Speciation with GP based Hybrid PSO Muhammad Rashid 1  and Abdul Rauf Baig 2 1,2 Department of Computer Science, National University of Computer and Emerging Sciences, A.K. Brohi Road, Sector H-11/4, Islamabad, Pakistan Abstract. In this study we present an extension to the PSOGP algorithm for multimodal optimization problems. PSOGP avoids premature convergence by utilizing a method wherein the swarm is made more diverse by employing a mechanism which allows each particle to use a different equation to update its velocity. This equation is also continuously evolved through the use of genetic programming to ensure adaptability. Enhancements have been proposed which make PSOGP suitable for finding solutions to multimodal optimization problems. We propose a partial random initialization strategy and a generation gap strategy. We also suggest the use of speciation which enables PSOGP to locate multiple solutions. We compare the performance of SPSOGP with SPSO and NichePSO on 5 multimodal test functions. Keywords: particle swarm optimization, genetic programming, multimodal function optimization, evolution, force generating function, species 1. Introduction Kennedy and Eberhart [10] proposed the PSO algorithm which uses a swarm of particles to explore the search space. The individual particles move about the search space in an effort to find the optima taking guidance from other particles which have higher fitness as well as from their own experiences. Each particle keeps track of its current position, current velocity and personal best position. In every iteration the velocity of the particles are updated using a force generating function which uses information about that particle’s best position, the global best position and random values to determine the change in velocity. The new velocity is then used to update the position of the particle thus enabling it to move through the search space. In PSOGP [16], enhancements were suggested which allowed both evolution and diversity to be incorporated into PSO. PSOGP utilizes different force generating functions for each particle to ensure diversity in the swarm. So in addition to keeping track of its current position, current velocity, personal best position and global best position, the particle will also keep track of the force generating function used to update its velocity. The force generating function is also evolved throughout the execution of the PSOGP, thus allowing it to adapt to the specific problem. The GP that is used to evolve the force generating function differs from the classical GP in the sense that the population size is limited (i.e. the number of programs in a generation are equal to the number of particles). The function set includes the functions +, -, × and the protected division DIV. The terminal set includes the position of the particle x, the velocity of the particle v, the personal best position of the particle p, the global best of the swarm g and a constant c. In the beginning while initializing the position of the particle the force generating function of each particle is randomly initialized. Within each iteration of PSOGP algorithm, along with updating the position of the particle and the velocity, the force generating function is also evolved using the cross over and mutation operators of genetic programming. One or two parents are selected from the original swarm at random depending upon the operator that is being applied. The particles having better fitness have a greater probability of being selected. The force generating functions of all particles are replaced with their children in every iteration. By allowing each particle to have a different force generating function and by evolving those equations through  Corresponding author. Tel.: +923335137267; fax: +92514100619. E-mail address: rashid.nuces@gmail.com. ISBN xxx-x-xxxxx-xxx-x Proceedings of 2009 IACSIT Autumn Conference Singapore, 9-11 October, 2009, pp. xxx-xxx