Application of Metaheuristic Algorithm for Solving Fully Fuzzy Linear Equations System

The cuckoo search (CS) algorithm, which is a new meta-heuristic optimization algorithm, is an efficient approach to solve continuous function optimization problems. Normally, the parameters of the CS are fixed constants. This may result in affecting the algorithm efficiency. To cope with this issue, we properly tune the parameters of the CS and propose an adaptive cuckoo search (ACS) algorithm to enhance the convergence rate and accuracy of the CS. Then, we validate the proposed ACS against test functions and compare its performance with those of particle swarm optimization (PSO), improved cuckoo search algorithm (ICS) and CS by simulation. The simulation results demonstrate that the ACS obtains some solutions better than those obtained by PSO, ICS and CS.

Maximum power point tracking (MPPT) control is one of the essential requirements in harnessing wind power of wind energy conversion systems (WECS). The more precise the maximum power point (MPP) is determined, the more optimal the WECS is operated. Amongst MPPT algorithms, a hill-climb search (HCS) algorithm is preferred because of its simplicity however it also has few drawbacks such as the difficulty of selecting an appropriate step size, the premature convergence phenomenon and the speed-efficiency trade-off. A cuckoo search (CS) algorithm is proposed in this paper for finding out a MPP of a WECS driven by a doubly-fed induction generator (DFIG) under various wind speeds which mostly overcomes the above disadvantages. Then, the DFIG-WECS is controlled to track the MPP. This ensures that the DFIG-WECS is always operated at MPPs regardless of various wind speeds. It is realized that the proposed CS algorithm is also a population-based algorithm inspired from the breeding behavior of cuckoos but it is quite simple, powerful and especially requires less parameters to define optimal solutions than a genetic algorithm (GA) and a particle swarm optimization (PSO) algorithm. Though numerical results, the CS algorithm shows its effectiveness in finding out MPPs in the DFIG-WECS. Furthermore, the obtained results using the CS algorithm are also compared with those using the HCS and PSO algorithms. The comparison demonstrates that the convergence value and speed of the CS algorithm are always better than those of the HCS and PSO algorithms in the MPPT application in the DFIG-WECS.

The current research attempts to offer a new method for solving fuzzy linear Volterra integral equations system. This method converts the given fuzzy system into a linear system in crisp case by using the Taylor expansion method. Now the solution of this system yields the unknown Taylor coefficients of the solution functions. The proposed method is illustrated by an example and also results are compared with the exact solution by using computer simulations.

There exists a direct need to automate the process of test suite generation to get the most optimal results as testing accounts for more than 40% of total cost. One method to solve this problem is the use of meta-heuristic algorithms which iteratively improve the test data to reach the most optimized test suites. This study focuses on the performance evaluation of six meta-heuristic algorithms namely: hill-climbing algorithm (HCA), particle swarm optimization (PSO), firefly algorithm (FA), cuckoo search algorithm (CS), bat algorithm (BA) and artificial bee colony algorithm (ABC) by using their standard implementation to optimize the path coverage and branch coverage produced by the test data. The goal of the study was to find the best-suited algorithm to narrow down the future research in the field of test automation for path coverage-based optimization approaches. Each algorithm was first implemented to automatically generate test suites based on the program under test. This was followed by the performance evaluation of each algorithm for five programs written in Java. The algorithms were compared using process metrics: average time, best time, worst time and product metrics: path coverage & objective function values of the generated test suites. Results indicated ABC as the best-suited algorithm as it gave the most optimal test suites in reasonable time. BA was found to be the fastest but produced less optimal results. FA was found to be the slowest algorithm, while CS, PSO and HCA performed in between. These results show the relative performance of the six algorithms for this scenario and may be used by the future researchers to narrow down and improve the best performing algorithms for path coverage-based optimization approaches.

