Search results for: hybrid differential evolution

Authors: K. Y. Tseng, C. Y. Wu

Abstract:

This paper employs a heuristic algorithm to solve engineering problems including truss structure optimization and optimal chiller loading (OCL) problems. Two different type algorithms, real-valued differential evolution (DE) and modified binary differential evolution (MBDE), are successfully integrated and then can obtain better performance in solving engineering problems. In order to demonstrate the performance of the proposed algorithm, this study adopts each one testing case of truss structure optimization and OCL problems to compare the results of other heuristic optimization methods. The result indicates that the proposed algorithm can obtain similar or better solution in comparing with previous studies.

Keywords: differential evolution, Truss structure optimization, optimal chiller loading, modified binary differential evolution

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Authors: Mohammad Besharatloo

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Intrusion detection is an important research topic in network security because of increasing growth in the use of computer network services. Intrusion detection is done with the aim of detecting the unauthorized use or abuse in the networks and systems by the intruders. Therefore, the intrusion detection system is an efficient tool to control the user's access through some predefined regulations. Since, the data used in intrusion detection system has high dimension, a proper representation is required to show the basis structure of this data. Therefore, it is necessary to eliminate the redundant features to create the best representation subset. In the proposed method, a hybrid model of differential evolution and firefly algorithms was employed to choose the best subset of properties. In addition, decision tree and support vector machine (SVM) are adopted to determine the quality of the selected properties. In the first, the sorted population is divided into two sub-populations. These optimization algorithms were implemented on these sub-populations, respectively. Then, these sub-populations are merged to create next repetition population. The performance evaluation of the proposed method is done based on KDD Cup99. The simulation results show that the proposed method has better performance than the other methods in this context.

Keywords: intrusion detection system, differential evolution, firefly algorithm, support vector machine, decision tree

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Authors: Mahmood Otadi, Maryam Mosleh

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

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Authors: Xuezhang Hou

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In the present paper, a hybrid hyperbolic dynamic system formulated by partial differential equations with initial and boundary conditions is considered. First, the system is transformed to an abstract evolution system in an appropriate Hilbert space, and spectral analysis and semigroup generation of the system operator is discussed. Subsequently, a sliding model control problem is proposed and investigated, and an equivalent control method is introduced and applied to the system. Finally, a significant result that the state of the system can be approximated by an ideal sliding mode under control in any accuracy is derived and examined.

Keywords: hyperbolic dynamic system, sliding model control, semigroup of linear operators, partial differential equations

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Authors: T. Vamsee Kiran, A. Gopi

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The undesired torque and flux ripple may occur in conventional direct torque control (DTC) induction motor drive. DTC can improve the system performance at low speeds by continuously tuning the regulator by adjusting the Kp, Ki values. In this differential evolution (DE) is proposed to adjust the parameters (Kp, Ki) of the speed controller in order to minimize torque ripple, flux ripple, and stator current distortion.The DE based PI controller has resulted is maintaining a constant speed of the motor irrespective of the load torque fluctuations.

Keywords: differential evolution, direct torque control, PI controller

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Authors: Fouzi Aboura

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The fractional order proportional-integral-derivative (FOPID) controller or fractional order (PIλDµ) is a proportional-integral-derivative (PID) controller where integral order (λ) and derivative order (µ) are fractional, one of the important application of classical PID is the Automatic Voltage Regulator (AVR).The FOPID controller needs five parameters optimization while the design of conventional PID controller needs only three parameters to be optimized. In our paper we have proposed a comparison between algorithms Differential Evolution (DE) and Hybrid Genetic Algorithm Particle Swarm Optimization (HGAPSO) ,we have studied theirs characteristics and performance analysis to find an optimum parameters of the FOPID controller, a new objective function is also proposed to take into account the relation between the performance criteria’s.

Keywords: FOPID controller, fractional order, AVR system, objective function, optimization, GA, PSO, HGAPSO

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Abdullah M. Almeshal, Mohammad R. Alenezi, Muhammad Moaz

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In this paper, we discuss the performance of applying hybrid spiral dynamic bacterial chemotaxis (HSDBC) optimisation algorithm on an intelligent controller for a differential drive robot. A unicycle class of differential drive robot is utilised to serve as a basis application to evaluate the performance of the HSDBC algorithm. A hybrid fuzzy logic controller is developed and implemented for the unicycle robot to follow a predefined trajectory. Trajectories of various frictional profiles and levels were simulated to evaluate the performance of the robot at different operating conditions. Controller gains and scaling factors were optimised using HSDBC and the performance is evaluated in comparison to previously adopted optimisation algorithms. The HSDBC has proven its feasibility in achieving a faster convergence toward the optimal gains and resulted in a superior performance.

