This paper proposes a new hybrid chaotic map and a different way of using optimization technique to improve the performance of encryption algorithms. Compared to other chaotic functions, the proposed chaotic map establishes an excellent randomness performance and sensitivity. Based on its Lyapunov exponents and entropy measure, the characteristics of the new mathematical function are better than those of classical maps. We propose a new image cipher based on confusion/diffusion Shannon properties. The substitution phase of the proposed encryption algorithm, which depends on a new optimized substitution box, was carried out by chaotic Jaya optimization algorithm to generate S-boxes according to their nonlinearity score. The goal of the optimization process is to have a bijective matrix with high nonlinearity score. Furthermore, a dynamic key depending on the output of encrypted image is proposed. Security analysis indicates that the proposed encryption scheme can withstand different crypt analytics attacks.

An image encryption scheme based on a new hybrid chaotic map and optimized substitution box

Modified JAYA algorithm for optimal power flow incorporating renewable energy sources considering the cost, emission, power loss and voltage profile improvement

Part One: One-Dimensional Dynamics Examples of Dynamical Systems Preliminaries from Calculus Elementary Definitions Hyperbolicity An example: the quadratic family An Example: the Quadratic Family Symbolic Dynamics Topological Conjugacy Chaos Structural Stability Sarlovskiis Theorem The Schwarzian Derivative Bifurcation Theory Another View of Period Three Maps of the Circle Morse-Smale Diffeomorphisms Homoclinic Points and Bifurcations The Period-Doubling Route to Chaos The Kneeding Theory Geneaology of Periodic Units Part Two: Higher Dimensional Dynamics Preliminaries from Linear Algebra and Advanced Calculus The Dynamics of Linear Maps: Two and Three Dimensions The Horseshoe Map Hyperbolic Toral Automorphisms Hyperbolicm Toral Automorphisms Attractors The Stable and Unstable Manifold Theorem Global Results and Hyperbolic Sets The Hopf Bifurcation The Hnon Map Part Three: Complex Analytic Dynamics Preliminaries from Complex Analysis Quadratic Maps Revisited Normal Families and Exceptional Points Periodic Points The Julia Set The Geometry of Julia Sets Neutral Periodic Points The Mandelbrot Set An Example: the Exponential Function

An introduction to chaotic dynamical systems (2nd edition), by Robert L. Devaney. Pp 336. £34·95. 1989. ISBN 0-201-13046-7 (Addison-Wesley)

In this paper, new metaheuristic technique cuckoo search optimization (CSO) is explored for an optimal and robust power system stabilizer (PSS) designing for multimachine power systems and performance is evaluated by comparing with well-established techniques, i.e., genetic algorithm (GA), particle swarm optimization (PSO), and new harmony search optimization (HSO). An eigenvalue-based multiobjective function is implemented for simultaneous control of damping factor and damping ratio to damp out low-frequency local and interarea modes of oscillations. The PSS parameters are so intended that unstable and/or lightly damped mode eigenvalues are shifted to a specified D-shape zone in the left half of the s -plane. The selected metaheuristic techniques GA, PSO, HSO, and CSO are used to obtain PSS parameters for 10-machines, 39-bus New England Power System and the controllers designed are named as GAPSS, PSOPSS, HSOPSS, and CSOPSS, respectively. The performance of all designed PSSs controllers is evaluated by eigenvalues analysis, nonlinear simulations, and performance indices for various operating conditions under different scenarios of severe disturbances and their comparative analysis is observed. The robustness of all designed PSSs controllers is observed by testing them on unseen operating conditions and results are compared for the same. The performance of CSOPSS is found to be better than other controllers designed.

Cuckoo Search Optimization Algorithm for Designing of a Multimachine Power System Stabilizer

Recently, numerous meta-heuristic-based approaches are deliberated to reduce the computational complexities of several existing approaches that include tricky derivations, very large memory space requirement, initial value sensitivity, etc. However, several optimization algorithms namely firefly algorithm, sine–cosine algorithm, and particle swarm optimization algorithm have few drawbacks such as computational complexity and convergence speed. So to overcome such shortcomings, this paper aims in developing a novel chaotic sine–cosine firefly (CSCF) algorithm with numerous variants to solve optimization problems. Here, the chaotic form of two algorithms namely the sine–cosine algorithm and the firefly algorithms is integrated to improve the convergence speed and efficiency thus minimizing several complexity issues. Moreover, the proposed CSCF approach is operated under various chaotic phases and the optimal chaotic variants containing the best chaotic mapping are selected. Then numerous chaotic benchmark functions are utilized to examine the system performance of the CSCF algorithm. Finally, the simulation results for the problems based on engineering design are demonstrated to prove the efficiency, robustness and effectiveness of the proposed algorithm.

