1. Introduction
In the past three decades, energy consumption in developing countries has increased more than fourfold and, as expected, it may increase rapidly in the upcoming years. The rapid growth of population and continuous economic development are the main reasons for increasing energy consumption in developing countries. The population is expected to increase by 15% by 2040 [
1] in the developing countries, in which the energy consumption will increase rapidly.
According to the Organization of the Petroleum Exporting Countries (OPEC), oil is still the main energy resource. The recent statistics show that oil consumption is estimated to increase from 86.5 mobe/d (million barrel of oil equivalent per day) to 92.3 mobe/d in 2020. It is estimated to increase to 97.9 mobe/d and 100.7 mobe/d in 2030 and 2040, respectively. Coal consumption in 2015, 2020, 2030, and 2040 are expected be 87.8 mobe/d, 80.7 mobe/d, 85.8 mobe/d, and 86.2 mobe/d, respectively. Gas consumption in 2015, 2020, 2030, and 2040 are expected to be 59.2 mobe/d, 65.2 mobe/d, 79.9 mobe/d and 93.2 mobe/d, respectively. Thus, oil can be considered as the main energy resource in the world. Therefore, it is very critical to forecast a country’s oil consumption to fomulate the necessary strategies for the major economic and social problems. From 2015 to 2040, the global population is estimated to increase by 1.8 billion people (from 7.3 billion in 2015 to 9.2 billion in 2040). This increased population will mainly come from developing countries, specifically from Middle East countries, African countries, and India [
1].
Oil consumption is a strategic problem because it is not only related to the issue of economic strategies and plans, but the the environmental impact is also a critical issue. It plays a vital role in environmental issues such as air pollution problems and green energy solutions. Many studies have been presented to estimate oil consumption in different countries. Yu et al. [
2] presented an online big data driven model to forecast oil consumption by using the power of Google trend. The proposed model contains two steps: the relationship investigation and the prediction improvement. They also used the Granger causality analysis to test the power of Google trend. They concluded that Google trend improves forecasting results. Azadeh et al. [
3] presented a Fuzzy regression model for forecasting oil consumption in the US, Japan, Australia, and Canada. They used the analysis of variance method to select the conventional regression or fuzzy regression to estimate the future demand. Their proposed method achieved the minimum absolute percentage error. Li et al. [
4] used a combination of artificial intelligence algorithms to predict oil consumption in China. They concluded that the combination model outperforms traditional forecasting models in terms of performance and forecasting results.
Moreover, the Adaptive Neuro-Fuzzy Inference System (ANFIS) has received more attention since it is a universal model and a hybrid intelligent system, which combines the learning and modeling power of the fuzzy inference system (FIS), and neural networks into an adaptive inference system. Furthermore, ANFIS outperforms nonlinear mathematical prediction models, such as those in [
5,
6]. Therefore, ANFIS can be applied to more advanced applications such as recommender systems [
7] and image segmentation [
8]. Moreover, ANFIS has been successfully applied to several time series prediction applications such as water consumption prediction [
9], used cars price prediction [
10], water treatment [
11], forecasting the success of tourism services [
12], and wind power forecasting [
13]. Yurdusev et al. [
9] used several predicting methods including ANFIS to forecast water consumption. Wu et al. [
10] proposed an ANFIS forecasting model for used cars prices. The proposed model was compared to a neural network model and the evaluation results showed that ANFIS had more possibilities to predict used car prices. Mandal et al. [
11] presented an ANFIS based forecasting method for the removal of Hexavalent chromium and arsenite from water. The proposed method achieved good accuracy with small average absolute relative percentage error. Atsalakis et al. [
12] presented an ANFIS model to forecast the success of tourism services. They collected data through a questionnaire related to tourism services development. The evaluation results show that ANFIS provided an intelligent way to find the relationships of input and output variables that improved forecasting results. Liu et al. [
13] proposed a combination model of ANFIS and neural network to forecast wind power in China. The evaluation showed that the combination model outperforms traditional forecasting models.
However, ANFIS is influenced by the approaches that are used to learn its parameters. The consequent and premise parameters are the two sets of ANFIS adjustable parameters. Some methods have been employed to determine the optimal parameter values of ANFIS such as the least square method (LSM). However, LSM can get stuck at a local optimal point. Thus, a hybrid between LSM and back-propagation (BP) is presented [
14].
Recently, meta-heuristics (MH) algorithms have been used to train ANFIS parameters such as Particle Swarm Optimization (PSO) [
15], Genetic Algorithm (GA) [
16], and Sine–Cosine Algorithm (SCA) [
17].