Keywords: differential drive robot, hybrid fuzzy controller, optimization, path tracking, unicycle robot

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Authors: Shu-Yu Hsu, Chen-Chien Hsu, Wei-Yen Wang

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Color segmentation is a basic and simple way for recognizing the visual markers in a robotic tracking system. In this paper, we propose a new method for color segmentation by incorporating differential evolution algorithm and connected component labeling to autonomously preset the HSV threshold of visual markers. To evaluate the effectiveness of the proposed algorithm, a ROBOTIS OP2 humanoid robot is used to conduct the experiment, where five most commonly used color including red, purple, blue, yellow, and green in visual markers are given for comparisons.

Keywords: color segmentation, differential evolution, connected component labeling, humanoid robot

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Authors: Maryam Mosleh, Mahmood Otadi

Abstract:

The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: Fuzzy number, parametric form of a fuzzy number, fuzzy integrodifferential equation, homotopy analysis method

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Authors: Nur Azzammudin Rahmat, Ismail Musirin, Ahmad Farid Abidin

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Economic load dispatch is performed by the utilities in order to determine the best generation level at the most feasible operating cost. In order to guarantee satisfying energy delivery to the consumer, a precise calculation of generation level is required. In order to achieve accurate and practical solution, several considerations such as prohibited operating zones, valve-point effect and ramp-rate limit need to be taken into account. However, these considerations cause the optimization to become complex and difficult to solve. This research focuses on the valve-point effect that causes ripple in the fuel-cost curve. This paper also proposes Differential Evolution Immunized Ant Colony Optimization (DEIANT) in solving economic load dispatch problem with valve-point effect. Comparative studies involving DEIANT, EP and ACO are conducted on IEEE 30-Bus RTS for performance assessments. Results indicate that DEIANT is superior to the other compared methods in terms of calculating lower operating cost and power loss.

Keywords: ant colony optimization (ACO), differential evolution (DE), differential evolution immunized ant colony optimization (DEIANT), economic load dispatch (ELD)

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Authors: Ammara Mehmood, Aneela Zameer, Muhammad Asif Zahoor Raja, Muhammad Faisal Fateh

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In this work, the strength of bio-inspired computational intelligence based technique is exploited for parameter estimation for the periodic signals using Continuous Differential Evolution (CDE) by defining an error function in the mean square sense. Multidimensional and nonlinear nature of the problem emerging in sinusoidal signal models along with noise makes it a challenging optimization task, which is dealt with robustness and effectiveness of CDE to ensure convergence and avoid trapping in local minima. In the proposed scheme of Continuous Differential Evolution based Signal Parameter Estimation (CDESPE), unknown adjustable weights of the signal system identification model are optimized utilizing CDE algorithm. The performance of CDESPE model is validated through statistics based various performance indices on a sufficiently large number of runs in terms of estimation error, mean squared error and Thiel’s inequality coefficient. Efficacy of CDESPE is examined by comparison with the actual parameters of the system, Genetic Algorithm based outcomes and from various deterministic approaches at different signal-to-noise ratio (SNR) levels.

Keywords: parameter estimation, bio-inspired computing, continuous differential evolution (CDE), periodic signals

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Authors: Mamidi Ramakrishna Rao

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Doubly-fed induction generators (DFIG) due to their advantages like speed variation and four-quadrant operation, find its application in wind turbines. DFIG besides supplying power to the grid has to support reactive power (kvar) under grid voltage variations, should contribute minimum fault current during faults, have high efficiency, minimum weight, adequate rotor protection during crow-bar-operation from +20% to -20% of rated speed.  To achieve the optimum performance, a good electromagnetic design of DFIG is required. In this paper, a simple and heuristic global optimization – Differential Evolution has been used. Variables considered are lamination details such as slot dimensions, stack diameters, air gap length, and generator stator and rotor stack length. Two operating conditions have been considered - voltage and speed variations. Constraints included were reactive power supplied to the grid and limiting fault current and torque. The optimization has been executed separately for three objective functions - maximum efficiency, weight reduction, and grid fault stator currents. Subsequent calculations led to the conclusion that designs determined through differential evolution help in determining an optimum electrical design for each objective function.

