Nonconvex economic load dispatch using an efficient real-coded genetic algorithm

An efficient optimisation procedure based on real-coded genetic algorithm (RCGA) is proposed for the solution of economic load dispatch (ELD) problem with continuous and nonsmooth/nonconvex cost function and with various constraints being considered. The effectiveness of the proposed algorithm has been demonstrated on different systems considering the transmission losses and valve point loading effect in thermal units. The proposed algorithm is equipped with an effective constraint handling technique, which eliminates the need for penalty parameters. For the purpose of comparison, the same problem has also been solved using binary-coded genetic algorithm (BCGA) and three other popular RCGAs. In the proposed RCGA, simulated binary crossover and polynomial mutation are used against the single point crossover and bit-flipping mutation in BCGA. It has been observed from the test results that the proposed RCGA is more efficient in terms of thermal cost minimisation and execution time for ELD problem with continuous search space than BCGA and some other popular RCGAs.     

A novel and effective particle swarm optimization like algorithm with extrapolation technique

A novel competitive approach to particle swarm optimization (PSO) algorithms is proposed in this paper. The proposed method uses extrapolation technique with PSO (ePSO) for solving optimization problems. By considering the basics of the PSO algorithm, the current particle position is updated by extrapolating the global best particle position and the current particle positions in the search space. The position equation is formulated with the global best (gbest) position, local best position (pbest) and the current position of the particle. The proposed method is tested with a set of 13 standard optimization benchmark problems and the results are compared with those obtained through two existing PSO algorithms, the canonical PSO (cPSO), the Global-Local best PSO (GLBest PSO). The cPSO includes a time-varying inertia weight (TVIW) and time-varying acceleration co-efficients (TVAC) while the GLBest PSO consists of Global-Local best inertia weight (GLBest IW) with Global-Local best acceleration co-efficient (GLBestAC). The simulation results clearly elucidate that the proposed method produces the near global optimal solution. It is also observed from the comparison of the proposed method with cPSO and GLBest PSO, the ePSO is capable of producing a quality of optimal solution with faster convergence rate. To strengthen the comparison and prove the efficacy of the proposed method a real time application of steel annealing processing (SAP) is also considered. The optimal control objectives of SAP are computed through the above said three PSO algorithms and also through two versions of genetic algorithms (GA), namely, real coded genetic algorithm (RCGA) and hybrid real coded genetic algorithm (HRCGA) and the results are analyzed with the proposed method. From the results obtained through benchmark problems and the real time application of SAP, it is clearly seen that the proposed ePSO method is competitive to the existing PSO algorithms and also to GAs.     

Structural inverse analysis by hybrid simplex artificial bee colony algorithms

A hybrid simplex artificial bee colony algorithm (HSABCA) which combines Nelder–Mead simplex method with artificial bee colony algorithm (ABCA) is proposed for inverse analysis problems. The proposed algorithm is applied to parameter identification of concrete dam-foundation systems. To verify the performance of HSABCA, it is compared with the basic ABCA and a real coded genetic algorithm (RCGA) on two examples: a gravity dam and an arc dam. Results show that the proposed algorithm is an efficient tool for inverse analysis and it performs much better than ABCA and RCGA on such problems.     

STEREO CAMERA CALIBRATION USING PARTICLE SWARM OPTIMIZATION

Camera calibration is an essential issue in many computer vision tasks in which quantitative information of a scene is to be derived from its images. It is concerned with the determination of a set of parameters from the given images. In literature, it has been modeled as a nonlinear global optimization problem and has been solved using various optimization techniques. In this article, a recently developed variant of a very popular global optimization technique—the particle swarm optimization (PSO) algorithm—has been used for solving this problem for a stereo camera system modeled by pin-hole camera model. Extensive experiments have been performed on synthetic data to test the applicability of the technique to this problem. The simulation results, which have been compared with those obtained by a real coded genetic algorithm (RCGA) in literature, show that the proposed PSO performs a bit better than RCGA in terms of computational effort.     

