A new MOPSO algorithm for solving mathematical test functions and control engineering problems

Abstract

In this article, a new multiobjective particle swarm optimization (MOPSO) algorithm is introduced to improve the performance of a sliding mode based robust fuzzy proportional–integral–derivative (PID) controller. In this regard, the non-dominated solution having minimum number of neighbors is considered as the global best position, while the sigma values of the members are employed to determine the personal best position. A modified multiple-crossover operator is combined with the operators of the particle swarm optimization to significantly increase the convergence speed of the algorithm. To limit the size of the archive, a dynamical elimination scheme defined in the Euclidean space is introduced. Besides, iteration-based linear relations are implemented to adaptively compute the inertia weight and learning coefficients. To evaluate the effectiveness of the introduced MOPSO algorithm, the requirements are conducted by means of three benchmark functions with regard to generational distance, spacing, and maximum spread metrics. This analysis demonstrates that the proposed algorithm operates better through comparison with well-known elitist multiobjective evolutionary algorithms. Moreover, the MOPSO algorithm is applied for optimal design of a hybrid robust fuzzy PID controller for a pneumatic system with two bellows. Conflicting objective functions are considered as the normalized values of overshoot and settling time of the displacement between the bellows that should be simultaneously minimized. The feasibility and efficiency of the strategy are assessed in comparison with the conventional controllers.