Enhancing particle swarm optimization with binary quantum wave modulation and joint guiding forces

The searching mechanism of particle swarm optimization (PSO) derives from two principal forces of the moving direction to guide the particles toward their personal best (pbest) and the global best (gbest) positions. Modifying the behavior of the particles provides a solution to relieve the problem of local optimum trapping and increase the convergence speed. Inspired from quantum mechanics, we propose a continuous global optimization algorithm called binary quantum wave modulated particle swarm optimization (BQWPSO). The quantum particles are modulated with the binary form of wave functions, where the real positions of the particles have uncertainty that extend the searching areas. Unlike the unilateral force exerted on the particles in standard PSO and some other PSO variants, in BQWPSO both the attractive and repellent forces are jointly exerted on a particle so as to be led to a better direction to search the optimal solution. The artificial Laplacian operator is formulated to convey such information, which characterizes the momentum of a given particle. Experiments conducted on several test functions demonstrate the effectiveness of BQWPSO in solving optimization problems.