [41]. Nonlinear dusty plasma systems are analyzed with the help of NAR-RBFs neural networks [42].…”

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confidence: 99%

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Analysis of Multi-Phase Flow Through Porous Media for Imbibition Phenomena by Using the LeNN-WOA-NM Algorithm

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The flow of fluids in multi-phase porous media results due to many interesting natural phenomena. The counter-current water imbibition phenomena, that occur during oil extraction through a cylindrical well is an interesting problem in petroleum engineering. During the secondary oil recovery process, water is injected into a porous media having heterogenous and homogenous characteristics. Due to the difference in viscosities of fluids in oil wells, the counter-current imbibition phenomenon occurs. At that moment, the imbibition equation V i = −V n is satisfied by the viscosities of oil and water. In this paper, we have analyzed the governing mathematical model of the imbibition phenomenon occurring during the secondary oil recovery process. A new soft computing algorithm is designed and adapted to analyze the mathematical model of dual-phase flow in detail. Weighted Legendre polynomials based artificial neural networks are hybridized with an efficient global optimizer the Whale Optimization Algorithm (WOA) and a local optimizer the Nelder-Mead algorithm. It is established, that our algorithm LeNN-WOA-NM is efficient and reliable in calculating high-quality solutions in less time. We have compared our experimental outcome with state-of-the-art results. The quality of our solutions is judged based on values of absolute errors, MAD, TIC, and ENSE. It is obvious that LeNN-WOA-NM algorithm can solve real application problems efficiently and accurately. INDEX TERMS Counter-current imbibition phenomena, homogeneous porous media, heterogeneous porous media, capillary pressure, soft computing algorithm, weighted Legendre neural networks, Nelder-Mead algorithm, whale optimization algorithm. I. INTRODUCTION T HIS paper models the phenomena of counter-current imbibition in the multi-phase flow of two immiscible fluids through heterogeneous and homogenous porous mediums that occurs during the secondary oil recovery process or water flooding [1]. In applied sciences, various changes occur in porous mediums having multi-phase flows of different fluids. In the past few decades, researchers are focused on studying the flows in underground petroleum reservoirs [2]. The primary recovery process includes the production of oil by simple natural decompression with no effect of external forces at wells [3]. In secondary oil recovery or water flooding process, fluids like water, polymer, steam are injected into a reservoir through injection wells located in rocks that have fluid communication with production wells. This process is called the immiscible displacement process [3].

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Fitness Function Formulationmentioning

confidence: 99%

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Analysis of Multi-Phase Flow Through Porous Media for Imbibition Phenomena by Using the LeNN-WOA-NM Algorithm

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“…Such stochastic computing techniques use artificial neural networks to model approximate solutions. These numerical solvers have wide applications in various fields including petroleum engineering [ 23 ], wireless communication [ 24 ], heat transfer [ 25 , 26 , 27 ], fuzzy systems [ 28 ], plasma system [ 29 ], civil engineering [ 30 , 31 ], wire coating dynamics [ 32 ] and Diabetic retinopathy classification [ 33 ]. The techniques mentioned earlier inspire the authors to explore and incorporate the soft computing architectures as an alternative, precise and feasible way for solving the mathematical model of micro-disk biosensors.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Analysis of Reaction–Diffusion Equations Modeling the Michaelis–Menten Kinetics in a Micro-Disk Biosensor

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In this study, we have investigated the mathematical model of an immobilized enzyme system that follows the Michaelis–Menten (MM) kinetics for a micro-disk biosensor. The film reaction model under steady state conditions is transformed into a couple differential equations which are based on dimensionless concentration of hydrogen peroxide with enzyme reaction (H) and substrate (S) within the biosensor. The model is based on a reaction–diffusion equation which contains highly non-linear terms related to MM kinetics of the enzymatic reaction. Further, to calculate the effect of variations in parameters on the dimensionless concentration of substrate and hydrogen peroxide, we have strengthened the computational ability of neural network (NN) architecture by using a backpropagated Levenberg–Marquardt training (LMT) algorithm. NNs–LMT algorithm is a supervised machine learning for which the initial data set is generated by using MATLAB built in function known as “pdex4”. Furthermore, the data set is validated by the processing of the NNs–LMT algorithm to find the approximate solutions for different scenarios and cases of mathematical model of micro-disk biosensors. Absolute errors, curve fitting, error histograms, regression and complexity analysis further validate the accuracy and robustness of the technique.

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“…In recent times, stochastic computing paradigms based on artificial intelligence have been used extensively to find numerical solutions for different problems arising in various fields, such as fuzzy systems [ 16 , 17 , 18 ], petroleum engineering [ 19 ], carbon capture process [ 20 , 21 , 22 ], wire coating dynamics [ 23 ], biological systems [ 24 , 25 ], civil engineering [ 26 , 27 ], coal-fired power plant retrofitted [ 28 ], and electrical and thermal engineering [ 29 , 30 , 31 ]. These contributions motivated the authors to investigate the absorption of carbon dioxide (CO

) into solutions of phenyl glycidyl ether (PGE) by strengthening the computational ability of neural networks.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Analysis on Absorption of Carbon Dioxide (CO2) into Solutions of Phenyl Glycidyl Ether (PGE) Using Nonlinear Autoregressive Exogenous Neural Networks

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In this paper, we analyzed the mass transfer model with chemical reactions during the absorption of carbon dioxide (CO2) into phenyl glycidyl ether (PGE) solution. The mathematical model of the phenomenon is governed by a coupled nonlinear differential equation that corresponds to the reaction kinetics and diffusion. The system of differential equations is subjected to Dirichlet boundary conditions and a mixed set of Neumann and Dirichlet boundary conditions. Further, to calculate the concentration of CO2, PGE, and the flux in terms of reaction rate constants, we adopt the supervised learning strategy of a nonlinear autoregressive exogenous (NARX) neural network model with two activation functions (Log-sigmoid and Hyperbolic tangent). The reference data set for the possible outcomes of different scenarios based on variations in normalized parameters (α1,α2,β1,β2,k) are obtained using the MATLAB solver “pdex4”. The dataset is further interpreted by the Levenberg–Marquardt (LM) backpropagation algorithm for validation, testing, and training. The results obtained by the NARX-LM algorithm are compared with the Adomian decomposition method and residual method. The rapid convergence of solutions, smooth implementation, computational complexity, absolute errors, and statistics of the mean square error further validate the design scheme’s worth and efficiency.

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A novel population initialization strategy for accelerating Levy flights based multi-verse optimizer

Cited by 41 publications

References 31 publications

Analysis of Multi-Phase Flow Through Porous Media for Imbibition Phenomena by Using the LeNN-WOA-NM Algorithm

Analysis of Multi-Phase Flow Through Porous Media for Imbibition Phenomena by Using the LeNN-WOA-NM Algorithm

Mathematical Analysis of Reaction–Diffusion Equations Modeling the Michaelis–Menten Kinetics in a Micro-Disk Biosensor

Theoretical Analysis on Absorption of Carbon Dioxide (CO2) into Solutions of Phenyl Glycidyl Ether (PGE) Using Nonlinear Autoregressive Exogenous Neural Networks

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