Introducing the fractional-order Darwinian PSO

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 M. S. Couceiro (B) · N. M. F. Ferreira RoboCorp, Department of Electrotechnics Engineering, Engineering Institute of Coimbra, Coimbra, Portugal e-mail: [email protected] N. M. F. Ferreira e-mail: [email protected] M. S. Couceiro · R. P. Rocha Mobile Robotics Laboratory, Institute of Systems and Robotics, University of Coimbra, Pólo 2, Portugal e-mail: [email protected] R. P. Rocha e-mail: [email protected] J. A. T. Machado Department of Electrotechnics Engineering, Engineering Institute of Porto, Porto, Portugal e-mail: [email protected] 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.