Viviana Cocco Mariani

Correction to "Combining of Chaotic Differential Evolution and Quadratic Programming for Economic Dispatch Optimization with Valve-Point Effect"

Evolutionary algorithms are heuristic methods that have yielded promising results for solving nonlinear, nondifferentiable, and multi-modal optimization problems in the power systems area. The differential evolution (DE) algorithm is an evolutionary algorithm that uses a rather greedy and less stochastic approach to problem solving than do classical evolutionary algorithms, such as genetic algorithms, evolutionary programming, and evolution strategies. DE also incorporates an efficient way of self-adapting mutation using small populations. The potentialities of DE are its simple structure, easy use, convergence property, quality of solution, and robustness. This paper proposes a new approach for solving economic load dispatch problems with valve-point effect. The proposed method combines the DE algorithm with the generator of chaos sequences and sequential quadratic programming (SQP) technique to optimize the performance of economic dispatch problems. The DE with chaos sequences is the global optimizer, and the SQP is used to fine-tune the DE run in a sequential manner. The combined methodology and its variants are validated for two test systems consisting of 13 and 40 thermal units whose incremental fuel cost function takes into account the valve-point loading effects. The proposed combined method outperforms other state-of-the-art algorithms in solving load dispatch problems with the valve-point effect.

Use of chaotic sequences in a biologically inspired algorithm for engineering design optimization

Recent computational developments in ant colony systems have proved fruitful for transforming discrete domains of application into continuous ones. In this paper, new combinations of an ant colony inspired algorithm (ACA) and chaotic sequences (ACH) are employed in well-studied continuous optimization problems of engineering design. Two case studies are described and evaluated in this work. Our results indicate that ACA and ACH handle such problems efficiently in terms of precision and convergence and, in most cases, they outperform the results presented in the literature.

Improved differential evolution approach based on cultural algorithm and diversity measure applied to solve economic load dispatch problems

Evolutionary algorithms (EAs) are general-purpose stochastic search methods that use the metaphor of evolution as the key element in the design and implementation of computer-based problems solving systems. During the past two decades, EAs have attracted much attention and wide applications in a variety of fields, especially for optimization and design. EAs offer a number of advantages: robust and reliable performance, global search capability, little or no information requirement, and others. Among various EAs, differential evolution (DE), which characterized by the different mutation operator and competition strategy from the other EAs, has shown great promise in many numerical benchmark problems and real-world optimization applications. The potentialities of DE are its simple structure, easy use, convergence speed and robustness. To improve the global optimization property of DE, in this paper, a DE approach based on measure of populations diversity and cultural algorithm technique using normative and situational knowledge sources is proposed as alternative method to solving the economic load dispatch problems of thermal generators. The traditional and cultural DE approaches are validated for two test systems consisting of 13 and 40 thermal generators whose nonsmooth fuel cost function takes into account the valve-point loading effects. Simulation results indicate that performance of the cultural DE present best results when compared with previous optimization approaches in solving economic load dispatch problems.

Firefly algorithm approach based on chaotic Tinkerbell map applied to multivariable PID controller tuning

Nowadays, a variety of controllers used in process industries are still of the proportional-integral-derivative (PID) types. PID controllers have the advantage of simple structure, good stability, and high reliability. A relevant issue for PID controllers design is the accurate and efficient tuning of parameters. In this context, several approaches have been reported in the literature for tuning the parameters of PID controllers using evolutionary algorithms, mainly for single-input single-output systems. The systematic design of multi-loop (or decentralized) PID control for multivariable processes to meet certain objectives simultaneously is still a challenging task. This paper proposes a new chaotic firefly algorithm approach based on Tinkerbell map (CFA) to tune multi-loop PID multivariable controllers. The firefly algorithm is a metaheuristic algorithm based on the idealized behavior of the flashing characteristics of fireflies. To validate the performance of the proposed PID control design, a multi-loop multivariable PID structure for a binary distillation column plant (Wood and Berry column model) and an industrial-scale polymerization reactor are taken. Simulation results indicate that a suitable set of PID parameters can be calculated by the proposed CFA. Besides, some comparison results of a genetic algorithm, a particle swarm optimization approach, traditional firefly algorithm, modified firefly algorithm, and the proposed CFA to tune multi-loop PID controllers are presented and discussed.

A chaotic firefly algorithm applied to reliability-redundancy optimization

The reliability-redundancy allocation problem can be approached as a mixed-integer programming problem. It has been solved by using optimization techniques such as dynamic programming, integer programming, and mixed-integer nonlinear programming. On the other hand, a broad class of meta-heuristics has been developed for reliability-redundancy optimization. Recently, a new meta-heuristics called firefly algorithm (FA) algorithm has emerged. The FA is a stochastic metaheuristic approach based on the idealized behavior of the flashing characteristics of fireflies. In FA, the flashing light can be formulated in such a way that it is associated with the objective function to be optimized, which makes it possible to formulate the firefly algorithm. This paper introduces a modified FA approach combined with chaotic sequences (FAC) applied to reliability-redundancy optimization. In this context, an example of mixed integer programming in reliability-redundancy design of an overspeed protection system for a gas turbine is evaluated. In this application domain, FAC was found to outperform the previously best-known solutions available.

