ORIGINAL ARTICLE A hybrid optimization method with PSO and GA to automatically design Type-1 and Type-2 fuzzy logic controllers Ricardo Martı ´nez-Soto • Oscar Castillo • Luis T. Aguilar • Antonio Rodriguez Received: 9 October 2012 / Accepted: 8 April 2013 Ó Springer-Verlag Berlin Heidelberg 2013 Abstract In this paper we propose the use of a hybrid PSO- GA optimization method for automatic design of fuzzy logic controllers (FLC) to minimize the steady state error of a plant’s response. We test the optimal FLC obtained by the hybrid PSO-GA method using benchmark control plants. The bio-inspired and the evolutionary methods are used to ﬁnd the parameters of the membership functions of the FLC to obtain the optimal controller. Simulation results are obtained to show the feasibility of the proposed approach. A comparison is also made among the proposed Hybrid PSO-GA, GA and PSO to determine if there is a signiﬁcant difference in the results. Keywords Fuzzy logic controllers  Genetic algorithms  Particle swarm optimization 1 Introduction Optimization is a term used to refer to a branch of com- putational science concerned with ﬁnding the ‘‘best’’ solution to a problem. Here, ‘‘best’’ refers to an acceptable (or satisfactory) solution to a problem, which may be the absolute best over a set of candidate solutions, or a good alternative of the candidate solutions. The characteristics and requirements of the problem determine whether the overall best solution can be found [10]. Bio-inspired opti- mization algorithms are search methods, where the goal is to ﬁnd a solution to an optimization problem, such that a given objective function is optimized, possibly subject to a set of constraints [10, 23–25, 30]. Some optimization methods are based on populations of solutions [30]. Unlike the classic methods of optimization, in this case, each iteration of the algorithm maintains a set of solutions. These methods are based on generating, selecting, com- bining and replacing a set of solutions. Since they maintain and they manipulate a set, instead of a unique solution throughout the entire search process, they use more com- puter time than other meta-heuristic methods. This fact can be aggravated because the ‘‘convergence’’ of the popula- tion requires a great number of iterations. For this reason a concerted effort has been dedicated to obtaining methods that are more aggressive and manage to obtain solutions of quality in a nearer horizon. This paper is concerned with bio-inspired optimization methods, and in particular the hybrid PSO-GA approach that is proposed. In this case, we combine each individual method in order to obtain the best features to design an optimal fuzzy logic controller (FLC) applied to the benchmark problems. Better results are expected of the hybrid PSO-GA method than those of traditional methods, like GA and PSO, because of the mixing of the best characteristics of both individual methods. We are also comparing the proposed method with genetic algorithms and particle swarm optimization used separately. The bio- inspired methods are used to ﬁnd the parameters of the R. Martı ´nez-Soto  A. Rodriguez School of Engineering UABC University, Tijuana, Mexico e-mail: mc.ricardo.martinez@hotmail.com A. Rodriguez e-mail: ardiaz@uabc.mx O. Castillo (&) Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Mexico e-mail: ocastillo@tectijuana.mx; ocastillo@hafsamx.org L. T. Aguilar Centro de Investigacio ´n y Desarrollo de Tecnologı ´a Digital, Instituto Polite ´cnico Nacional, Tijuana, Mexico e-mail: luis.aguilar@ieee.org 123 Int. J. Mach. Learn. & Cyber. DOI 10.1007/s13042-013-0170-8