A penalty approach to handle inequality constraints in particle swarm optimization

This paper proposes a penalty method for solving nonlinear optimization problems with inequalities by the particle swarm optimization (PSO) algorithm. The proposed method is not only very simple but also useful. One should only search for the global solution of a series of unconstrained minimization problems simply by a standard PSO algorithm. It does not require to check the feasibility of search points during the search. Moreover, it is shown that the global best solution gets feasible as the penalty parameter is increased to a sufficiently but finitely large value. The proposed method is verified by numerical experiments to famous benchmark problems.