###### Abstract
However, recent studies have shown that cuckoo search (CS) is potentially more efficient than other algorithms in solving optimization problems in terms of better-obtained solutions [8], its well-balanced intensification/diversification search strategies [3; 28; 29; 30], robustness and precision of obtained results [7], and faster convergence speed [31]. Like almost all nature-inspired algorithms, the CS algorithm can be referred to as a meta-heuristic algorithm with two important features that make it so efficient at solving optimization problems, one is intensification or exploitation and the other is diversification or exploration. Intensification refers to focus on the search in a local region by exploiting information when a good solution has been found while diversification means the generation of diverse solutions far enough from good solutions to explore the search space on the global scale more efficiently [2; 3; 7; 29; 32; 33]. On the other hand, in contrast to classical control theory that has been successful in controlling well defined deterministic systems, many engineering problems require more sophisticated control techniques due to the presence of strong non-linearities, embedded in a changing environment with uncertainty, or are difficult to model [34]. Fuzzy logic control (FLC) technique provides a formal methodology to represent, manipulate, compute and incorporate human intelligence directly into automatic control systems [34; 35] offering potential advantages over conventional control schemes in less dependency on quantitative models, natural decision making, learning capability, a greater degree of autonomy, ease of implementation, and a friendly user interface [34; 36; 37; 38; 39]. By using the linguistic approach provided by the fuzzy theory [40], human knowledge about the system to be controlled can be integrated into control theory [41]. An analysis of the literature about FLC parameter optimization using nature-inspired CS algorithm reveals some works which will be briefly described next. In [8] CS is used to adjust the shape of the controller's triangular and trapezoidal MF for the energy management of a hybrid power system. In [42] an image edge detection system based on a type-2 fuzzy is optimized by adjusting the shape of Gaussian MF. In [43], CS is used to adjust the shape of the fuzzy controller for liquid level control. In [11], a modified CS is used to tune MF's positions of an FLC for a stationary battery storage system. In this regard, the objective of this paper is to propose a methodology to optimize FLC parameters which involve not only the MF's positions but also the RB, which is the novelty of the presented approach, using for this purpose the CS algorithm. This procedure can be applied to any problem which involves a system where this control technique is required. The CS is applied to a FLC to achieve a better performance in comparison to conventional design and according to some predefined objectives. Referring to the magnetic levitation system (MLS), these objectives are steady-state vertical position, maximum overshoot, and settling time. Based on the aim discussed above, the major contribution of this research is the new methodology for FLC parameter optimization using CS, including the RB as another degree of freedom, in such a way that a better solution for the problem to optimize is more feasible to achieve. This paper is organized as follows: The mathematical model of the MLS system is detailed in Section 2. In Section 3, The FLC design to control the MLS is presented. This FLC optimization procedure using the CS algorithm is given in Section 4, with a detailed description of the algorithm used. Finally, the simulation results and discussions are presented in Section 5.