A simple and efficient real-coded genetic algorithm for constrained optimization

This paper presents a simple and efficient real-coded genetic algorithm (RCGA) for constrained real-parameter optimization. Different from some conventional RCGAs that operate evolutionary operators in a series framework, the proposed RCGA implements three specially designed evolutionary operators, named the ranking selection (RS), direction-based crossover (DBX), and the dynamic random mutation (DRM), to mimic a specific evolutionary process that has a parallel-structured inner loop. A variety of benchmark constrained optimization problems (COPs) are used to evaluate the effectiveness and the applicability of the proposed RCGA. Besides, some existing state-of-the-art optimization algorithms in the same category of the proposed algorithm are considered and utilized as a rigorous base of performance evaluation. Extensive comparison results reveal that the proposed RCGA is superior to most of the comparison algorithms in providing a much faster convergence speed as well as a better solution accuracy, especially for problems subject to stringent equality constraints. Finally, as a specific application, the proposed RCGA is applied to optimize the GaAs film growth of a horizontal metal-organic chemical vapor deposition reactor. Simulation studies have confirmed the superior performance of the proposed RCGA in solving COPs.     

Design and analysis of SSSC-based supplementary damping controller

Power-system stability improvement by a static synchronous series compensator (SSSC)-based damping controller is thoroughly investigated in this paper. The design problem of the proposed controller is formulated as an optimization problem, and real coded genetic algorithm (RCGA) is employed to search for the optimal controller parameters. Both local and remote signals with associated time delays are considered in the present study and a comparison has been made between the two signals. The performances of the proposed controllers are evaluated under different disturbances for both single-machine infinite-bus power system and multi-machine power system. Simulation results are presented and compared with a recently published modern heuristic optimization technique under various disturbances to show the effectiveness and robustness of the proposed approach.     

A comparison study of self-adaptation in evolution strategies and real-coded genetic algorithms

This paper discusses the self-adaptive mechanisms of evolution strategies (ES) and real-coded genetic algorithms (RCGA) for optimization in continuous search spaces. For multi-membered evolution strategies, a self-adaptive mechanism of mutation parameters has been proposed by Schwefel. It introduces parameters such as standard deviations of the normal distribution for mutation into the genetic code and lets them evolve by selection as well as the decision variables. In the RCGA, crossover or recombination is used mainly for search. It utilizes information on several individuals to generate novel search points, and therefore, it can generate offspring adaptively according to the distribution of parents without any adaptive parameters. The present paper discusses characteristics of these two self-adaptive mechanisms through numerical experiments. The self-adaptive characteristics such as translation, enlargement, focusing, and directing of the distribution of children generated by the ES and the RCGA are examined through experiments.     

一种自由曲线廓形误差的高效可靠评价方法

为实现对自由曲线廓形误差的高效可靠评价,提出了一种结合多项式方程求根与 实数编码遗传算法(RCGA)的评价方法。首先,根据最小二乘准则建立了廓形误差评价的优化模 型;进而,通过构造多项式方程,并采用 Halley 迭代对方程求根,实现了点到自由曲线距离的 高效计算;然后,采用 RCGA 完成了优化模型的求解,并与分割逼近法得到的结果进行了对比。 结果表明,该方法高效可靠,相同条件下计算时间约为分割逼近法的 5%,能够满足自由曲线 廓形误差的评价。     

New Real-Coded Genetic Algorithm Operators for Minimization of Molecular Potential Energy Function

The global minimum of the potential energy of a molecule corresponds to its most stable conformation and it dictates most of its properties. Due to the extensive search space and the massive number of local minima that propagate exponentially with molecular size, determining the global minimum of a potential energy function could prove to be significantly challenging. This study demonstrates the application of newly designed real-coded genetic algorithm (RCGA) called RX-STPM, which incorporates the use of Rayleigh crossover (RX) and scale-truncated Pareto mutator (STPM) as defined earlier for minimizing molecular potential energy functions. Computational results for problems with up to 100 degrees of freedom are compared with five other existing methods from the literature. The numerical results indicate the underlying reliability (robustness) and efficiency of the proposed approach compared to other existing algorithms with low computational costs.     

A taxonomy for the crossover operator for real‐coded genetic algorithms: An experimental study

The main real‐coded genetic algorithm (RCGA) research effort has been spent on developing efficient crossover operators. This study presents a taxonomy for this operator that groups its instances in different categories according to the way they generate the genes of the offspring from the genes of the parents. The empirical study of representative crossovers of all the categories reveals concrete features that allow the crossover operator to have a positive influence on RCGA performance. They may be useful to design more effective crossover models. © 2003 Wiley Periodicals, Inc.     

