Shrinking hypersphere based trajectory of particles in PSO

This paper proposes a new Shrinking Hypersphere PSO (SHPSO) for continuous function optimization. The global best and personal best fly in the search space in the form of a hypersphere instead of particles. The hyperspheres keep on shrinking as the iterations proceed and the velocity and position update equations are applied at each iteration. The theoretical convergence of the SHPSO is proved. Then the performance of the proposed SHPSO is compared with five well known PSO variants namely basic PSO, Trelea I PSO, Trelea II PSO, Clerc PSO and SPSO 2011. The basis of comparison is 24 benchmark problems selected from collection of CEC benchmark problem set. The analysis is performed with t-Test, performance index, empirical cumulative distribution and time complexity. It is concluded that the proposed SHPSO is a promising new variant of PSO which will open new doors of research in this area.