Robust optimization of ANFIS based on a new modified GA

doi:10.1016/j.neucom.2015.03.060

Neurocomputing

Volume 166, 20 October 2015, Pages 357-366

https://doi.org/10.1016/j.neucom.2015.03.060 Get rights and content

Abstract

Adaptive Network-based Fuzzy Inference Systems (ANFIS) is one of the most well-known predictions modeling technique utilized to find the superlative relationship between input and output parameters in different processes. Training the adaptive modeling parameters in ANFIS is still a challengeable problem which has been recently considered by researchers. Hybridizing of a robust optimization algorithm with ANFIS as its training algorithm provides a scope to improve the effectiveness of membership functions and fuzzy rules in the model. In this paper, a new Modified Genetic Algorithm (MGA) by using a new type of population is proposed to optimize the modeling parameters for membership functions and fuzzy rules in ANFIS. As well, a case study on a machining process is considered to illustrate the robustness of the proposed training technique in prediction of machining performances. The prediction results have demonstrated the superiority of the presented hybrid ANFIS–MGA in term of prediction accuracy (with 97.74%) over the other techniques such as hybridization of ANFIS with Genetic Algorithm (GA), Taguchi-GA, Hybrid Learning algorithm (HL), Leave-One-Out Cross-Validation (LOO-CV), Particle Swarm Optimization (PSO) and Grid Partition method (GP), as well as RBFN and basic Grid Partition Method (GPM). In addition, an attempt is done to specify the effectiveness of different improvement rates on the prediction result and measuring the number of function evaluations required. The comparison result reveals that MGA with improvement rate 0.8 raises the convergence speed and accuracy of the prediction results compared to GA.

Introduction

Modeling techniques are classified into mechanistic and empirical. Mechanistic models such as regression require complex physical understanding of the modeling process [3], [47]. Also there are not enough suitable explicit models for the various processes [4]. Thus, empirical models such as artificial neural network (ANN) and fuzzy logic (FL) are commonly employed by many processes [27].

ANN is the most common empirical techniques applied for modeling. On the other hand, FL also plays an important role in input–output and in-process parameter relationship modeling [33] to describe human thinking and reasoning in a mathematical framework [34]. As well, integration of ANN and FL or adaptive network-based fuzzy inference systems (ANFIS) is considered efficiently as a modeling technique. ANFIS is a hybrid technique which integrates the advantage of learning in ANN and employing a set of fuzzy if–then rules with appropriate membership functions to generate input–output pairs with high degree of accuracy [18], [24], [2], [32]. In the recent years, ANFIS system is widely employed to produce non-linear models of processes to determine the input–output relationship. As well, the authors Cus et al. [6] and Mukherjee and Ray [33] observed that ANFIS technique is an effective means of control in complex manufacturing process.

Although, ANFIS is a robust modeling technique in various applications, but it has some disadvantages of artificiality, randomness and irregularity [48] and needs to be trained to work successfully. Consequently, an effective training algorithm is applied to find optimal values of adaptive modeling parameters. The main problem discussed is complexity of training membership functions׳ parameters (premise parameters) and fuzzy rules׳ parameters (consequent parameters). So they become very important parameters in training process [38]. The basic and most usual training algorithm is based on gradient descent (GD), while calculation of that in each step of training is difficult and the use of chain rule may cause trapping into local minimum [18], [21].

In the recent years, some affords have been done to find optimal value for modeling parameters in order to decline training error and increase the modeling accuracy such as Li et al. [23]. Genetic algorithm (GA) is an optimization technique which has been employed effectively by the previous researchers to determine optimal values of modeling parameters [16] and improve the training accuracy performance [21]. The researchers, Rangajanardhaa and Rao [36], Carrano et al. [5], Wei and Cheng [42], and Wang et al. [41] employed GA as a training algorithm to increase the accuracy of ANFIS and minimize the prediction error during training and testing of the network. As well, Wei [43] utilized ANFIS–GA model for Stock market forecasting. In addition, Ho et al. [15] applied a new modified GA based on Taguchi method as ANFIS training algorithm. Also, [37] developed a training algorithm for ANFIS based on HL which is the integration of least squares and back propagation gradient descent methods. Furthermore, LOO-CV approach was employed by Dong and Wang [11] for training a prediction model based on ANFIS. As well, Sharkawy [37] developed radial basis function neural networks to get the best prediction accuracy for a process. Moreover, Yang et al. [44], [45] presented the Grid Partition Method (GPM) to integrate the advantages of GA and genetic programming in ANFIS training.

