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The concept of particle swarms, although initially introduced for simulating human social behaviors, has become very popular these days as an efficient means for intelligent search and optimization. The particle swarm optimization (PSO), as it is called now, does not require any gradient information of the function to be optimized, uses only primitive mathematical operators and is conceptually very simple. This paper investigates a novel approach to the designing of two-dimensional zero phase infinite impulse response (IIR) digital filters using the PSO algorithm. The design task is reformulated as a constrained minimization problem and is solved by a modified PSO algorithm. Numerical results are presented. The paper also demonstrates the superiority of the proposed design method by comparing it with two recently published filter design methods and two other state of the art optimization techniques.

This paper suggests chaotic fast convergence evolutionary programming (CFCEP) for solving multi-region dynamic economic dispatch (MRDED) problem, multi-region economic dispatch (MRED) problem and economic dispatch (ED) problem. MRDED problem is based on multi-reservoir cascaded hydro plant with time delay, thermal plants with nonsmooth fuel cost function, wind and solar power units with uncertainty and pumped hydro energy storage. MRED problem deals with tie line constraints, transmission losses, valve point effect and proscribed workable area of thermal generators. ED problem deals with valve point effect, proscribed workable area and ramp rate limits of thermal generators. In the recommended technique, chaotic sequences have been pertained for acquiring the dynamic scaling factor setting in fast convergence evolutionary programming (FCEP). The efficacy of the proposed technique has been verified on convoluted three-area system for MRDED problem, four-area system for MRED problem and 140-unit Korean system for ED problem. Test results acquired from the suggested CFCEP technique have been fit to that acquired from FCEP, differential evolution (DE) and particle swarm optimization (PSO). It has been observed from the comparison that the recommended CFCEP technique has the capability to bestow with better-quality solution.

Based on Cuckoo Search (CS) and Differential Evolution (DE), a novel hybrid optimization algorithm, called CSDE, is proposed in this paper to solve constrained engineering problems. CS has strong ability on global search and less control parameters, but easy to suffer from premature convergence and lower the density of population. DE specializes in local search and good robustness, however, its convergence rate is too late to find the satisfied solution. Furthermore, these two algorithms are both proved to be especially suitable for engineering problems. This work divides population into two subgroups and adopts CS and DE for these two subgroups independently. By division, these two subgroups can exchange useful information and these two algorithms can utilize each other’s advantages to complement their shortcoming, thus avoid premature convergence, balance the quality of solution and the computation consumption, and find satisfactory global optima. Due to the tremendous design variables and constrained conditions of engineering problems, single optimizer failed to meet the requirement of precision, so hybrid optimization algorithms (such like CSDE) is the most promising mean to complete this job. Simulation results reveal that CSDE has more ability to find promising results than other 12 algorithms (including traditional algorithms and state-of-the-art algorithm) on 30 unconstrained benchmark functions, 10 constrained benchmark functions and 6 constrained engineering problems.

Over the last few decades, a considerable number of evolutionary algorithms (EAs) have been proposed for solving constrained optimization problems (COPs). As for most of these problems, the optimal solution exists on the boundary of the feasible space, we aim to focus the search process around the boundary. In this paper a new concept, called reduced search space (R2S), is introduced. In the process, we first identify active constraints, based on the current solutions, and then define R2S around those constraint’s boundaries. However, the search may be conducted either in the entire R2S or in some portions of it. To judge the impact of this concept, we have incorporated it with a number of state-of-the-art algorithms, and we have comprehensively tested it on three sets of benchmark test functions, namely, 24 test functions taken from IEEE CEC2006, 18 test functions with 10 D and 30 D taken from IEEE CEC2010 and 10 test functions taken from IEEE CEC2011. The results show that our proposed mechanism significantly improves the performances of state-of-the-art algorithms.