Keywords: design optimization, performance, DFIG, differential evolution

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Authors: Muhammad Bilal Ameen, M. Zubair Akbar Qureshi

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The current investigation of two-dimensional hybrid nanofluid flows with two coaxial parallel disks has been presented. Consider the hybrid nanofluid has been taken as steady-state. Consider the coaxial disks that have been porous. Consider the heat equation to examine joule heating and viscous dissipation effects. Nonlinear partial differential equations have been solved numerically. For shear stress and heat transfer, results are tabulated. Hybrid nanoparticles and Eckert numbers are increasing for heat transfer. Entropy generation is expanded with radiation parameters Eckert, Reynold, Prandtl, and Peclet numbers. A set of ordinary differential equations is obtained to utilize the capable transformation variables. The numerical solution of the continuity, momentum, energy, and entropy generation equations is obtaining using the command bvp4c of Matlab as a solver. To explore the impact of main parameters like suction/infusion, Prandtl, Reynold, Eckert, Peclet number, and volume fraction parameters, various graphs have been plotted and examined. It is concluded that a convectional nanofluid is highly compared by entropy generation with the boundary layer of hybrid nanofluid.

Keywords: entropy generation, hybrid nano fluid, heat transfer, porous disks

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Authors: A. M. Sagir

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This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: block method, hybrid, linear multistep, self-starting, third order ordinary differential equations

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Authors: F. J. Adeyeye, D. Eni, K. M. Okedoye

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In this paper we present a Hybrid of Adomian decomposition method (ADM). This is the substitution of a One-step method of Taylor’s series approximation of orders I and II, into the nonlinear part of Adomian decomposition method resulting in a convergent series scheme. This scheme is applied to solve some Logistic problems represented as Abelian differential equation and the results are compared with the actual solution and Runge-kutta of order IV in order to ascertain the accuracy and efficiency of the scheme. The findings shows that the scheme is efficient enough to solve logistic problems considered in this paper.

Keywords: Adomian decomposition method, nonlinear part, one-step method, Taylor series approximation, hybrid of Adomian polynomial, logistic problem, Malthusian parameter, Verhulst Model

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Authors: Alaa Sheta

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Economic Load Dispatch (ELD) is one of the vital optimization problems in power system planning. Solving the ELD problems mean finding the best mixture of power unit outputs of all members of the power system network such that the total fuel cost is minimized while sustaining operation requirements limits satisfied across the entire dispatch phases. Many optimization techniques were proposed to solve this problem. A famous one is the Quadratic Programming (QP). QP is a very simple and fast method but it still suffer many problem as gradient methods that might trapped at local minimum solutions and cannot handle complex nonlinear functions. Numbers of metaheuristic algorithms were used to solve this problem such as Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO). In this paper, another meta-heuristic search algorithm named Differential Evolution (DE) is used to solve the ELD problem in power systems planning. The practicality of the proposed DE based algorithm is verified for three and six power generator system test cases. The gained results are compared to existing results based on QP, GAs and PSO. The developed results show that differential evolution is superior in obtaining a combination of power loads that fulfill the problem constraints and minimize the total fuel cost. DE found to be fast in converging to the optimal power generation loads and capable of handling the non-linearity of ELD problem. The proposed DE solution is able to minimize the cost of generated power, minimize the total power loss in the transmission and maximize the reliability of the power provided to the customers.

Keywords: economic load dispatch, power systems, optimization, differential evolution

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Authors: K. P. Mredula, D. C. Vakaskar

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The article traces developments and evolution of various algorithms developed for solving partial differential equations using the significant combination of wavelet with few already explored solution procedures. The approach depicts a study over a decade of traces and remarks on the modifications in implementing multi-resolution of wavelet, finite difference approach, finite element method and finite volume in dealing with a variety of partial differential equations in the areas like plasma physics, astrophysics, shallow water models, modified Burger equations used in optical fibers, biology, fluid dynamics, chemical kinetics etc.

Keywords: multi-resolution, Haar Wavelet, partial differential equation, numerical methods

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Authors: Eugene Stepanov, Arkadi Ponossov

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Many mathematical models used in biological and other applications are ill-posed. The reason for that is the nature of differential equations, where the nonlinearities are assumed to be step functions, which is done to simplify the analysis. Prominent examples are switched systems arising from gene regulatory networks and neural field equations. This simplification leads, however, to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid feedback controls to regularize the problem. Roughly speaking, one attaches a finite state control (‘automaton’), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. This ‘hybridization’ is shown to regularize the original switched system and gives rise to efficient hybrid numerical schemes. Several examples are provided in the presentation, which supports the suggested analysis. The method can be of interest in other applied fields, where differential equations contain step-like nonlinearities.

