Simple paricle swarm optimization

It is well known that the dynamic properties of the particles in the particle swarm optimization (PSO) can be described by a second-order difference equation. The convergent properties of the particle are then governed by the roots of the characteristic equation. The roots, or referred to eigenvalues, are functions of the coefficients, which are determined by the inertia weight and acceleration constants of PSO. Inspecting the characteristic equation, it is found that using less parameter for PSO is possible. Two versions of simplified PSO are thus derived directly from the characteristic equation. By testing on a set of benchmark functions, the feasibility and effectiveness of the proposed algorithm are validated. The experimental results demonstrate good performance, especially in multimodal functions, compared with the classical PSO. A byproduct of saving computational operations is also achieved with fewer parameters.