Maritime inventory routing problem is addressed in this paper to satisfy the demand at different ports during the planning horizon. It explores the possibilities of integrating slow steaming policy as mentioned in Kontovas et al. (2011) and Norstad et al. (2011) within ship routing. A mixed integer non-linear programming model is presented considering various scheduling and routing constraints, loading/unloading constraints and vessel capacity constraints. Non-linear equation between fuel consumption and vessel speed has been incorporated to capture the sustainability aspects. Several time window constraints are inculcated in the mathematical model to enhance the service level at each port. Penalty costs are incurred if the ship arrives early before the starting of the time window or if it finishes its operation after the ending of the time window. Costs associated with the violation of time window helps in maintaining a proper port discipline. Now, owing to the inherent complexity of the aforementioned problem, an effective search heuristics named Particle Swarm Optimization for Composite Particle (PSO-CP) is employed. Particle Swarm Optimization Differential Evolution (PSO-DE), Basic PSO and Genetic Algorithm (GA) are used to validate the result obtained from PSO-CP. Computational results provided for different problem instances shows the superiority of PSO-CP over the other algorithms in terms of the solution obtained.

Metaheuristic algorithms are typically used for optimizing a function f : A → R , where A is a subset of R N . Nevertheless, many real-life problems require A to be a set of functions which makes f a functional. In this paper, we present a methodology to address the optimization of functionals by using the evolutionary algorithm known as Differential Evolution. Unlike traditional techniques where continuity and differentiability assumptions are required to solve some associated differential equations—like calculus of variations, Pontryagin’s principle or dynamic programming, the optimization is carried out directly on the functional without the need of any of the assumptions mentioned before. Lagrangians involving derivatives are considered, these derivatives are computed implementing Automatic Differentiation with dual numbers. To the best of our knowledge, this is the first time that a metaheuristic optimization approach has been applied to directly optimize a broad variety of functionals. The effectiveness of our methodology is validated by solving two problems. The first problem is related to the implementation of quarantine and isolation in SARS epidemics and the second validation problem deals with the well-known brachistochrone curve problem. The results of both validation problems are in outstanding agreement with those obtained with the application of traditional techniques, specifically with the Forward–Backward-Sweep method in the first problem, and with the calculus of variations for the latter problem. We also found that interpolation may be employed to solve the large scale global optimization problems arisen in the optimization of functionals.

Population-based optimization algorithms have been successfully applied to hydrological forecasting recently owing to their powerful ability of global optimization. This paper investigates three algorithms, i.e. differential evolution (DE), artificial bee colony (ABC) and ant colony optimization (ACO), to determine the optimal one for forecasting downstream river flow. A hybrid neural network (HNN) model, which incorporates fuzzy pattern-recognition and a continuity equation into the artificial neural network, is proposed to forecast downstream river flow based on upstream river flows and areal precipitation. The optimization algorithm is employed to determine the premise parameters of the HNN model. Daily data from the Altamaha River basin of Georgia is applied in the forecasting analysis. Discussions on the forecasting performances, convergence speed and stability of various algorithms are presented. For completeness' sake, particle swarm optimization (PSO) is included as a benchmark case for the comparison of forecasting performances. Results show that the DE algorithm attains the best performance in generalization and forecasting. The forecasting accuracy of the DE algorithm is comparable to that of the PSO, and yet presents weak superiority over the ABC and ACO. The Diebold-Mariano (DM) test indicates that each pair of algorithms has no difference under the null hypothesis of equal forecasting accuracy. The DE and ACO algorithms are both favorable for searching parameters of the HNN model, including the recession coefficient and initial storage. Further analysis reveals the drawback of slow convergence and time-consumption of the ABC algorithm. The three algorithms present stability and reliability with respect to their control parameters on the whole. It can be concluded that the DE and ACO algorithms are considerably more adaptive in optimizing the forecasting problem for the HNN model. Comparison of performances of population-based optimization algorithms in forecasting downstream river flow.Differential evolution (DE), artificial bee colony and ant colony optimization (ACO).Particle swarm optimization is included as a benchmark comparison for forecasting performances.Hybrid neural network (HNN) model incorporating fuzzy pattern-recognition and continuity equation.DE and ACO algorithms are considerably more adaptive in optimizing the forecasting problem for the HNN model.

