Constrained optimization by improved particle swarm optimization with the equivalent penalty coefficient method

The penalty function method has been widely used to solve constrained optimization problems. In the method, an extended objective function, which is the sum of the objective value and the constraint violation weighted by the penalty coefficient, is optimized. However, it is difficult to control the coefficient properly because the proper control depends on each problem. Recently, the equivalent penalty coefficient (EPC) method, which is a new adaptive penalty method for population-based optimization algorithms (POAs), has been proposed. The EPC method can be applied to POAs where a new solution is compared with the old solution. The EPC value, which makes the two extended objective values of the solutions the same, is used to control the coefficient. In this study, we propose to apply the EPC method to particle swarm optimization (PSO) where a new solution is compared with the best solution found so far. To improve the performance of constrained optimization, a mutation operation is also proposed. The proposed method is examined using two topologies of PSO. The advantage of the proposed method is shown by solving well-known constrained optimization problems and comparing the results with those obtained by PSO with a standard constraint-handling technique.