In [
15], a PSO model is adopted to train ANFIS to forecast the biochar yield. However, the main drawback of PSO is its sensitivity to neighborhood topology. In [
16], a modified GA is used to optimize the modeling parameters for membership functions and fuzzy rules in ANFIS. However, GA suffers from its slow convergence speed.
In [
17], an SCA method is presented to train the ANFIS model to build an oil consumption prediction model. Although SCA outperforms GA and PSO, it has some drawbacks such as its exploration ability is higher than its exploitation in the search domain. Moreover, the No Free Lunch (NFL) theorem [
18] assumes that no optimization approach can be applied to solve different problems with the same accuracy. In the same context, the Multi-verse Optimizer (MVO) is an MH algorithm [
19]. Three basic concepts inspired MVO: white hole, black hole, and wormhole. These three concepts are improved to enhance exploration, exploitation, and local search, respectively. As described in [
19], MOV outperformed several optimization algorithms in five real engineering problems. Therefore, MVO has been successfully applied in different applications. Faris et al. [
20] employed MVO to select the optimal features and to optimize the parameters of the Support Vector Machine (SVM) algorithm. They found that, by applying MVO, the number of features is reduced but the prediction is still high. Wang et al. [
21] also applied MVO to optimize the parameters of SVM to build a prediction model for energy consumption in China. In this paper, we present an oil consumption forecasting model, namely MVO-ANFIS. The proposed method leverages the power of ANFIS to make the prediction and the power of MVO to select the accurate parameters. MVO is employed for optimizing ANFIS parameters to improve ANFIS prediction performance. The MVO-ANFIS method was evaluated by forecasting oil consumption in two countries: Korea and Italy. Moreover, MVO-ANFIS was compared to other modified ANFIS models, such as SCA-ANFIS, PSO-ANFIS, GA-ANFIS, and Whale Optimization Algorithm (WOA-ANFIS).
The main contribution of this study can be summarized as follows:
We present a novel time series prediction model, namely MVO-ANFIS. To the best of our knowledge, this is the first study that applies MVO for optimizing ANFIS.
The proposed model was employed to forecast oil consumption in two countries and achieved a robust prediction result.
We compared the proposed method with other modified ANFIS models, and the proposed method outperformed them in prediction result and speed.
The paper is organized as follows.
Section 2 presents the basic structure of the MVO-ANFIS algorithm.
Section 3 describes the dataset and experiments. The evaluated results and the conclusion are described in
Section 4 and
Section 5, respectively.
3. The Proposed Method
The proposed oil consumption forecasting model based on the modified ANFIS model using MVO is introduced in this section. The proposed MVO-ANFIS approach aims to find the set of ANFIS’s parameters using MVO that leads to minimizing the RMSE between the target and its prediction. The structure of MVO-ANFIS is similar to the traditional ANFIS model, which contains five layers, as discussed in
Section 2.1. The first layer aims to receive the historical consumption of the oil then its output to the second layer. The nodes in the second layer compute their output using Equation (
3) and the fuzzy logic rules at the third layer compute the output of this layer using Equation (
4). Meanwhile, the Takagi–Sugeno–Kang model is used in the fourth layer by using the consequent parameters. The last layer computes the prediction of oil consumption using Equation (
5). The MVO-ANFIS model starts by preprocessing the historical oil consumption by using the auto-correlation function (ACF) to determine the suitable features for using them during the forecasting process. The next step is to randomly split the dataset into training and testing, which represent 70% and 30% of the dataset, respectively. Then, MVO-ANFIS, using the fuzzy c-mean, selects the suitable number of membership functions by clustering the dataset into different groups. Thereafter, MVO (as discussed in
Section 2.2) is used to find the two types of ANFIS parameters through considering a set of solutions, each of them representing a different ANFIS model. To evaluate the quality of each solution, the Root Mean Square Error (RMSE) is used, as defined in the following equation:
where
T and
P represent the actual training oil consumption and its prediction value, respectively. Thereafter, the best solution is determined, which has the smallest fitness value (
$Fi{t}_{b}$). This best solution represents the optimal ANFIS model at the current iteration. Then, other solutions are updated based on this solution and this process is repeated until reaching the maximum number of iterations, which represents the stop condition. The next step in MVO-ANFIS is to test the quality of the best ANFIS model by applying the testing set and evaluate the prediction value using a set of measures. The last step in MVO-ANFIS is to predict oil consumption (forecasting process) for the next month. The stages of the proposed model are given in
Figure 2.