This paper proposes the design of non-fragile multivariable PI controller for industrial Multi Input Multi Output (MIMO) processes using Diversity Controlled Self-Adaptive Differential Evolution with Local Search (DCSaDE-LS) algorithm. The proposed non-fragile multivariable PI controller design is formulated as a single objective optimization problem with the objective of robustness subject to non-fragileness constraint. Monte Carlo Simulation is used to evaluate the non-fragileness constraint against stochastic uncertainty of controller parameters. Wood and Berry Distillation process and a real time Level-Temperature reactor process model with simple de-coupler are considered as a test systems. For constraint handling, Constraint Domination Principle (CDP) and Penalty Parameter Less (PPL) methods are incorporated in DCSaDE-LS, seperately. Also, the performance of DCSaDE-LS is compared with the recent adaptive DE algorithms namely Ensemble of mutation strategies and control parameters in Differential Evolution (EPSDE), Composite Differential Evolution (CoDE) and SaDE. The robustness and non-fragileness of the controller is analyzed under +40% and -40% variations in nominal process and controller parameters. The results demonstrated that the DCSaDE-LS designed non-fragile multivariable PI controller has good time domain performance, better robustness and non-fragileness than the reported multivariable PI controllers namely Maghade-PI, IMC-PI and NDT-PI.

As the performance of Linear Quadratic Regulator (LQR) controllers greatly depends on its weighting matrices, i.e. Q and R, designing these two matrices is one of the most important components in the LQR problem which is a tedious and challenging work in the applications of LQR. Hence, a novel LQR approach based on the Pareto-based Multi-objective Binary Probability Optimization Algorithm (MBPOA) is proposed in this paper, in which MBPOA is utilized to search for the optimal weighting matrices to relieve the effort of parameter settings and improve the control performance according to the pre-defined objective functions. By combining LQR with MBPOA, the optimal controllers can be obtained easily and effortless. Moreover, the control performance can be adjusted further conveniently to meet the requirements of applications as a set of Pareto-optimal LQR controllers is offered. The simulation and experiment results on the double-parallel inverted pendulum system demonstrate the effectiveness and efficiency of the developed MBPOA-based LQR method. Considering the characteristics such as robustness, the optimal dynamic performance and easy implementation without prior knowledge, the MBPOA-based LQR is a promising control approach for engineering applications.

Parameter optimization of proton exchange membrane fuel cell (PEMFC) model has received considerable attention recently. In order to estimate the unknown parameters of PEMFC model faster and obtain more accurate solutions, in this paper, an improved multi-strategy adaptive differential evolution (DE) is presented for the parameter optimization problems of PEMFC model. The approach is referred to as rank-MADE, for short. In rank-MADE, the multiple mutation strategies of DE are adaptively selected to avoid choosing a suitable strategy for a specific problem by trial-and-error method. Furthermore, the ranking-based vector selection technique is employed in different mutation strategies to accelerate the process of parameter optimization of PEMFC model. In order to verify the performance of rank-MADE, it is applied to estimate the parameters of the Ballard Mark V FC, the SR-12 Modular PEM Generator, the BCS 500-W stack, the Temasek FC, and the WNS-FC model. In addition, rank-MADE is compared with other advanced DE variants and other evolutionary algorithms (EAs). Experimental results show that rank-MADE is able to provide higher quality of solutions, faster convergence speed, and higher success rate compared with other DE variants. Additionally, the V-I characteristics obtained by rank-MADE agree well with the experimental data in all cases. Therefore, rank-MADE can be an effective alternative in the field of other complex parameter optimization problems of fuel cell models.

This paper presents a new approach for solving short-term hydrothermal scheduling (HTS) using an integrated algorithm based on teaching learning based optimization (TLBO) and oppositional based learning (OBL). The practical hydrothermal system is highly complex and possesses nonlinear relationship of the problem variables, cascading nature of hydro reservoirs, water transport delay and scheduling time linkage that make the problem of optimization difficult using standard optimization methods. To overcome these problems, the proposed quasi-oppositional teaching learning based optimization (QOTLBO) is employed. To show its efficiency and robustness, the proposed QOTLBO algorithm is applied on two test systems. Numerical results of QOTLBO are compared with those obtained by two phase neural network, augmented Lagrange method, particle swarm optimization (PSO), improved self-adaptive PSO (ISAPSO), improved PSO (IPSO), differential evolution (DE), modified DE (MDE), fuzzy based evolutionary programming (Fuzzy EP), clonal selection algorithm (CSA) and TLBO approaches. The simulation results reveal that the proposed algorithm appears to be the best in terms of convergence speed, solution time and minimum cost when compared with other established methods. This method is considered to be a promising alternative approach for solving the short-term HTS problems in practical power system.

