An improved heterogeneous multi-swarm PSO algorithm to generate an optimal T-S fuzzy model of a hydraulic process

In this paper, a new methodology to develop an Optimal Fuzzy model (OptiFel) using an improved Multi-swarm Particle Swarm Optimization (MsPSO) algorithm is proposed with a new adaptive inertia weight based on Grey relational analysis. Since the classical MsPSO suffers from premature convergence and can be trapped into local optima, which significantly affects the model accuracy, a modified MsPSO algorithm is presented here. The most important advantage of the proposed algorithm is the adjustment of fewer parameters in which the main parameter is the inertia weight. In fact, the control of this parameter could facilitate the convergence and prevent an explosion of the swarm. The performance of the proposed algorithm is evaluated by adopting standard tests and indicators which are reported in the specialized literature. The proposed Grey MsPSO is first applied to solve the optimization problems of six benchmark functions and then, compared with the other nine variants of particle swarm optimization. In order to demonstrate the higher search performance of the proposed algorithm, the comparison is then made via two performance tests such as the standard deviation and central processing unit time. To further validate the generalization ability of the Improved OptiFel approach, the proposed algorithm is secondly applied on the Box–Jenkins Gas Furnace system and on a irrigation station prototype. A comparative study based on Mean Square Error is then performed between the proposed approach and other existing methods. As a result, the improved Grey MsPSO is well adopted to find an optimal model for the real processes with high accuracy and strong generalization ability.