CSCF: a chaotic sine cosine firefly algorithm for practical application problems

Jaya algorithm is one of the recent algorithms developed to solve optimization problems. The basic concept of this algorithm consists in moving the obtained solution, for a given problem, toward the best solution and avoiding the worst one. However, it severely suffers from premature convergence problem and therefore can be easily trapped in local optimums. This study aimed to alleviate these drawbacks and improve the performance of the original Jaya algorithm. Here, three new mutation strategies were implemented in the original Jaya to improve both its global and local search abilities. Chaotic maps were proved to be able to boost the search capabilities of meta-heuristic algorithms. Therefore, after demonstrating its chaotic behavior through the sensitivity to initial conditions, topological transitivity and the density of periodic points, we proposed a new 2D cross chaotic map. The chaotic sequences provided by the proposed chaotic map were embedded into the original Jaya algorithm to generate the initial population and control the search equations. It is worth mentioning that the modifications incorporated in the original algorithm did not affect its two essential characteristics, i.e., simplicity and nonrequirement of additional control parameters. As case studies, sixteen benchmark functions were used to evaluate the performance of the proposed chaotic Jaya algorithm (C-Jaya) regarding solution accuracy and convergence speed. Comparisons with some other meta-heuristic algorithms for low-, middle- and high-dimensional benchmark functions show that the proposed C-Jaya algorithm enhances the performance of original Jaya significantly. Moreover, it offers the fastest global convergence, the highest solution quality and it is the most robust on almost all the test functions among all the algorithms. Nonparametric statistical procedures, i.e., Friedman test, Friedman aligned ranks test and Quade test, conducted to analyze the obtained results, show the superiority of the proposed algorithm.

A novel chaotic Jaya algorithm for unconstrained numerical optimization

A novel chaotic teaching–learning-based optimization algorithm for multi-machine power system stabilizers design problem

One of the most effective approaches to reduce carbon emissions is the integration of renewable energy sources into electrical power networks. Currently, wind turbines are the fastest growing among all renewable sources. With the integration of wind farms into electrical grids, the economic emission dispatch (EED) problem is becoming more complicated due to the stochastic availability of wind energy. In this study, a new approach is proposed to solve the EED problem incorporating wind farms. The problem is formulated as a chance-constrained problem to deal with the stochastic characteristic of wind power. A novel chaotic sine–cosine algorithm (CSCA) is proposed to provide the optimal generation schedule to minimise simultaneously the generation cost and emission. Some weakness has been encountered in exploitation and exploration capabilities in standard sine cosine algorithm (SCA). Hence, the chaos is integrated into the original SCA to improve its performance. In addition, a new mutation strategy is added to the SCA. In this study, the new algorithm is based on three mutually exclusive equations. The new technique is applied on the 69-bus ten-unit and 40-unit test systems with and without wind energy. The results performed by CSCA are compared with those generated by other recent techniques.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-rpg.2019.1081

Chaotic sine–cosine algorithm for chance-constrained economic emission dispatch problem including wind energy

Power system stabilizers (PSSs) associated with generators are mandatory requirements for damping low-frequency oscillations of a multimachine power system. Nevertheless, PSSs work well at particular network configuration and steady-state conditions for which they were designed. Therefore, the aim of this paper is the design of a robust PSS able to ensure the stability of the system for a wide range of loading conditions and various faults with higher performance. The main motivation for this design is to simultaneously shift as much as could be possible the lightly damped and undamped system electromechanical modes, at different loading conditions and system configurations, into pre-specified zone in the s-plane called D-shape sector. Hence, the problem of robustly tuning the PSSs parameters is formulated as a multiobjective optimization problem (MOP) with an eigenvalue-based objective functions. An improved version of non-dominated sorting genetic algorithms (NSGAII) is proposed to solve this MOP. The performance of the proposed NSGAII-based PSS (NSGAII-PSS) under different loading conditions, system configurations and disturbances is tested and examined for different multimachine power systems. Eigenvalue analysis and nonlinear simulations show the effectiveness and robustness of the proposed controllers NSGAII-PSSs and their ability to provide efficient damping of low-frequency oscillations.

Anouar Farah

Papers

An image encryption scheme based on a new hybrid chaotic map and optimized substitution box

A novel chaotic Jaya algorithm for unconstrained numerical optimization

A novel chaotic teaching–learning-based optimization algorithm for multi-machine power system stabilizers design problem

Chaotic sine–cosine algorithm for chance-constrained economic emission dispatch problem including wind energy

Robust design of multimachine power system stabilizers based on improved non-dominated sorting genetic algorithms