Keywords: hybrid feedback control, ill-posed problems, singular perturbation analysis, step-like nonlinearities

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Authors: Behzad Ali Khan, M. Zubair Akbar Qureshi

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The article analyzes the Darcy Forchheimer 2D Hybrid ferrofluid. The flow of a Hybrid ferrofluid is made due to an unsteady porous channel. The classical liquid water is treated as a based liquid. The flow in the permeable region is characterized by the Darcy-Forchheimer relation. Heat transfer phenomena are studied during the flow. The transformation of a partial differential set of equations into a strong ordinary differential frame is formed through appropriate variables. The numerical Shooting Method is executed for solving the simplified set of equations. In addition, a numerical analysis (ND-Solve) is utilized for the convergence of the applied technique. The influence of some flow model quantities like Pr (Prandtle number), r (porous medium parameter), F (Darcy-porous medium parameter), Re (Reynolds number), Pe (Peclet number) on velocity and temperature field are scrutinized and studied through sketches. Certain physical factors like f ''(η) (skin friction coefficient) and θ^'(η) (rate of heat transfer) are first derived and then presented through tables.

Keywords: darcy forcheimer, hybrid ferro fluid, porous medium, porous channel

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Authors: Eugene Stepanov, Arcady Ponosov

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To model gene regulatory networks one uses ordinary differential equations with switching nonlinearities, where the initial value problem is known to be well-posed if the trajectories cross the discontinuities transversally. Otherwise, the initial value problem is usually ill-posed, which lead to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid dynamical systems, rather than switched ones, to regularize the problem. 'Hybridization' of the switched system means that one attaches a dynamic discrete component ('automaton'), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness of the initial value problem making it well-posed. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. Several examples are provided in the presentation, which support the suggested analysis. The method can also be of interest in other applied fields, where differential equations contain switchings, e.g. in neural field models.

Keywords: hybrid dynamical systems, ill-posed problems, singular perturbation analysis, switching nonlinearities

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Authors: A. Azizi, M. Toubane, L. Chetibi

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Differential scanning calorimetry (DSC) is a widely used technique for the study of phase transformations, particularly in the study of precipitation. The kinetic of the precipitation and dissolution is always related to the concept of activation energy Ea. The determination of the activation energy gives important information about the kinetic of the precipitation reaction. In this work, we were interested in the study of the isothermal and non-isothermal treatments on the decomposition of the supersaturated solid solution in the alloy AZ91 (Mg-9 Al-Zn 1-0.2 Mn. mass fraction %), using Differential Calorimetric method. Through this method, the samples were heat treated up to 425° C, using different rates. To calculate the apparent activation energies associated with the formation of precipitated phases, we used different isoconversional methods. This study was supported by other analysis: X-ray diffraction and microhardness measurements.

Keywords: calorimetric, activation energy, AZ91 alloys, microstructural evolution

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Authors: Ibtisam Masmali, Edwin Beggs

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In this paper, we take example of differential calculi, on the finite group A4. Then, we apply methods of non-commutative of non-commutative differential geometry to this example, and see how similar the results are to those of classical differential geometry.

Keywords: differential calculi, finite group A4, Christoffel symbols, covariant derivative, torsion compatible

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Authors: Tahseen Saad, Halim Ceylan, Jonathan Weaver, Osman Nuri Çelik, Onur Gungor Sahin

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A new concept of uniform delay offset dependent mathematical optimization problem is derived as the main objective for this study using a differential evolution algorithm. To control the coordination problem, which depends on offset selection and to estimate uniform delay based on the offset choice in a traffic signal network. The assumption is the periodic sinusoidal function for arrival and departure patterns. The cycle time is optimized at the entry links and the optimized value is used in the non-entry links as a common cycle time. The offset optimization algorithm is used to calculate the uniform delay at each link. The results are illustrated by using a case study and are compared with the canonical uniform delay model derived by Webster and the highway capacity manual’s model. The findings show new model minimizes the total uniform delay to almost half compared to conventional models. The mathematical objective function is robust. The algorithm convergence time is fast.

Keywords: area traffic control, traffic flow, differential evolution, sinusoidal periodic function, uniform delay, offset variable

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Authors: Y. A. Yahaya, Ahmad Tijjani Asabe

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This paper focuses on the formulation of 3-step hybrid Adams type method for the solution of first order differential equation (ODE). The methods which was derived on both grid and off grid points using multistep collocation schemes and also evaluated at some points to produced Block Adams type method and Adams moulton method respectively. The method with the highest order was selected to serve as the corrector. The convergence was valid and efficient. The numerical experiments were carried out and reveal that hybrid Adams type methods performed better than the conventional Adams moulton method.