The main benefits of fuzzy logic control (FLC) allow a qualitative knowledge of the desired system’s behavior to be included as IF-THEN linguistic rules for the control of dynamical systems where either an analytic model is not available or is too complex due, for instance, to the presence of nonlinear terms. The computational structure requires the definition of the FLC parameters namely, membership functions (MF) and a rule base (RB) defining the desired control policy. However, the optimization of the FLC parameters is generally carried out by means of a trial and error procedure or, more recently by using metaheuristic nature-inspired algorithms, for instance, particle swarm optimization, genetic algorithms, ant colony optimization, cuckoo search, etc. In this regard, the cuckoo search (CS) algorithm as one of the most promising and relatively recent developed nature-inspired algorithms, has been used to optimize FLC parameters in a limited variety of applications to determine the optimum FLC parameters of only the MF but not to the RB, as an extensive search in the literature has shown. In this paper, an optimization procedure based on the CS algorithm is presented to optimize all the parameters of the FLC, including the RB, and it is applied to a nonlinear magnetic levitation system. Comparative simulation results are provided to validate the features improvement of such an approach which can be extended to other FLC based control systems.

A cuckoo search algorithm with scale-free population topology

A general fuzzy linear system of equations is investigated using embedding approach. In the literature of fuzzy systems two types of linear systems are more important: 1) Fuzzy Linear Systems, 2) Fully Fuzzy Linear Systems. In both class of these systems usually the authors considered triangular type of fuzzy numbers. In this paper, we introduce a linear system of equations with trapezoidal fuzzy numbers as an extension of the fuzzy linear systems which was first introduced by Friedman et al. [6]. Conditions for the existence of a trapezoidal fuzzy solution to n×n linear system are derived and a numerical procedure for calculating the solution is illustrated with some examples.

This paper presents an optimal design of low noise amplifier (LNA) using an efficient swarm-based optimizer called firefly algorithm (FA). Many researchers have used firefly algorithm to solve various nonlinear engineering problems and reported outstanding results. In view of this, FA is implemented for the first time in this paper to optimize the parameters of LNA like gain and noise figure (NF). Two case studies have been performed which includes the minimization of NF and maximization of gain. Optimization of these two parameters has been carried out by considering each parameter as a single objective function. Penalty factor method is considered for handling the constraints. Other parameters of LNA like power consumption, linearity, and stability are also discussed for both the cases. The designed LNA has a cascode structure with inductive source degeneration topology and is implemented in UMC 0.18-μm CMOS technology using CADENCE software. LNA is designed for 5.5-GHz frequency. The performance of FA in optimizing the parameters of LNA is also compared with the performance of other similar contemporary algorithms like particle swarm optimization (PSO), human behavior PSO (HB-PSO), backtracking search algorithm, and cuckoo search algorithm (CSA). The optimized value of LNA parameter using FA and other algorithms when simulated in MATLAB environment is compared with the simulated result of CADENCE. Statistical analysis is also performed for each case study, and the results are compared with the above-mentioned optimization algorithms. Simulation results, comparative study, and statistical analysis confirm the superiority of FA over other methods in terms of its computational efficiency, consistency, and robustness.

Optimization studies in high speed turning of Ti-6Al-4V

A hybrid approach for optimal location and capacity of UPFC to improve the dynamic stability of the power system

System of simultaneous linear equations plays a vital role in mathematics, Operations Research, Statistics, Physics, Engineering and Social Sciences etc. In many applications at least some of the system's parameters and measurements are represented by fuzzy numbers rather than crisp numbers. Therefore it is imperative to develop mathematical models and numerical procedures to solve such a fuzzy linear system. The general model of a fuzzy linear system whose coefficient matrix is crisp and the right hand side column is an arbitrary fuzzy vector. In the fully fuzzy linear system all the parameters are considered to be fuzzy numbers. Since triangular fuzzy numbers is a special case of trapezoidal fuzzy numbers, hence in this paper we considered fully fuzzy linear system with trapezoidal fuzzy numbers. LU decomposition method for a crisp matrix is well known in solving linear system of equations. We discuss LU decomposition of the coefficient matrix of the fully fuzzy linear system, in which the coefficients are trapezoidal fuzzy numbers.

