## 1 Introduction
However, clustering centers of traditional FCM are optimized according to gradient descent algorithm, which has the disadvantage of being time-consuming [19] and sensitive to initial centroids [20]. Moreover, many problems have no priori knowledge on the number of clusters in practice. In these circumstances, the optimization may fall into local extremum, rather than a global optimal solution. In [21], in order to improve the calculation efficiency of FCM, a random sampling plus extension FCM (rseFCM) algorithm was proposed to cluster big data. On the basis of rseFCM, geometric progressive FCM (GPFCM) and minimum sample estimate random FCM (MSERFCM) were designed in [22]. To search global optimal centroids, many intelligent iterative optimization algorithms were applied. In [20], a genetic algorithm (GA) was integrated to optimize the membership functions and centroids in the FCM model. The experimental tests are conducted to verify the effectiveness of the proposed approach. The traffic volume data collected at different temporal scales were treated as the testing dataset, and three different indicators, including root mean square error, correlation coefficient, and relative accuracy, were utilized to quantify the imputation performance compared with some conventional methods. In [23], particle swarm optimization FCM (PSO-FCM) was applied for image segmentation, and the results of the experiments showed that the accuracy and the calculation time were, respectively, 97.86% and 15.7419 s for the composite image. A hybrid algorithm, unsupervised ant colony optimization (UACO), was proposed by combining FCM and ant colony optimization (ACO) for medical image segmentation in [24]. It can be summarized from the literature that improvements on FCM mainly focus on reducing the calculation time and avoiding falling into local optimal clustering centers. Since the 1960s, many meta-heuristic intelligent optimization algorithms have been proposed to solve multi-object extremum, such as GA [25], particle swarm optimization (PSO) [26], artificial bee colony (ABC) [27], tabu search [28], differential evolution algorithm [29], et al. A considerable number of them are inspired by natural behavior and embody the principle of \"select the most superior solution from superior solutions\" [30]. While the above methods are often focused on only part of the links during the searching process, none of them has a comprehensive performance in all aspects. GA has outstanding ability in global searching, while the genetic operations are complex and time-consuming [31]. The iteration time of PSO and ABC is relatively rapid, but easily falls into local extremes [32]. The artificial fish swarm algorithm (AFSA) has a slow convergence rate in the later phase of iterations [33]. In order to overcome the disadvantages of single optimization algorithm, a hybrid PSO-GA algorithm was proposed to solve the scheduling problem in machine tool production in [34]. In [35], ABC and GA were integrated for neural network training and the clustering process. To forecast electricity load, a forecasting model based on GA and ACO was proposed in [36], and the experimental results showed that the proposed hybrid model performed better in load prediction 24 h ahead in terms of mean absolute percentage error than the other methods. In 2012, a fruit fly optimization algorithm (FOA) was first proposed by [PERSON] through simulating the food finding process of fruit flies and resulted in extensive attention [37]. As the characteristics of fast convergence and simple structure compared with other solutions, FOA was widely applied in parameter optimization [38], forecasting [39], scheduling [40], etc. However, like other optimization algorithms, the basic FOA also has the possibility of falling into local extremum due to poor population diversity during the iterative process [41]. In [42], in order to avoid local optimal solution, swarm collaboration and random perturbation were added into the original FOA to solve the joint replenishment problems.