Training ANFIS by using the artificial bee colony algorithm

Turkish Journal of Electrical Engineering & Computer Sciences http://journals.tubitak.gov.tr/elektrik/ Turk J Elec Eng & Comp Sci (2017) 25: 1669 – 1679 c TÜBİTAK ⃝ doi:10.3906/elk-1601-240 Research Article Training ANFIS by using the artificial bee colony algorithm Derviş KARABOĞA1 , Ebubekir KAYA2,∗ Department of Computer Engineering, Faculty of Engineering, Erciyes University, Kayseri, Turkey 2 Department of Computer Technologies, Nevşehir Vocational College, Nevşehir Hacı Bektaş Veli University, Nevşehir, Turkey 1 Received: 21.01.2016 • Accepted/Published Online: 09.06.2016 • Final Version: 29.05.2017 Abstract: In this study, a new adaptive network-based fuzzy inference system (ANFIS) training algorithm, the artificial bee colony (ABC) algorithm, is presented. Antecedent and conclusion parameters existing in the structure of ANFIS are optimized with the ABC algorithm and ANFIS training is realized. Identification of a set of nonlinear dynamic systems is performed in order to analyze the suggested training algorithm. The ABC algorithm is operated 30 times for each identification case and the average root mean square error (RMSE) value is obtained. Training RMSE values calculated for the four examples considered are 0.0325, 0.0215, 0.0174, and 0.0294, respectively. In addition, test error values for the same cases are respectively computed as 0.0270, 0.0186, 0.0167, and 0.0435. The results obtained are compared with those of known neuro-fuzzy-based methods frequently used in the literature in identification studies of nonlinear systems. It is shown that ANFIS can be trained successfully by using the ABC algorithm for the identification of nonlinear systems. Key words: ANFIS, swarm intelligence, artificial bee colony algorithm, nonlinear system identification 1. Introduction The adaptive network-based fuzzy inference system (ANFIS) is based on the idea of combining the learning ability of artificial neural networks and superiorities of fuzzy logic, such as humanlike decision-making and the easiness of providing expert knowledge [1]. Thus, although the learning and calculation power of artificial neural networks can be given to fuzzy logic inference systems, the ability of fuzzy logic inference systems for humanlike decision-making and provision of expert knowledge is gained by artificial neural networks. ANFIS uses artificial neural networks found in its internal structure to create the system structure and determine its variables [2]. Therefore, algorithms used in ANFIS training are important. In recent years, many studies have been conducted in this field and different algorithms have been suggested for this purpose. We can categorize these studies on the training of ANFIS into three groups: the first group is to develop a new learning algorithm for ANFIS; the second is to perform ANFIS training with existing optimization algorithms (at this stage, known optimization algorithms may be updated for ANFIS training); and the third is to perform ANFIS training by using known optimization algorithms to solve individual problems, although this group is very similar to the second. However, the second group aims to develop a more general training algorithm for ANFIS. The main learning algorithm of ANFIS is the hybrid learning algorithm, created by jointly using the least squares method and the backpropagation learning algorithm. It is seen that the number of training ∗ Correspondence: 1669 KARABOĞA and KAYA/Turk J Elec Eng & Comp Sci algorithms used for ANFIS is increasing daily, together with the recently conducted studies. We can generally list training algorithms used for ANFIS as derivative-based ones and nonderivative heuristics. Since derivativebased algorithms trip over local minima in the determination of parameters belonging to membership functions, demand for global heuristic algorithms increases. Therefore, several researchers have recently proposed heuristic search-based training algorithms for ANFIS. Ho et al. [3] performed ANFIS training with the hybrid Taguchigenetic algorithm to estimate the adequacy of vancomycin regimen. Nariman-Zadeh et al. [4] used a genetic algorithm and the singular value decomposition approach to determine antecedent and conclusion parameters of ANFIS. Chen [5] constructed a model with ANFIS for predicting business failures and used particle swarm optimization (PSO) for optimization of ANFIS parameters. Shoorehdeli et al. [6] suggested PSO and a Kalman filter-based training algorithm for ANFIS. In this study, whereas the parameters belonging to the membership functions found in the structure of ANFIS are optimized with PSO, a Kalman filter is used to find the values of the conclusion parameters. In another study conducted by Shoorehdeli et al. [7], a new hybrid learning algorithm is proposed, where PSO is used for training the antecedent part and the forgetting factor recursive least squares algorithm is employed for training the conclusion part. Jalali-Heravi and Asadollahi-Baboli [8] suggested modified ant colony algorithm-based ANFIS training for the prediction of the inhibitory activity of quinazolinone derivatives on serotonin. Khazraee et al. [9] trained ANFIS with a differential evolution for model reduction and optimization of reactive batch distillation. Priyadharsini et al. [10] proposed an artifact removal study based on ANFIS and used an artificial immune algorithm to optimize the parameters of ANFIS. In our previous study, we used the artificial bee colony (ABC) algorithm to train ANFIS for identifying nonlinear static and dynamic systems. In this study, we present an extended version of previous conference papers [11,12]. When reviewing the literature, it is seen that swarm intelligence-based algorithms, such as PSO and ACO, are used for the training of ANFIS. In this study, ANFIS training is performed with a different algorithm, which is also based on swarm intelligence, known as the ABC algorithm. The ABC algorithm, invented by Karaboga in 2005, is an optimization algorithm showing the intelligent foraging behavior of honey bee swarms [13,14]. It found a wide application area and is used to solve real-world problems [15–17]. The ABC algorithm was used in many different applications and fields: neural networks, such as feed-forward neural networks; multilayer perception neural networks; RBF neural networks; and recurrent neural networks, which were trained by using the ABC algorithm [18]. At the same time, many studies have been conducted in the fields of electrical engineering, electronics engineering, civil engineering, software engineering, control engineering, industrial engineering, and mechanical engineering [15–18]. In addition, the ABC algorithm has been applied to different fields including data mining, sensor networks, image processing, numerical problems, and protein structure optimization [17–19]. Besides these studies, different versions of the ABC algorithm have been developed, namely c (...truncated)