Wavelength-Division Multiplexing (WDM) in optical networks has revolutionized the Telecommunication field. This technology is able to exploit the enormous bandwidth capability of this kind of networks, allowing communication between end users via all-optical WDM channels (lightpath). Given a set of demands, the problem of setting up lightpaths by routing and assigning a wavelength to each connection is known as Routing and Wavelength Assignment (RWA) problem. There are two types of connection demands: static (demands are given in advance) and dynamic (demands are given in real-time). In this paper we present two different Multiobjective Evolutionary Algorithms (MOEA) with the aim of solving the static RWA problem. The first one is a population-based algorithm, the Differential Evolution (DE), but incorporating the Pareto Tournament concept (DEPT). The second one is a multiobjective version of the Variable Neighborhood Search (VNS), MO-VNS. In order to prove the goodness of our metaheuristics, we have compared them with the standard Fast Non-Dominated Sorting Genetic Algorithm (NSGA-II), typical heuristics in the Telecommunication field, and different varieties of Multiobjective Ant Colony Optimization Algorithms. On the whole, we conclude that our approaches have obtained very promising results.

Motion estimation is one of the major problems in developing video coding applications. Among all motion estimation approaches, block-matching (BM) algorithms are the most popular methods due to their effectiveness and simplicity for both software and hardware implementations. A BM approach assumes that the movement of pixels within a defined region of the current frame (macro block, MB) can be modeled as a translation of pixels contained in the previous frame. In this procedure, the motion vector is obtained by minimizing the sum of absolute differences (SAD) produced by the MB of the current frame over a determined search window from the previous frame. The SAD evaluation is computationally expensive and represents the most consuming operation in the BM process. The most straightforward BM method is the full search algorithm (FSA), which finds the most accurate motion vector, exhaustively calculating the SAD values for all the elements of the search window. Over this decade, several fast BM algorithms have been proposed to reduce the number of SAD operations by calculating only a fixed subset of search locations at the cost of poor accuracy. In this paper, a new algorithm based on differential evolution (DE) is proposed to reduce the number of search locations in the BM process. To avoid computing several search locations, the algorithm estimates the SAD values (fitness) for some locations using the SAD values of previously calculated neighboring positions. As the proposed algorithm does not consider any fixed search pattern or any other different assumption, a high probability for finding the true minimum (accurate motion vector) is expected. In comparison with other fast BM algorithms, the proposed method deploys more accurate motion vectors, yet delivering competitive time rates.

In this paper, a comparison of evolutionary-based optimization techniques for structural design optimization problems is presented. Furthermore, a hybrid optimization technique based on differential evolution algorithm is introduced for structural design optimization problems. In order to evaluate the proposed optimization approach a welded beam design problem taken from the literature is solved. The proposed approach is applied to a welded beam design problem and the optimal design of a vehicle component to illustrate how the present approach can be applied for solving structural design optimization problems. A comparative study of six population-based optimization algorithms for optimal design of the structures is presented. The volume reduction of the vehicle component is 28.4% using the proposed hybrid approach. The results show that the proposed approach gives better solutions compared to genetic algorithm, particle swarm, immune algorithm, artificial bee colony algorithm and differential evolution algorithm that are representative of the state-of-the-art in the evolutionary optimization literature.

The search capabilities of the Differential Evolution (DE) algorithm - a global optimization technique - make it suitable for finding both the architecture and the best internal parameters of a neural network, usually determined by the training phase. In this paper, two variants of the DE algorithm (classical DE and self-adaptive mechanism) were used to obtain the best neural networks in two distinct cases: for prediction and classification problems. Oxygen mass transfer in stirred bioreactors is modeled with neural networks developed with the DE algorithm, based on the consideration that the oxygen constitutes one of the decisive factors of cultivated microorganism growth and can play an important role in the scale-up and economy of aerobic biosynthesis systems. The coefficient of mass transfer oxygen is related to the viscosity, superficial speed of air, specific power, and oxygen-vector volumetric fraction (being predicted as function of these parameters) using stacked neural networks. On the other hand, simple neural networks are designed with DE in order to classify the values of the mass transfer coefficient oxygen into different classes. Satisfactory results are obtained in both cases, proving that the neural network based modeling is an appropriate technique and the DE algorithm is able to lead to the near-optimal neural network topology.

