Empirically characteristic analysis of chaotic PID controlling particle swarm optimization

• Published in: PloS one Vol. 12; no. 5; p. e0176359
• Main Authors: Yan, Danping, Lu, Yongzhong, Zhou, Min, Chen, Shiping, Levy, David
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 04.05.2017; Public Library of Science (PLoS)
• Subjects: Algorithms; Analysis; Atoms & subatomic particles; Biology and Life Sciences; Catfish; Chaos theory; Circuits; Computational neuroscience; Computer and Information Sciences; Computer applications; Computer programs; Convergence; Cost function; Data collection; Data processing; Dynamical systems; Empirical analysis; Empirical Research; Engineering; Evaluation; Evolution; Exploratory behavior; Forecasting; Gene mapping; Genetic algorithms; Geology; Heuristic; Hybridization; Inertia; Initial conditions; Interactive learning; Learning algorithms; Meteorology; Microbiology; Models, Theoretical; Neural networks; Neurocomputing; Nonlinear Dynamics; Nonlinear systems; Optimization; Optimization algorithms; Optimization techniques; Optimization theory; Parameter estimation; Particle swarm optimization; Philosophy; Physical Sciences; Physics; Politics; Problem solving; Proportional integral derivative; Quadratic programming; Reproductive fitness; Research and Analysis Methods; Robotics; Science; Searching; Security; Sensitivity; Simulation; Stochasticity; Studies; Swarm intelligence; Symbiosis; Technology; Australia; China; New South Wales Australia
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0176359

Since chaos systems generally have the intrinsic properties of sensitivity to initial conditions, topological mixing and density of periodic orbits, they may tactfully use the chaotic ergodic orbits to achieve the global optimum or their better approximation to given cost functions with high probability. During the past decade, they have increasingly received much attention from academic community and industry society throughout the world. To improve the performance of particle swarm optimization (PSO), we herein propose a chaotic proportional integral derivative (PID) controlling PSO algorithm by the hybridization of chaotic logistic dynamics and hierarchical inertia weight. The hierarchical inertia weight coefficients are determined in accordance with the present fitness values of the local best positions so as to adaptively expand the particles' search space. Moreover, the chaotic logistic map is not only used in the substitution of the two random parameters affecting the convergence behavior, but also used in the chaotic local search for the global best position so as to easily avoid the particles' premature behaviors via the whole search space. Thereafter, the convergent analysis of chaotic PID controlling PSO is under deep investigation. Empirical simulation results demonstrate that compared with other several chaotic PSO algorithms like chaotic PSO with the logistic map, chaotic PSO with the tent map and chaotic catfish PSO with the logistic map, chaotic PID controlling PSO exhibits much better search efficiency and quality when solving the optimization problems. Additionally, the parameter estimation of a nonlinear dynamic system also further clarifies its superiority to chaotic catfish PSO, genetic algorithm (GA) and PSO.