A finite-time particle swarm optimization algorithm

This paper deals with a class of optimization problems by designing and analyzing a finite-time particle swarm optimization (FPSO) algorithm. Two versions of the FPSO algorithm, which consist of a continuous-time FPSO algorithm and a discrete-time FPSO algorithm, are proposed. Firstly, the continuous-time FPSO algorithm is derived from the continuous model of the particle swarm optimization (PSO) algorithm by introducing a nonlinear damping item that can enable the continuous-time FPSO algorithm to converge within a finite-time interval and a parameter that can enhance the exploration capability of the continuous-time FPSO algorithm. Secondly, the corresponding discrete-time version of the FPSO algorithm is proposed by employing the same discretization scheme as the generalized particle swarm optimization (GPSO) such that the exploiting capability of the discrete-time FPSO algorithm is improved. Thirdly, a Lyapunov approach is used to analyze the finite-time convergence of the continuous-time FPSO algorithm and the stability region of the discrete-time FPSO algorithm is also given. Finally, the performance capabilities of the proposed discrete-time FPSO algorithm are illustrated by using three wellknown benchmark functions (global minimum surrounded by multiple minima): Griewank, Rastrigin, and Ackley. In terms of numerical simulation results, the proposed continuous-time FPSO algorithm is used to deal with the problem of odor source localization by coordinating a group of robots.

[1]  José Neves,et al.  The fully informed particle swarm: simpler, maybe better , 2004, IEEE Transactions on Evolutionary Computation.

[2]  Jacek M. Zurada,et al.  An approach to multimodal biomedical image registration utilizing particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[3]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[4]  Reza Olfati-Saber,et al.  Flocking for multi-agent dynamic systems: algorithms and theory , 2006, IEEE Transactions on Automatic Control.

[5]  J. Fernández-Martínez,et al.  Stochastic Stability Analysis of the Linear Continuous and Discrete PSO Models , 2011, IEEE Transactions on Evolutionary Computation.

[6]  I. Couzin,et al.  Effective leadership and decision-making in animal groups on the move , 2005, Nature.

[7]  J. Farrell,et al.  Filament-Based Atmospheric Dispersion Model to Achieve Short Time-Scale Structure of Odor Plumes , 2002 .

[8]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[9]  Long Wang,et al.  Finite-time formation control for multi-agent systems , 2009, Autom..

[10]  Juan Luis Fern.  Stochastic Stability Analysis of the Linear Continuous and Discrete PSO Models , 2011 .

[11]  Russell C. Eberhart,et al.  Parameter Selection in Particle Swarm Optimization , 1998, Evolutionary Programming.

[12]  Jorge Cortés,et al.  Finite-time convergent gradient flows with applications to network consensus , 2006, Autom..

[13]  J. F. Martínez,et al.  The generalized PSO: a new door to PSO evolution , 2008 .

[14]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[15]  Qiang Lu,et al.  A distributed coordination control scheme for odor source localization , 2010, IECON 2010 - 36th Annual Conference on IEEE Industrial Electronics Society.

[16]  Visakan Kadirkamanathan,et al.  Stability analysis of the particle dynamics in particle swarm optimizer , 2006, IEEE Transactions on Evolutionary Computation.

[17]  Juan Luis Fernández-Martínez,et al.  Theoretical analysis of particle swarm trajectories through a mechanical analogy , 2008 .