Fractional Order Darwinian Particle Swarm Optimization (original) (raw)

Particle swarm optimization with fractional-order velocity

Nonlinear Dynamics, 2010

This paper proposes a novel method for controlling the convergence rate of a particle swarm optimization algorithm using fractional calculus (FC) concepts. The optimization is tested for several wellknown functions and the relationship between the fractional order velocity and the convergence of the algorithm is observed. The FC demonstrates a potential for interpreting evolution of the algorithm and to control its convergence.

Introducing the fractional-order Darwinian PSO

2012

One of the most well-known bio-inspired algorithms used in optimization problems is the particle swarm optimization (PSO), which basically consists on a machinelearning technique loosely inspired by birds flocking in search of food. More specifically, it consists of a number of particles that collectively move on the search space in search of the global optimum. The Darwinian particle swarm optimization (DPSO) is an evolutionary algorithm that extends the PSO using natural selection, or survival of the fittest, to enhance the ability to escape from local optima. This paper firstly presents a survey on PSO algorithms mainly focusing on the DPSO. Afterward, a method for controlling the convergence rate of the DPSO using fractional calculus (FC) concepts is proposed. The fractional-order optimization algorithm, denoted as FO-DPSO, is tested using several well-known functions, and the relationship between the fractional-order velocity and the convergence of the algorithm is observed. Moreover, experimental results show that the FO-DPSO significantly outperforms the previously presented FO-PSO.

Fractional Particle Swarm Optimization

Mathematical Methods in Engineering, 2014

The paper addresses new perspective of the PSO including a fractional block. The local gain is replaced by one of fractional order considering several previous positions of the PSO particles. The algorithm is evaluated for several well known test functions and the relationship between the fractional order and the convergence of the algorithm is observed. The fractional order influences directly the algorithm convergence rate demonstrating a large potencial for developments.

Fractional Order Dynamics in a Particle Swarm Optimization Algorithm

Seventh International Conference on Intelligent Systems Design and Applications (ISDA 2007), 2007

Although many mathematicians have searched on the fractional calculus since many years ago, its application in engineering, especially in modeling and control, does not have many antecedents. Since there is much freedom in choosing the order of differentiator and integrator in fractional calculus, it is possible to model the physical systems accurately. This paper deals with the time-domain identification fractional-order chaotic systems, where conventional derivation is replaced by a fractional one with the help of a non-integer derivation. This operator is itself approximated by an N-dimensional system composed of an integrator and a phase-lead filter. A hybrid particle swarm optimization (PSO)-genetic algorithm (GA) method is applied to estimate the parameters of the approximated non-linear fractional-order chaotic system modeled by a statespace representation. The feasibility of this approach is demonstrated through identifying the parameters of the approximated fractional-order Lorenz chaotic system. The performance of the proposed algorithm is compared with GA and standard particle swarm optimization (SPSO) in terms of parameter accuracy and cost function. In order to evaluate the identification accuracy, the time-domain output error is designed as the fitness function for parameter optimization. The simulation results show that the proposed method is more successful than the other algorithms for parameter identification of the fractional-order chaotic systems.

Fractional dynamics in particle swarm optimization

Systems, Man and …, 2007

This paper studies the fractional dynamics during the evolution of a Particle Swarm Optimization (PSO). Some swarm particles of the initial population are randomly changed for stimulating the system response. After the result is compared with a reference situation. The perturbation effect in the PSO evolution is observed in the perspective of the time behavior of the fitness of the best individual position visited by the replaced particles. The dynamics is investigated through the median of a sample of experiments, while adopting the Fourier analysis for describing the phenomena. The influence of the PSO parameters upon the global dynamics is also analyzed by performing several experiments for distinct values.

An Optimal Fractional Order Controller for an AVR System Using Particle Swarm Optimization Algorithm

Conference on Power Engineering Large Engineering Systems, 2007

Application of fractional order PID (FOPID) controller to an automatic voltage regulator (AVR) is presented and studied in this paper. An FOPID is a PID whose derivative and integral orders are fractional numbers rather than integers. Design stage of such a controller consists of determining five parameters. This paper employs particle swarm optimization (PSO) algorithm to carry out the aforementioned

Fractional particle swarm optimization in multidimensional search space

2010

Abstract In this paper, we propose two novel techniques, which successfully address several major problems in the field of particle swarm optimization (PSO) and promise a significant breakthrough over complex multimodal optimization problems at high dimensions. The first one, which is the so-called multidimensional (MD) PSO, re-forms the native structure of swarm particles in such a way that they can make interdimensional passes with a dedicated dimensional PSO process.

Dynamic multi-swarm particle swarm optimization with fractional global best formation

2010

Abstract Particle swarm optimization (PSO) has been initially proposed as an optimization technique for static environments; however, many real problems are dynamic, meaning that the environment and the characteristics of the global optimum can change over time. Thanks to its stochastic and population based nature, PSO can avoid being trapped in local optima and find the global optimum.

Introducing the fractional order robotic Darwinian PSO

2012

A high power ion thruster for deep space missions Rev. Sci. Instrum. 83, 073306 (2012) Design and control of a decoupled two degree of freedom translational parallel micro-positioning stage Rev. Sci. Instrum. 83, 045105 (2012) Magnetic navigation system for the precise helical and translational motions of a microrobot in human blood vessels J. Appl. Phys. 111, 07E702 Robotic reconnaissance platform. I. Spectroscopic instruments with rangefinders Rev. Sci. Instrum. 82, 113107 Actuation of a robotic fish caudal fin for low reaction torque Rev. Sci. Instrum. 82, 075114 Additional information on AIP Conf. Proc. is an evolutionary algorithm that extends the Particle Swarm Optimization using natural selection to enhance the ability to escape from sub-optimal solutions. An extension of the DPSO to multi-robot applications has been recently proposed and denoted as Robotic Darwinian PSO (RDPSO), benefiting from the dynamical partitioning of the whole population of robots, hence decreasing the amount of required information exchange among robots. This paper further extends the previously proposed algorithm using fractional calculus concepts to control the convergence rate, while considering the robot dynamical characteristics. Moreover, to improve the convergence analysis of the RDPSO, an adjustment of the fractional coefficient based on mobile robot constraints is presented and experimentally assessed with 2 real platforms. Afterwards, this novel fractional-order RDPSO is evaluated in 12 physical robots being further explored using a larger population of 100 simulated mobile robots within a larger scenario. Experimental results show that changing the fractional coefficient does not significantly improve the final solution but presents a significant influence in the convergence time because of its inherent memory property.

Fractional-order quantum particle swarm optimization

PLOS ONE, 2019

Motivated by the concepts of quantum mechanics and particle swarm optimization (PSO), quantum-behaved particle swarm optimization (QPSO) was developed to achieve better global search ability. This paper proposes a new method to improve the global search ability of QPSO with fractional calculus (FC). Based on one of the most frequently used fractional differential definitions, the Grü nwald-Letnikov definition, we introduce its discrete expression into the position updating of QPSO. Extensive experiments on well-known benchmark functions were performed to evaluate the performance of the proposed fractional-order quantum particle swarm optimization (FQPSO). The experimental results demonstrate its superior ability in achieving optimal solutions for several different optimizations.