This paper presents a constrained Self-adaptive Differential Evolution (SaDE) algorithm for the design of robust optimal fixed structure controllers with uncertainties and disturbance. Almost all real world optimization problems have constraints which should be satisfied along with the best optimal solution for the problem. In evolutionary algorithms (EAs) the presence of constraints reduces the feasible region and complicates the search process. Therefore, a suitable method to handle the constraints must also be executed. In the SaDE algorithm, four mutation strategies and the control parameter CR are self-adapted. Self-adaptive Penalty (SP) method is introduced into the SaDE algorithm for constraint handling. The performance of SaDE algorithm is demonstrated on the design of robust optimal fixed structure controller of three systems, namely the linearized magnetic levitation system, F-8 aircraft linearized model and a SISO plant. For the comparison purpose, reported results of constrained PSO algorithm and five DE algorithms with different strategies and parameter values are taken into account. Statistical performance in 20 independent runs is considered to compare the performance of algorithms. From the obtained results, it is observed that SaDE algorithm is able to self-adapt the mutation strategy and the crossover rate and hence performs better than the other variants of DE and the constrained PSO algorithm. Better performance of SaDE is achieved by sustained maintenance of diversity throughout the evolutionary process thus producing better individuals consistently. This also aids the algorithm to escape from local optima thereby avoiding premature convergence.

Parametric reconfiguration plays a key role in non-iterative concurrent design of mechatronic systems. This is because it allows the designer to select, among different competitive solutions, the most suitable without sacrificing sub-optimal characteristics. This paper presents a method based on an evolutionary algorithm to improve the parametric reconfiguration feature in the optimal design of a continuously variable transmission and a five-bar parallel robot. The approach considers a solution-diversity mechanism coupled with a memory of those sub-optimal solutions found during the process. Furthermore, a constraint-handling mechanism is added to bias the search to the feasible region of the search space. Differential Evolution is utilized as the search algorithm. The results obtained in a set of five experiments performed per each mechatronic system show the effectiveness of the proposed approach.

In this paper, an effective and reliable algorithm, termed as evolving ant direction differential evolution (EADDE) algorithm, for solving the optimal power flow problem with non-smooth and non-convex generator fuel cost characteristics is presented. In this method, suitable mutation operator for differential evolution (DE) is found by ant colony search. The genetic algorithm evolves the ant colony parameters and the Newton-Raphson method solves the power flow problem. The proposed algorithm has been examined on the standard IEEE 30-bus and IEEE 57-bus systems with three different objective functions. Different cases were considered to investigate the robustness of the proposed method in finding the global solution. The EADDE provides better results compared to classical DE and other methods recently reported in the literature as demonstrated by simulation results.

The dynamic economic dispatch (DED), with the consideration of valve-point effects, is a complicated non-linear constrained optimization problem with non-smooth and non-convex characteristics. In this paper, three chaotic differential evolution (CDE) methods are proposed based on the Tent equation to solve DED problem with valve-point effects. In the proposed methods, chaotic sequences are applied to obtain the dynamic parameter settings in DE. Meanwhile, a chaotic local search (CLS) operation for solving DED problem is designed to help DE avoiding premature convergence effectively. Finally, in order to handle the complicated constraints with efficiency, new heuristic constraints handling methods and feasibility based selection strategy are embedded into the proposed CDE methods. The feasibility and effectiveness of the proposed CDE methods are demonstrated for two test systems. The simulation results reveal that, compared with DE and those other methods reported in literatures recently, the proposed CDE methods are capable of obtaining better quality solutions with higher efficiency.

This paper presents a novel iterative hybrid algorithm for subcarrier and power allocation in a cognitive orthogonal frequency division multiple access (OFDMA) downlink. In the considered setup a primary base station forwards information to K distant receivers by using a single OFDM waveform, whereas a secondary base station – subject to stringent per-user rate constraints – interferes with the former by sending information from users to the same set of destinations. Power and user allocation at both base stations is jointly performed by the proposed algorithm to maximize the overall throughput of the setup while satisfying, at the same time, the imposed rate constraints. Our proposal, which stems from an hybridization of the harmony search (HS) and differential evolution (DE) algorithms along with a greedy local repair method, is shown – through computer simulations over the extended vehicular A ITU channel model – to be an effective and practical resource allocation procedure for cognitive OFDMA downlinks.