In this paper, a new modified GA is employed as ANFIS training algorithm to estimate the most suitable membership function and fuzzy rules for the model and find the best prediction model by improving prediction accuracy. An experimental dataset on a machining process is considered as a test case in this study to show the effectiveness of proposed hybrid modeling technique (ANFIS–GA). Additionally, the prediction results of the proposed model are compared with several techniques considered in the literature. Moreover, some results are given to show the performance of various MGA factors on prediction error.

Section snippets

ANFIS training

The basic architecture of ANFIS consists of five layers [20] with different functions. Two layers in the model include adaptive parameters while the parameters considered in the others are fixed. Adaptive parameters are classified into premise and consequent parameters. Premise parameters in the model are related to the membership functions determined in the first layer [18] such as Gaussian function (see Eq. (1)). $μ_{i} (x) = e^{\frac{- {(x - c_{i})}^{2}}{2 {a_{i}}^{2}}}$ where $a_{i}$ and $c_{i}$ are the premise parameters. By changing the

Modified genetic algorithm (MGA)

Genetic algorithm (GA) is a stochastic optimization technique which starts with a collection of random solutions (chromosome). These chromosomes progress in consecutive iterations and are measured by a fitness function. As the evolution procedure continues, GA search procedure finally converges to an optimal chromosome [32]. Optimization result in GA is started with generating a random population (as current population) and is based on three basic functions called selection, crossover, and

The proposed hybrid prediction model

MGA optimization technique is developed in this paper as training algorithm to optimize the modeling parameters of the ANFIS. This technique is organized to minimize the following objective function, $\min G (s_{1}, s_{2}, \dots, s_{β})$ where G is RMSE value of the performances predicted by ANFIS while it is set by modeling parameters $s_{1}, s_{2}, \dots, s_{β}$ . As well, $β$ is the number of modeling parameters which need to be optimized. Also, there are some constraints on the input parameters values bounds which are satisfied by

Experimental design

The proposed hybrid approach (ANFIS–MGA) is applied and evaluated to model an end milling process with the experimental data conducted by Lou and Chen [26] where it is then referred by Dong and Wang [11], Lo [24], and Ho et al. [15]. In the experiment, a high-speed steel (HSS) four-flute end milling cutter with a diameter of 3/4″ was used to machine 6061 aluminum alloy. Spindle speed ( $S_{S}$ ), feed rate ( $F_{r}$ ) and depth of cut ( $D_{c}$ ) have been selected as the machining parameters with three linguistic

Modeling results

The proposed algorithms were implemented by using Matlab R2009a. The modeling result is presented in two parts. In the first part, the optimization result of modeling parameters after training process are addressed to show the best fuzzy rules and membership function in the experiment. Then, the prediction results of the ANFIS model using testing dataset are measured to indicate the effectiveness of the proposed training algorithm.

Conclusion and future works

In this paper, a hybrid technique based on ANFIS and modified genetic algorithm (MGA) was proposed as an effective prediction model in machining processes. In the proposed hybrid technique, MGA was utilized to find optimal modeling parameters to generate the best membership functions and fuzzy rules for ANFIS. MGA employed a new type of population and fitness function to considerably enhance the quality of the initial population, convergence speed and accuracy of the model. The main properties

Arezoo Sarkheyli Ph.D. Researcher in Soft Computing Research Group, Faculty of Computing, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia.

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Arezoo Sarkheyli Ph.D. Researcher in Soft Computing Research Group, Faculty of Computing, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia.

Azlan Mohd Zain Senior Lecturer in Soft Computing Research Group, Faculty of Computing, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia.

Safian Sharif Associate Professor in Department of Manufacturing and Industrial Engineering, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia.

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Robust optimization of ANFIS based on a new modified GA

Abstract

Introduction

Section snippets

ANFIS training

Modified genetic algorithm (MGA)

The proposed hybrid prediction model

Experimental design

Modeling results

Conclusion and future works

Appl. Math. Model.

Expert Syst. Appl.

Expert Syst. Appl.

Appl. Soft Comput.

J. Mater. Process. Technol.

J. Mater. Process. Technol.

Ecol. Model.

Expert Syst. Appl.

Comput. Ind. Eng.

J. Hydrol.

Int. J. Mach. Tools Manuf.

Applied Soft Computing

Expert Syst. Appl.

Combining fuzzy logic and neural networks in modeling landfill gas production

World Acad. Sci. Eng. Technol.