Comparison of Various PSO Variants with Different Mathematical Functions

The optimality of solutions is based on one or several criteria that are usually problem and user dependent. User or problem may pose some constraints on it. So, we have to find the optimal solution of constrained, complex and unpredictable problems. Various Metaheuristics can be used to solve these kinds of problems with more or less certainty. But reproducibility (or refinement) of result can be assured by quality and problem specific algorithm and efficient programming. We have tried to compare results of two variants of PSO (Neighbourhood varying inertia weight (nVIW) and Neighbourhood varying inertia weight with constriction factor (CnVIW)) on two mathematical functions (Goldstein Price function and Rosenbrock Function). These functions have shown some interesting behaviours and convergence pattern by varying different parameters. Constriction factor has proved efficacious in some cases as swarm approaches towards gbest but it was not as significant as inertia factor was in case of standard PSO. We have used Java for programming purpose which proved to be a very strong tool in dealing with complex calculations.