System identification is a challenging and complex optimization problem due to nonlinearity of the systems and even more in a dynamic environment. Adaptive infinite impulse response (IIR) systems are preferably used in modeling real world systems because of their reduced number of coefficients and better performance over the finite impulse response filters. Particle swarm optimization (PSO) and its other variants has been a subject of research for the past few decades for solving complex optimization problems. In this paper, PSO with quantum infusion (PSO-QI) is used in identification of benchmark IIR systems and a real world problem in power systems. PSO-QI's performance is compared with PSO and differential evolution PSO (DEPSO) algorithms. The results show that PSO-QI has better performance over these algorithms in identifying dynamical systems.

Optimal trajectory planning for robot manipulators is always a hot spot in research fields of robotics. This paper presents two new novel general methods for computing optimal motions of an industrial robot manipulator (STANFORD robot) in presence of obstacles. The problem has a multi-criterion character in which three objective functions, a maximum of 72 variables and 103 constraints are considered. The objective functions for optimal trajectory planning are minimum traveling time, minimum mechanical energy of the actuators and minimum penalty for obstacle avoidance. By far, there has been no planning algorithm designed to treat the objective functions simultaneously. When existing optimization algorithms of trajectory planning tackle the complex instances (obstacles environment), they have some notable drawbacks viz.: (1) they may fail to find the optimal path (or spend much time and memory storage to find one) and (2) they have limited capabilities when handling constraints. In order to overcome the above drawbacks, two evolutionary algorithms (Elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE) algorithm) are used for the optimization. Two methods (normalized weighting objective functions method and average fitness factor method) are combinedly used to select best optimal solution from Pareto optimal front. Two multi-objective performance measures (solution spread measure and ratio of non-dominated individuals) are used to evaluate strength of the Pareto optimal fronts. Two more multi-objective performance measures namely optimizer overhead and algorithm effort are used to find computational effort of NSGA-II and MODE algorithms. The Pareto optimal fronts and results obtained from various techniques are compared and analyzed.

This paper presents three memetic algorithms to solve the spread spectrum radar polyphase code design problem, based on Evolutionary Programming, Particle Swarm Optimization and Differential Evolution, respectively. These global search heuristics are hybridized with a gradient-based local search procedure which includes a dynamic step adaptation procedure to perform accurate and efficient local search for better solutions. We have compared the different memetic algorithms proposed in several numerical examples, and we have also demonstrated the performance of our approaches against existing approaches for this problem.

Force balancing is a very important issue in mechanism design and has only recently been introduced to the designing step of robotic mechanisms. In creating the best robot design, the statical balancing plays a vital role because it reduces the required motor power. To get a simple and more-effective control system, elimination or significant reduction of the gravity load at a powered joint is an important one. With utilization of these objectives an optimization problem is formulated. The average force on the gripper in the working area is taken as an objective function. The design variables are lengths of the links, angles between them and stiffness of springs. This paper describes the use of conventional and evolutionary optimization techniques such as Newton's method (NM), conjugate gradient method (CGM), Genetic Algorithm (GA), Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and differential evolution (DE) to solve the above problem. An industrial robot with 6-degree-of-freedom (6-DOF) (APR 20) is considered as a numerical example. The robot has a spring balancing system that has to be optimized. The existing optimization model is improved by adding two new variables. Also, a comprehensive user-friendly general-purpose software package has been developed using VC++ to obtain the optimal parameters using the proposed DE algorithm. The methods used in this article can be applied to find out solutions for a wide range of similar problems without further simplifications.

Robot system designers often face the challenge of selecting optimal parameter tolerances of a manipulator, which delivers optimal performance. This paper presents an approach to simulate the performance of manipulator and evolutionary optimization method to select optimal parameter tolerance. To determine optimal parameter tolerance, genetic algorithm, and differential evolution, optimization techniques have been used. The objective function maximizes SN Ratio, while manipulator performs a task. As differential evolution and GA are best suited for solving deterministic optimization problems, to handle performance of manipulator, a hybrid technique is proposed. The evolutionary optimization techniques are coupled with orthogonal array used in the Taguchi method to get optimal solution. The hybrid technique is illustrated by an example and concluded that it is best suited for manipulator parameter tolerance design. It is also observed that differential evolution technique converges quickly and require significantly less number of functional evaluations.