## 1 Introduction
in [28], a Whale optimization algorithm-based Sugeno FLC for fault ride-through improvement of grid-connected variable speed wind generators is presented by [PERSON] et al. in [29], a Fault tolerant trajectory tracking control design for interval-type-2 Takagi-Sugeno fuzzy logic system is outlined by [PERSON] et al. in [30], a Sugeno-Mamdani fuzzy system based soft computing approach toward sensor node localization with optimization is presented by [PERSON] et al. in [31], a hybrid technique of Mamdani and Sugeno-based fuzzy interference system approach is explained by [PERSON] et al. in [32], an optimization of fuzzy logic (Takagi-Sugeno) blade pitch angle controller in wind turbines by genetic algorithm is presented by [PERSON] in [33], a control and balancing of two-wheeled mobile robots using Sugeno fuzzy logic in the domain of AI techniques is presented by [PERSON] et al. in [34], and a stable Takagi-Sugeno fuzzy control designed by optimization is presented by [PERSON] et al. in [35]. The second important field in intelligent computing to evaluate metaheuristic algorithms is in mathematical functions, and some interesting related works include [PERSON] et al. presenting a New binary whale optimization algorithm for discrete optimization problems [36]; [PERSON] et al. presenting a DE with a fuzzy logic approach for dynamic parameter adjustment using benchmark functions [37]; [PERSON] et al. presenting an HS with dynamic adaptation of parameters for the optimization of a benchmark set of functions [38]; [PERSON] presents the Rao algorithms--three metaphor-less simple algorithms for solving optimization problems [39]; [PERSON] et al. presenting a barnacles mating optimizer--a new bio-inspired algorithm for solving engineering optimization problems [40]; [PERSON] et al. presenting a hybrid grasshopper optimization algorithm with invasive weed for global optimization [41]; and [PERSON] et al. presenting a bat algorithm comparison with genetic algorithm using benchmark functions [42]. Finally, an interesting work is presented by [PERSON] et al. as a combination of modified HS and DE optimization techniques in economic load dispatch [43]. Therefore, it is important to analyze the study cases that have been implemented in the works previously presented [37; 38]. In this paper, two metaheuristic algorithms are implemented, which are harmony search (HS) and differential evolutional (DE); the main purpose is to find the optimal parameters for each algorithm that allows the user to minimize the fitness functions in each of the study cases. Thus, an improvement on the original algorithm is proposed with the dynamic adaptation of parameters through the fuzzy logic system, specially to find the optimal design in the values for HS for harmony memory accepting (HMR) and pitch adjustment rate (PArate) to represent the optimized fuzzy harmony search (OFHS) and the dynamic parameters for mutation rate (F) and crossover rate (CR) for DE to represent the optimized fuzzy differential evolution (OFDE). The two proposed methods are applied for optimizing fuzzy controllers and mathematical functions, a statistical test is presented with the obtained results, and the main objective is to measure the efficiency in the performance of metaheuristic algorithms for the two study cases. The organization of the sections in this paper is described in the following. Section 2 describes two metaheuristics implemented in this paper; Differential Evolution and Harmony Search Algorithms, Section 3 describes the optimal design of fuzzy system approach for the two study cases. Section 4 describes two study cases to analyze--the first is the stabilization of trajectory for an autonomous mobile robot (AMR), and the second is the optimization in mathematical functions. Section 5 describes a comparative of the results for the metaheuristic algorithms, and a statistical test is also presented. Section 6 presents some relevant conclusions and future works for this paper.