An Improved Genetic Algorithm with Average-bound Crossover and Wavelet Mutation Operations

This paper presents a real-coded genetic algorithm (RCGA) with new genetic operations (crossover and mutation). They are called the average-bound crossover and wavelet mutation. By introducing the proposed genetic operations, both the solution quality and stability are better than the RCGA with conventional genetic operations. A suite of benchmark test functions are used to evaluate the performance of the proposed algorithm. Application examples on economic load dispatch and tuning an associative-memory neural network are used to show the performance of the proposed RCGA.     

Investigation of self-organizing map for genetic algorithm

This paper describes self-organizing maps for genetic algorithm (SOM-GA) which is the combinational algorithm of a real-coded genetic algorithm (RCGA) and self-organizing map (SOM). The self-organizing maps are trained with the information of the individuals in the population. Sub-populations are defined by the help of the trained map. The RCGA is performed in the sub-populations. The use of the sub-population search algorithm improves the local search performance of the RCGA. The search performance is compared with the real-coded genetic algorithm (RCGA) in three test functions. The results show that SOM-GA can find better solutions in shorter CPU time than RCGA. Although the computational cost for training SOM is expensive, the results show that the convergence speed of SOM-GA is accelerated according to the development of SOM training.     

Adaptive directed mutation for real-coded genetic algorithms

Adaptive directed mutation (ADM) operator, a novel, simple, and efficient real-coded genetic algorithm (RCGA) is proposed and then employed to solve complex function optimization problems. The suggested ADM operator enhances the abilities of GAs in searching global optima as well as in speeding convergence by integrating the local directional search strategy and the adaptive random search strategies. Using 41 benchmark global optimization test functions, the performance of the new algorithm is compared with five conventional mutation operators and then with six genetic algorithms (GAs) reported in literature. Results indicate that the proposed ADM-RCGA is fast, accurate, and reliable, and outperforms all the other GAs considered in the present study.     

Securing high resolution grayscale facial captures using a blockwise coevolutionary GA

In biometric systems, reference facial images captured during enrollment are commonly secured using watermarking, where invisible watermark bits are embedded into these images. Evolutionary Computation (EC) is widely used to optimize embedding parameters in intelligent watermarking (IW) systems. Traditional IW methods represent all blocks of a cover image as candidate embedding solutions of EC algorithms, and suffer from premature convergence when dealing with high resolution grayscale facial images. For instance, the dimensionality of the optimization problem to process a 2048 × 1536 pixel grayscale facial image that embeds 1 bit per 8 × 8 pixel block involves 49k variables represented with 293k binary bits. Such Large-Scale Global Optimization problems cannot be decomposed into smaller independent ones because watermarking metrics are calculated for the entire image. In this paper, a Blockwise Coevolutionary Genetic Algorithm (BCGA) is proposed for high dimensional IW optimization of embedding parameters of high resolution images. BCGA is based on the cooperative coevolution between different candidate solutions at the block level, using a local Block Watermarking Metric (BWM). It is characterized by a novel elitism mechanism that is driven by local blockwise metrics, where the blocks with higher BWM values are selected to form higher global fitness candidate solutions. The crossover and mutation operators of BCGA are performed on block level. Experimental results on PUT face image database indicate a 17% improvement of fitness produced by BCGA compared to classical GA. Due to improved exploration capabilities, BCGA convergence is reached in fewer generations indicating an optimization speedup.     

A support vector regression based prediction model of affective responses for product form design

In this paper, a state-of-the-art machine learning approach known as support vector regression (SVR) is introduced to develop a model that predicts consumers’ affective responses (CARs) for product form design. First, pairwise adjectives were used to describe the CARs toward product samples. Second, the product form features (PFFs) were examined systematically and then stored them either as continuous or discrete attributes. The adjective evaluation data of consumers were gathered from questionnaires. Finally, prediction models based on different adjectives were constructed using SVR, which trained a series of PFFs and the average CAR rating of all the respondents. The real-coded genetic algorithm (RCGA) was used to determine the optimal training parameters of SVR. The predictive performance of the SVR with RCGA (SVR–RCGA) is compared to that of SVR with 5-fold cross-validation (SVR–5FCV) and a back-propagation neural network (BPNN) with 5-fold cross-validation (BPNN–5FCV). The experimental results using the data sets on mobile phones and electronic scooters show that SVR performs better than BPNN. Moreover, the RCGA for optimizing training parameters for SVR is more convenient for practical usage in product form design than the timeconsuming CV.     