Keywords: adam-moulton type (amt), corrector method, off-grid, block method, convergence analysis

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Authors: Sai Sankalp Vemavarapu

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This paper discusses the application of machine learning in the field of transportation engineering for predicting engineering properties of pavement more accurately and efficiently. Predicting the elastic properties aid us in assessing the current road conditions and taking appropriate measures to avoid any inconvenience to commuters. This improves the longevity and sustainability of the pavement layer while reducing its overall life-cycle cost. As an example, we have implemented differential evolution (DE) in the back-calculation of the elastic modulus of multi-layered pavement. The proposed DE global optimization back-calculation approach is integrated with a forward response model. This approach treats back-calculation as a global optimization problem where the cost function to be minimized is defined as the root mean square error in measured and computed deflections. The optimal solution which is elastic modulus, in this case, is searched for in the solution space by the DE algorithm. The best DE parameter combinations and the most optimum value is predicted so that the results are reproducible whenever the need arises. The algorithm’s performance in varied scenarios was analyzed by changing the input parameters. The prediction was well within the permissible error, establishing the supremacy of DE.

Keywords: cost function, differential evolution, falling weight deflectometer, genetic algorithm, global optimization, metaheuristic algorithm, multilayered pavement, pavement condition assessment, pavement layer moduli back calculation

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Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili

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As all experts know most of engineering system behavior in practical are nonlinear process (especially heat, fluid and mass, etc.) and analytical solving (no numeric) these problems are difficult, complex and sometimes impossible like (fluids and gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure a innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will be emerged after comparing the achieved solutions by Numerical method (Runge-Kutte 4th) and so compare to other methods such as HPM, ADM,… and exact solutions. Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations(ODE and PDE). In this paper, we investigate and solve 4 types of the nonlinear differential equation with AGM method : 1-Heat and fluid, 2-Unsteady state of nonlinear partial differential, 3-Coupled nonlinear partial differential in wave equation, and 4-Nonlinear integro-differential equation.

Keywords: new method AGM, sets of coupled nonlinear equations at engineering field, waves equations, integro-differential, fluid and thermal

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Authors: Ladan Maijama’a, Jibril D. Jiya, Ejike C. Anene

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This paper presents Differential Evolution Algorithm (DEA) based Variable Structure Position Control (VSPC) of Laboratory DC servomotor (LDCSM). DEA is employed for the optimal tuning of Variable Structure Control (VSC) parameters for position control of a DC servomotor. The VSC combines the techniques of Sliding Mode Control (SMC) that gives the advantages of small overshoot, improved step response characteristics, faster dynamic response and adaptability to plant parameter variations, suppressed influences of disturbances and uncertainties in system behavior. The results of the simulation responses of the VSC parameters adjustment by DEA were performed in Matlab Version 2010a platform and yield better dynamic performance compared with the untuned VSC designed.

Keywords: differential evolution algorithm, laboratory DC servomotor, sliding mode control, variable structure control

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Authors: M. Caramihai, Irina Severin

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This paper deals with the design of an intelligent control structure for a bioprocess of Hansenula polymorpha yeast cultivation. The objective of the process control is to produce biomass in a desired physiological state. The work demonstrates that the designed Hybrid Control Techniques (HCT) are able to recognize specific evolution bioprocess trajectories using neural networks trained specifically for this purpose, in order to estimate the model parameters and to adjust the overall bioprocess evolution through an expert system and a fuzzy structure. The design of the control algorithm as well as its tuning through realistic simulations is presented. Taking into consideration the synergism of different paradigms like fuzzy logic, neural network, and symbolic artificial intelligence (AI), in this paper we present a real and fulfilled intelligent control architecture with application in bioprocess control.

Keywords: bioprocess, intelligent control, neural nets, fuzzy structure, hybrid techniques

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Authors: Abdulbaset Saad, Adel Younis, Zuomin Dong

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For design optimization with high-dimensional expensive problems, an effective and efficient optimization methodology is desired. This work proposes a series of modification to the Differential Evolution (DE) algorithm for solving computation Intensive Black-Box Problems. The proposed methodology is called Radial Basis Meta-Model Algorithm Assisted Differential Evolutionary (RBF-DE), which is a global optimization algorithm based on the meta-modeling techniques. A meta-modeling assisted DE is proposed to solve computationally expensive optimization problems. The Radial Basis Function (RBF) model is used as a surrogate model to approximate the expensive objective function, while DE employs a mechanism to dynamically select the best performing combination of parameters such as differential rate, cross over probability, and population size. The proposed algorithm is tested on benchmark functions and real life practical applications and problems. The test results demonstrate that the proposed algorithm is promising and performs well compared to other optimization algorithms. The proposed algorithm is capable of converging to acceptable and good solutions in terms of accuracy, number of evaluations, and time needed to converge.

Keywords: differential evolution, engineering design, expensive computations, meta-modeling, radial basis function, optimization

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