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This paper presents efficient chaotic invasive weed optimization (CIWO) techniques based on chaos for solving optimal power flow (OPF) problems with non-smooth generator fuel cost functions (non-smooth OPF) with the minimum pollution level (environmental OPF) in electric power systems. OPF problem is used for developing corrective strategies and to perform least cost dispatches. However, cost based OPF problem solutions usually result in unattractive system gaze emission issue (environmental OPF). In the present paper, the OPF problem is formulated by considering the emission issue. The total emission can be expressed as a non-linear function of power generation, as a multi-objective optimization problem, where optimal control settings for simultaneous minimization of fuel cost and gaze emission issue are obtained. The IEEE 30-bus test power system is presented to illustrate the application of the environmental OPF problem using CIWO techniques. Our experimental results suggest that CIWO techniques hold immense promise to appear as efficient and powerful algorithm for optimization in the power systems. [ABSTRACT FROM AUTHOR]

Abstract: Evolutionary Algorithms (EAs) are stochastic and robust meta-heuristics of evolutionary computation field useful to solve optimization problems in image processing applications. Recently, as special mechanism to avoid being trapped in local minimum, the ergodicity property of chaotic sequences has been used in various designs of EAs. Three differential evolution approaches based on chaotic sequences using logistic equation for image enhancement process are proposed in this paper. Differential evolution is a simple yet powerful evolutionary optimization algorithm that has been successfully used in solving continuous problems. The proposed chaotic differential evolution schemes have fast convergence rate but also maintain the diversity of the population so as to escape from local optima. In this paper, the image contrast enhancement is approached as a constrained nonlinear optimization problem. The objective of the proposed chaotic differential evolution schemes is to maximize the fitness criterion in order to enhance the contrast and detail in the image by adapting the parameters using a contrast enhancement technique. The proposed chaotic differential evolution schemes are compared with classical differential evolution to two testing images. Simulation results on three images show that the application of chaotic sequences instead of random sequences is a possible strategy to improve the performance of classical differential evolution optimization algorithm. [Copyright &y& Elsevier]

Abstract: This paper proposes a novel particle swarm optimization (PSO) algorithm, chaotically encoded particle swarm optimization algorithm (CENPSOA), based on the notion of chaos numbers that have been recently proposed for a novel meaning to numbers. In this paper, various chaos arithmetic and evaluation measures that can be used in CENPSOA have been described. Furthermore, CENPSOA has been designed to be effectively utilized in data mining applications. [Copyright &y& Elsevier]

Recently, krill herd algorithm (KHA) is proposed for the solution of global optimization problem. Various chaotic maps are considered in the proposed chaotic KHA (CKHA) of the present work to improve the performance of basic KHA method. It is observed that Logistic map based CKHA offers better results as compared other chaotic maps. The performance of the proposed CKHA is tested on standard 26-bus and IEEE 57-bus test power systems for the solution of optimal power flow of power system with different objectives that reflect minimization of fuel cost or active power loss or sum of total voltage deviation. Results obtained by using CKHA are compared to other evolutionary optimization techniques surfaced in the recent state-of-the-art literature. The results presented in this paper show that the proposed CKHA algorithm outperforms the other techniques in terms of convergence rate and global search ability. [ABSTRACT FROM AUTHOR]

Abstract: This paper introduces a novel hybrid optimization algorithm by taking advantage of the stochastic properties of chaotic search and the invasive weed optimization (IWO) method. In order to deal with the weaknesses associated with the conventional method, the proposed chaotic invasive weed optimization (CIWO) algorithm is presented which incorporates the capabilities of chaotic search methods. The functionality of the proposed optimization algorithm is investigated through several benchmark multi-dimensional functions. Furthermore, an identification technique for chaotic systems based on the CIWO algorithm is outlined and validated by several examples. The results established upon the proposed scheme are also supplemented which demonstrate superior performance with respect to other conventional methods. [Copyright &y& Elsevier]

Abstract: This paper demonstrates how the Groebner basis algorithm can be used for finding the bifurcation points in the generalized Mandelbrot set. It also shows how resultants can be used to find components of the generalized Mandelbrot set. [Copyright &y& Elsevier]

Abstract: This paper proposes new particle swarm optimization (PSO) methods that use chaotic maps for parameter adaptation. This has been done by using of chaotic number generators each time a random number is needed by the classical PSO algorithm. Twelve chaos-embedded PSO methods have been proposed and eight chaotic maps have been analyzed in the benchmark functions. It has been detected that coupling emergent results in different areas, like those of PSO and complex dynamics, can improve the quality of results in some optimization problems. It has been also shown that, some of the proposed methods have somewhat increased the solution quality, that is in some cases they improved the global searching capability by escaping the local solutions. [Copyright &y& Elsevier]

Abstract: This paper proposes a technique aiming to compute all global minimizers, while avoiding local minimizers, through chaotic ant swarm (CAS) optimization method. This technique incorporates the recently proposed deflection and repulsion techniques to alleviate local minimizers. Those approaches can be used in combination with CAS to detect all global minimizers effectively. The performance of the algorithm is illustrated on test problems of global optimization. Experimental results indicate the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: Parameter estimation for chaotic systems is an important issue in nonlinear science and has attracted increasing interests from various research fields, which could be essentially formulated as a multidimensional optimization problem. As a novel evolutionary computation technique, differential evolution algorithm (DE) has attracted much attention and wide applications, owing to its simple concept, easy implementation and quick convergence. However, to the best of our knowledge, there is no published work on DE for estimating parameters of chaotic systems. In this paper, a DE approach is applied to estimate the parameters of Lorenz system. Numerical simulation and the comparisons demonstrate the effectiveness and robustness of DE. Moreover, the effect of population size on the optimization performances is investigated as well. [Copyright &y& Elsevier]