Hybrid neural network and genetic algorithm based machining feature recognition

In this research, neural networks (NNs) and genetic algorithms (GAs) are used together in a hybrid approach to reduce the computational complexity of feature recognition problem. The proposed approach combines the characteristics of evolutionary technique and NN to overcome the shortcomings of feature recognition problem. Consideration is given to reduce the computational complexity of network with specific interest to design the optimum network architecture using GA input selection approach. In order to evaluate the performance of the proposed system, experimental results are compared with previous NN based feature recognition research.     

Real-coded genetic algorithm with variable rates of cross-over and mutation: a basis of global optimization for multi-modal functions via interval technique

A hybrid method consisting of a real-coded genetic algorithm (RCGA) and an interval technique is proposed for optimizing bound constrained non-linear multi-modal functions. This method has two different phases. In phase I, the search space is divided into several subregions and the simple genetic algorithm (SGA) is applied to each subregion to find the one(s) containing the best value of the objective function. In phase II, the selected subregion is divided into two equal halves and the advanced GA, i.e. the RCGA, is applied in each half to reject the subregion where the global solution does not exist. This process is repeated until the interval width of each variable is less than a pre-assigned very small positive number. In the RCGA, we consider rank-based selection, multi-parent whole arithmetical cross-over, and non-uniform mutation depending on the age of the population. However, the cross-over and mutation rates are assumed as variables. Initially, these rates are high and then decrease from generation to generation. Finally, the proposed hybrid method is applied to several standard test functions used in the literature; the results obtained are encouraging. Sensitivity analyses are shown graphically with respect to different parameters on the lower bound of the interval valued objective function of two different problems.     

Evolutionary learning of BMF fuzzy-neural networks using a reduced-form genetic algorithm

In this paper, a novel approach to adjust both the control points of B-spline membership functions (BMFs) and the weightings of fuzzy-neural networks using a reduced-form genetic algorithm (RGA) is proposed. Fuzzy-neural networks are traditionally trained by using gradient-based methods, which may fall into local minimum during the learning process. To overcome the problems encountered by the conventional learning methods, genetic algorithms are adopted because of their capabilities of directed random search for global optimization. It is well known, however, that the searching speed of the conventional genetic algorithms is not desirable. Such conventional genetic algorithms are inherently incapable of dealing with a vast number (over 100) of adjustable parameters in the fuzzy-neural networks. In this paper, the RGA is proposed by using a sequential-search-based crossover point (SSCP) method in which a better crossover point is determined and only the gene at the specified crossover point is crossed, serving as a single gene crossover operation. Chromosomes consisting of both, the control points of BMFs and the weightings of the fuzzy-neural network are coded as an adjustable vector with real number components that are searched by the RGA. Simulation results have shown that faster convergence of the evolution process searching for an optimal fuzzy-neural network can be achieved. Examples of nonlinear functions approximated by using the fuzzy-neural network via the RGA are demonstrated to illustrate the effectiveness of the proposed method.     

A K-Means-Galactic Swarm Optimization-Based Clustering Algorithm with Otsu’s Entropy for Brain Tumor Detection

Image segmentation is a technique in order to segment an image into various parts and derive meaningful information out of each one. In this article, problem of image segmentation is applied on brain MRI images. This is done in order to detect and capture the location, size and shape of five different types of tumors. Here, image segmentation is viewed as an clustering problem and a new hybrid K-means Galatic Swarm Optimization (GSO) algorithm is proposed for effective solution. The Otsus entropy measure is used as the fitness function for deriving the segments. Extensive simulation studies with five performance measures on five different brain MRI images reveal the superior performance of the proposed approach over GSO, Real Coded Genetic Algorithm (RCGA), and K-Means clustering algorithms.     

An Efficient Adaptive Real Coded Genetic Algorithm to Solve the Portfolio Choice Problem Under Cumulative Prospect Theory

Cumulative prospect theory (CPT) has become one of the most popular approaches for evaluating the behavior of decision makers under conditions of uncertainty. Substantial experimental evidence suggests that human behavior may significantly deviate from the traditional expected utility maximization framework when faced with uncertainty. The problem of portfolio selection should be revised when the investor’s preference is for CPT instead of expected utility theory. However, because of the complexity of the CPT function, little research has investigated the portfolio choice problem based on CPT. In this paper, we present an operational model for portfolio selection under CPT, and propose a real-coded genetic algorithm (RCGA) to solve the problem of portfolio choice. To overcome the limitations of RCGA and improve its performance, we introduce an adaptive method and propose a new selection operator. Computational results show that the proposed method is a rapid, effective, and stable genetic algorithm.