Modified imperialist competitive algorithm based on attraction and repulsion concepts for reliability-redundancy optimization

System reliability analysis and optimization are important to efficiently utilize available resources and to develop an optimal system design architecture. System reliability optimization has been solved by using optimization techniques including meta-heuristics. Meanwhile, the development of meta-heuristics has been an active research field of the reliability optimization wherein the redundancy, the component reliability, or both are to be determined. In recent years, a broad class of stochastic meta-heuristics, such as simulated annealing, genetic algorithm, tabu search, ant colony, and particle swarm optimization paradigms, has been developed for reliability-redundancy optimization of systems. Recently, a new kind of evolutionary algorithm called Imperialist Competitive Algorithm (ICA) was proposed. The ICA is based on imperialistic competition where the populations are represented by countries, which are classified as imperialists or colonies. However, the trade-off between the exploration (i.e. the global search) and the exploitation (i.e. the local search) of the search space is critical to the success of the classical ICA approach. An improvement in the ICA by implementing an attraction and repulsion concept during the search for better solutions, the AR-ICA approach, is proposed in this paper. Simulations results demonstrates the AR-ICA is an efficient optimization technique, since it obtained promising solutions for the reliability redundancy allocation problem when compared with the previously best-known results of four different benchmarks for the reliability-redundancy allocation problem presented in the literature.

Least squares support vector machines with tuning based on chaotic differential evolution approach applied to the identification of a thermal process

In the past decade, support vector machines (SVMs) have gained the attention of many researchers. SVMs are non-parametric supervised learning schemes that rely on statistical learning theory which enables learning machines to generalize well to unseen data. SVMs refer to kernel-based methods that have been introduced as a robust approach to classification and regression problems, lately has handled nonlinear identification problems, the so called support vector regression. In SVMs designs for nonlinear identification, a nonlinear model is represented by an expansion in terms of nonlinear mappings of the model input. The nonlinear mappings define a feature space, which may have infinite dimension. In this context, a relevant identification approach is the least squares support vector machines (LS-SVMs). Compared to the other identification method, LS-SVMs possess prominent advantages: its generalization performance (i.e. error rates on test sets) either matches or is significantly better than that of the competing methods, and more importantly, the performance does not depend on the dimensionality of the input data. Consider a constrained optimization problem of quadratic programing with a regularized cost function, the training process of LS-SVM involves the selection of kernel parameters and the regularization parameter of the objective function. A good choice of these parameters is crucial for the performance of the estimator. In this paper, the LS-SVMs design proposed is the combination of LS-SVM and a new chaotic differential evolution optimization approach based on Ikeda map (CDEK). The CDEK is adopted in tuning of regularization parameter and the radial basis function bandwith. Simulations using LS-SVMs on NARX (Nonlinear AutoRegressive with eXogenous inputs) for the identification of a thermal process show the effectiveness and practicality of the proposed CDEK algorithm when compared with the classical DE approach.

An Efficient Particle Swarm Optimization Approach Based on Cultural Algorithm Applied to Mechanical Design

Particle swarm optimization (PSO) is a population-based swarm intelligence algorithm driven by the simulation of a social psychological metaphor instead of the survival of the fittest individual. Based on the swarm intelligence theory, this paper discusses the use of PSO approaches using an operator and based on the Gaussian probability distribution function as a population space of a cultural algorithm, called cultural Gaussian PSO (GPSO-CA). Cultural algorithms are mechanisms that incorporate domain knowledge obtained during the evolutionary process, which increase the efficiency of the search process. These approaches are employed in a well-studied continuous optimization problem of mechanical engineering design.

A self-adaptive chaotic differential evolution algorithm using gamma distribution for unconstrained global optimization

Evolutionary algorithms (EAs) have yielded promising results for solving nonlinear, non-differentiable and multi-modal optimization problems. Due to its population-based nature, EAs can avoid being trapped in a local optimum, and consequently have the ability to find global optimal solutions. As a novel evolutionary technique, differential evolution (DE) has received increasing attention and wide applications in a variety of fields. DE algorithm uses an efficient way of self-adapting mutation using small populations for function optimization over continuous spaces. The potentialities of DE are its simple structure, easy use, convergence property, quality of solution, and robustness. In this paper, an effective self-adaptive DE algorithm based on Gaussian probability distribution, gamma distribution and chaotic sequence (DEGC) for solving continuous global optimization problems is proposed. The proposed DEGC algorithm is tested on several benchmark functions from the usual literature. Numerical results comparisons with a classical DE approach and a self-adaptive DE approach demonstrate the effectiveness and efficiency of the proposed DEGC algorithm.

Image thresholding segmentation based on a novel beta differential evolution approach

An improved beta differential evolution algorithm is proposed.The improved differential evolution is applied to image threholding segmentation.Simulation results demonstrate that the proposed differential evolution is superior to FODPSO. Image segmentation is the process of partitioning a digital image into multiple regions that have some relevant semantic content. In this context, histogram thresholding is one of the most important techniques for performing image segmentation. This paper proposes a beta differential evolution (BDE) algorithm for determining the n-1 optimal n-level threshold on a given image using Otsu criterion. The efficacy of BDE approach is illustrated by some results when applied to two case studies of image segmentation. Compared with a fractional-order Darwinian particle swarm optimization (PSO), the proposed BDE approach performs better, or at least comparably, in terms of the quality of the final solutions and mean convergence in the evaluated case studies.