Abstract: In this paper, we attempt to use the proportional-integral-derivative (PID) controller to achieve the chaos synchronization for delayed discrete chaotic systems. Three PID control gains can be optimally determined by means of using a novel optimization algorithm, called the particle swarm optimization (PSO). The algorithm is motivated from the organism behavior of fish schooling and bird flocking, and involves the social psychology principles in socio-cognition human agents and evolutionary computations. It has a good numerical convergence for solving optimization problem. To show the validity of the PSO-based PID control for chaos synchronization, several cases with different initial populations are considered and some simulation results are shown. [Copyright &y& Elsevier]

Abstract: Particle swarm optimization (PSO) algorithm has been developing rapidly and has been applied widely since it was introduced, as it is easily understood and realized. This paper presents an improved particle swarm optimization algorithm (IPSO) to improve the performance of standard PSO, which uses the dynamic inertia weight that decreases according to iterative generation increasing. It is tested with a set of 6 benchmark functions with 30, 50 and 150 different dimensions and compared with standard PSO. Experimental results indicate that the IPSO improves the search performance on the benchmark functions significantly. [Copyright &y& Elsevier]

Abstract: This paper applies a novel evolutionary algorithm named differential evolution (DE) to direct the orbits of discrete chaotic dynamical systems towards desired target region within a short time by adding only small bounded perturbations, which could be formulated as a multi-modal numerical optimization problem with high dimension. Moreover, the synchronization of chaotic systems is also studied, which can be dealt with as an online problem of directing orbits. Numerical simulations based on Hénon Map demonstrate the effectiveness and efficiency of DE, and the effects of some parameters are investigated as well. [Copyright &y& Elsevier]

Abstract: In this paper, a chaos search immune algorithm (CSIA) is proposed by integrating the chaos optimization algorithm and the clonal selection algorithm. First, optimization variables are expressed by chaotic variables through solution space transformation. Then, taking advantages of the ergodic and stochastic properties of chaotic variables, a chaos search is performed in the neighbourhoods of high affinity antibodies to exploit local solution space, and the motion of the chaotic variables in their ergodic space is used to explore the whole solution space. Furthermore, a generalized radial basis function neuro-fuzzy controller (GRBFNFC) is constructed and designed automatically by the proposed CSIA. Application of the CSIA-designed GRBFNFC to real-time control of an inverted pendulum system is discussed. Experimental results demonstrate that the designed GRBFNFC has very satisfactory performance. [Copyright &y& Elsevier]

Abstract: In this paper, a differential evolution (DE) algorithm is applied to parameter identification of Rossler’s chaotic system. The differential evolution has been shown to possess a powerful searching capability for finding the solutions for a given optimization problem, and it allows for parameter solution to appear directly in the form of floating point without further numerical coding or decoding. Three unknown parameters of Rossler’s Chaotic system are optimally estimated by using the DE algorithm. Finally, a numerical example is given to verify the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper applies a novel evolutionary computation algorithm named particle swarm optimization (PSO) to direct the orbits of discrete chaotic dynamical systems towards desired target region within a short time by adding only small bounded perturbations, which could be formulated as a multi-modal numerical optimization problem with high dimension. Moreover, the synchronization of chaotic systems is also studied, which can be dealt with as an online problem of directing orbits. Numerical simulations based on Hénon Map demonstrate the effectiveness and efficiency of PSO, and the effects of some parameters are also investigated. [Copyright &y& Elsevier]

In this paper, the design problem of dynamic output feedback controller for asymptotic stabilization of a class of neutral systems have been considered. A criterion for the existence of such controllers is derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the controllers is given in terms of the feasible solutions to the LMIs, which can be solved by various convex optimization algorithms. A numerical example is given to illustrate the proposed design method. [Copyright &y& Elsevier]

This paper investigated stability criterion of time-delay chaotic systems via delayed feedback control (DFC) using the Lyapunov stability theory and linear matrix inequality (LMI) technique. A stabilization criterion is derived in terms of LMIs which can be easily solved by efficient convex optimization algorithms. A numerical example is given to illuminate the design procedure and advantage of the result derived. [Copyright &y& Elsevier]

Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, this paper proposes a novel control method for stabilization of a class of time-delay chaotic systems. A stabilization criterion is derived in terms of LMIs which can be easily solved by efficient convex optimization algorithms. A numerical example is included to show the advantage of the result derived. [Copyright &y& Elsevier]

• The first work on performance improvement of OIO method is performed. • Different ergodic chaotic systems are used for the first time to generate chaotic values instead of random values in OIO processes in order to enhance performance. • Three new enhanced OIO methods are proposed. • A new application area for chaos is proposed. Metaheuristic optimization algorithms are efficiently used in many large-scale complex problems. Recently, a physics-based metaheuristic search and optimization method entitled Optics Inspired Optimization (OIO) has been proposed. OIO treats the search field of the interested problem to be optimized as a wavy mirror in which the concave mirror is represented as a valley and the convex mirror is represented as a peak. Each candidate solution represents an artificial light point. OIO is a very new metaheuristic method and different approaches should be integrated to obtain a faster convergence with high accuracy by balancing the exploitation and exploration. This paper is the first work on performance improvement of this method by preventing the falling into local optimum solutions and slow convergence speed. In this article, different ergodic chaotic systems are used for the first time to generate chaotic values instead of random values in OIO processes in order to enhance the global convergence speed and prevent stuck on local solutions of classical OIO algorithm. For this purpose, three new enhanced OIO methods are proposed. Furthermore, a new application area for chaos is proposed. The chaotic OIO algorithms proposed in this study are tested in unconstrained benchmark problems and constrained real-world engineering problems. Promising results are obtained from the detailed simulations. [ABSTRACT FROM AUTHOR]