Chaotic Quantum Double Delta Swarm Algorithm using Chebyshev Maps: Theoretical Foundations, Performance Analyses and Convergence Issues

Quantum Double Delta Swarm (QDDS) Algorithm is a new metaheuristic algorithm inspired by the convergence mechanism to the center of potential generated within a single well of a spatially co-located double-delta well setup. It mimics the wave nature of candidate positions in solution spaces and draws upon quantum mechanical interpretations much like other quantum-inspired computational intelligence paradigms. In this work, we introduce a Chebyshev map driven chaotic perturbation in the optimization phase of the algorithm to diversify weights placed on contemporary and historical, socially-optimal agents' solutions. We follow this up with a characterization of solution quality on a suite of 23 single-objective functions and carry out a comparative analysis with eight other related nature-inspired approaches. By comparing solution quality and successful runs over dynamic solution ranges, insights about the nature of convergence are obtained. A two-tailed t-test establishes the statistical significance of the solution data whereas Cohen's d and Hedge's g values provide a measure of effect sizes. We trace the trajectory of the fittest pseudo-agent over all function evaluations to comment on the dynamics of the system and prove that the proposed algorithm is theoretically globally convergent under the assumptions adopted for proofs of other closely-related random search algorithms.Comment: 27 pages, 4 figures, 19 table

A Chaotic Particle Swarm Optimization (CPSO) Algorithm for Solving Optimal Reactive Power Dispatch Problem

This paper presents a chaotic particle swarm algorithm for solving the multi-objective reactive power dispatch problem. To deal with reactive power optimization problem, a chaotic particle swarm optimization (CPSO) is presented to avoid the premature convergence. By fusing with the ergodic and stochastic chaos, the novel algorithm explores the global optimum with the comprehensive learning strategy. The chaotic searching region can be adjusted adaptively.  In order to evaluate the proposed algorithm, it has been tested on IEEE 30 bus system and simulation results show that (CPSO)   is more efficient than other algorithms in reducing the real power loss and maximization of voltage stability index. Keywords:chaotic particle swarm optimization, Optimization, Swarm Intelligence, optimal reactive power, Transmission loss

Optimum PID Control of Multi-wing Attractors in A Family of Lorenz-like Chaotic Systems

Multi-wing chaotic attractors are highly complex nonlinear dynamical systems with higher number of index-2 equilibrium points. Due to the presence of several equilibrium points, randomness of the state time series for these multi-wing chaotic systems is higher than that of the conventional double wing chaotic attractors. A real coded Genetic Algorithm (GA) based global optimization framework has been presented in this paper, to design optimum PID controllers so as to control the state trajectories of three different multi-wing Lorenz like chaotic systems viz. Lu, Rucklidge and Sprott-1 system.Comment: 6 pages, 21 figures; 2012 Third International Conference on Computing, Communication and Networking Technologies (ICCCNT'12), July 2012, Coimbator

Applications of fractional calculus in electrical and computer engineering

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of several systems. This article illustrates several applications of fractional calculus in science and engineering. It has been recognized the advantageous use of this mathematical tool in the modeling and control of many dynamical systems. In this perspective, this paper investigates the use of FC in the fields of controller tuning, electrical systems, digital circuit synthesis, evolutionary computing, redundant robots, legged robots, robotic manipulators, nonlinear friction and financial modeling.N/

Nature-inspired optimization algorithms: challenges and open problems

Many problems in science and engineering can be formulated as optimization problems, subject to complex nonlinear constraints. The solutions of highly nonlinear problems usually require sophisticated optimization algorithms, and traditional algorithms may struggle to deal with such problems. A current trend is to use nature-inspired algorithms due to their flexibility and effectiveness. However, there are some key issues concerning nature-inspired computation and swarm intelligence. This paper provides an in-depth review of some recent nature-inspired algorithms with the emphasis on their search mechanisms and mathematical foundations. Some challenging issues are identified and five open problems are highlighted, concerning the analysis of algorithmic convergence and stability, parameter tuning, mathematical framework, role of benchmarking and scalability. These problems are discussed with the directions for future research

A Survey on Particle Swarm Optimization for Association Rule Mining

Association rule mining (ARM) is one of the core techniques of data mining to discover potentially valuable association relationships from mixed datasets. In the current research, various heuristic algorithms have been introduced into ARM to address the high computation time of traditional ARM. Although a more detailed review of the heuristic algorithms based on ARM is available, this paper differs from the existing reviews in that we expected it to provide a more comprehensive and multi-faceted survey of emerging research, which could provide a reference for researchers in the field to help them understand the state-of-the-art PSO-based ARM algorithms. In this paper, we review the existing research results. Heuristic algorithms for ARM were divided into three main groups, including biologically inspired, physically inspired, and other algorithms. Additionally, different types of ARM and their evaluation metrics are described in this paper, and the current status of the improvement in PSO algorithms is discussed in stages, including swarm initialization, algorithm parameter optimization, optimal particle update, and velocity and position updates. Furthermore, we discuss the applications of PSO-based ARM algorithms and propose further research directions by exploring the existing problems.publishedVersio

HYBRID GENETIC AND PENGUIN SEARCH OPTIMIZATION ALGORITHM (GA-PSEOA) FOR EFFICIENT FLOW SHOP SCHEDULING SOLUTIONS

This paper presents a novel hybrid approach, fusing genetic algorithms (GA) and penguin search optimization (PSeOA), to address the flow shop scheduling problem (FSSP). GA utilizes selection, crossover, and mutation inspired by natural selection, while PSeOA emulates penguin foraging behavior for efficient exploration. The approach integrates GA's genetic diversity and solution space exploration with PSeOA's rapid convergence, further improved with FSSP-specific modifications. Extensive experiments validate its efficacy, outperforming pure GA, PSeOA, and other metaheuristics