As a key theoretical basis of fuzzy analysis, a new representation of the two-dimension fuzzy numbers is proposed in this paper. We also present a new method for solving the fuzzy system of linear equations with the two-dimension fuzzy data based on the new representation of the two-dimension fuzzy numbers, which may translate a fuzzy system of linear equations into two real systems of linear equations, one is an n × n real system of linear equations and the other is a (2 n ) × (2 n ) real system of linear equations, where the coefficients, the right hand term and the unknown term of the (2 n ) × (2 n ) real systems are all positive real numbers. Accordingly, we compare the classical methods with the technique on the basis of the study of the two-dimensional fuzzy linear system proposed in this paper for an one-dimensional fuzzy linear system, and the results shows that they have the same solutions. Finally, the conditions of the existence of the solutions for a fuzzy system of linear equations are discussed, and the examples are given to show the efficiency and effectiveness of the method investigated in this article.

The paper reviews and introduces the state-of-the-art nature-inspired metaheuristic algorithms in optimization, including Firefly algorithm, PSO algorithms and ABC algorithm. By implementing these algorithms in Matlab, we will use worked examples to show how each algorithm works. Firefly algorithm is one of the evolutionary optimization algorithms, and is inspired by the flashing behaviour of fireflies in nature. There are many noisy non-linear mathematical optimization problems that can be effectively solved by Metaheuristic Algorithms. Mathematical optimization or programming is the study of such planning and design problems using mathematical tools. Nowadays, computer simulations become an indispensable tool for solving such optimization problems with various efficient search algorithms. Nature-inspired algorithms are among the most powerful algorithms for optimization. Firefly algorithm is one of the new metaheuristic algorithms for optimization problems. The algorithm is inspired by the flashing behaviour of fireflies. A Firefly Algorithm (FA) is a recent nature inspired optimization algorithm, which simulates the flash pattern and characteristics of fireflies. It is a powerful swarm intelligence algorithm inspired by the flash phenomenon of the fireflies. In this context, three types of meta-heuristics called Artificial bee Colony algorithm, Particle Swarm Optimization (PSO) and Firefly algorithms were devised to find optimal solutions of noisy non-linear continuous mathematical models. A series of computational experiments using each algorithm were conducted. The stimulation result of this experiment were analyzed and compared to the best solutions found so The Firefly algorithm in each noisy non linear optimization function seems to perform better and efficient.

A novel performance criterion approach to optimum design of PID controller using cuckoo search algorithm for AVR system

One of the most used artificial intelligence techniques for maximum power point tracking is artificial neural networks. In order to achieve successful results in maximum power point tracking, the training process of artificial neural networks is important. Metaheuristic algorithms are used extensively in the literature for neural network training. An important group of metaheuristic algorithms is swarm-intelligent-based optimization algorithms. In this study, feed-forward neural network training is carried out for maximum power point tracking by using 13 swarm-intelligent-based optimization algorithms. These algorithms are artificial bee colony, butterfly optimization, cuckoo search, chicken swarm optimization, dragonfly algorithm, firefly algorithm, grasshopper optimization algorithm, krill herd algorithm, particle swarm optimization, salp swarm algorithm, selfish herd optimizer, tunicate swarm algorithm, and tuna swarm optimization. Mean squared error is used as the error metric, and the performances of the algorithms in different network structures are evaluated. Considering the results, a success ranking score is obtained for each algorithm. The three most successful algorithms in both training and testing processes are the firefly algorithm, selfish herd optimizer, and grasshopper optimization algorithm, respectively. The training error values obtained with these algorithms are 4.5 × 10−4, 1.6 × 10−3, and 2.3 × 10−3, respectively. The test error values are 4.6 × 10−4, 1.6 × 10−3, and 2.4 × 10−3, respectively. With these algorithms, effective results have been achieved in a low number of evaluations. In addition to these three algorithms, other algorithms have also achieved mostly acceptable results. This shows that the related algorithms are generally successful ANFIS training algorithms for maximum power point tracking.