Probabilistic Opposition-based Particle Swarm Optimization with Velocity Clamping Farrukh Shahzad farrukh.shahzad@nexginrc.org Next Generation Intelligent Networks Research Center, FAST-National University of Computer and Emerging Sciences, Islamabad, 44000, Pakistan Sohail Masood rsmbhatti@gmail.com FAST-National University of Computer and Emerging Sciences, Islamabad, 44000, Pakistan Naveed Kazim Khan naveed.kazim@nu.edu.pk FAST-National University of Computer and Emerging Sciences, Islamabad, 44000, Pak- istan Received: Jul 26, 2012 – Revised: Jan 30, 2013 – Accepted: Feb 18, 2013 Abstract A probabilistic Opposition-based Particle Swarm Optimization algorithm with Veloc- ity Clamping and inertia weights (OvcPSO) is designed for function optimization – to accelerate the convergence speed and to optimize solution’s accuracy on standard benchmark functions. In this work, probabilistic opposition-based learning for parti- cles is incorporated with PSO to enhance the convergence rate – it uses velocity clamp- ing and inertia weights to control the position, speed and direction of particles to avoid premature convergence. A comprehensive set of 58 complex benchmark functions in- cluding a wide range of dimensions have been used for experimental verification. It is evident from the results that OvcPSO can deal with complex optimization problems effectively and efficiently. A series of experiments have been performed to investigate the influence of population size and dimensions upon the performance of different PSO variants. It also outperforms FDR-PSO, CLPSO, FIPS, CPSO-H and GOPSO on various benchmark functions. Last but not the least, OvcPSO has also been compared with Opposition-based Differential Evolution (ODE); it outperforms ODE on lower swarm population and higher dimensional functions. Keywords Swarm Intelligence, Function Optimization, Particle Swarm Optimiza- tion, Probabilistic Opposition-based Learning 1 Introduction Particle swarm optimization (PSO) is a population based stochastic algorithm devel- oped for continuous optimization problem by Kennedy et al. [14]. The inspiration has come from bird flocking in nature. Researchers have developed numerous variants and applications of PSO [3], [13] and [18] etc. Some researcher have also used PSO for feature selection and parameter tuning etc. [16] and multi-objective optimization [4]. In PSO, each bird is referred as a particle. All particles are initialized with random position and random velocity. Each particle moves to the new position on the basis of its own experience and the experience of all particles in its neighborhood. The particle updates its velocity and position parameters using equation (1) and (2) respectively. c 2012 Knowl. Info. Sys. x(x): xxx-xxx