Breeder hybrid algorithm approach for natural gas

Energy 141 (2017) 1269e1284

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Energy journal homepage: www.elsevier.com/locate/energy

Breeder hybrid algorithm approach for natural gas demand forecasting model Yusuf Karadede a, b, *, Gultekin Ozdemir a, Erdal Aydemir a a b

Suleyman Demirel University, Engineering Faculty, Department of Industrial Engineering, 32260, Isparta, Turkey Kafkas University, Faculty of Engineering and Architecture, Department of Industrial Engineering, 36100, Kars, Turkey

a r t i c l e i n f o

a b s t r a c t

Article history: Received 27 September 2016 Received in revised form 25 August 2017 Accepted 26 September 2017 Available online 27 September 2017

A breeder hybrid algorithm consisting of the constitution of nonlinear regression-based breeder genetic algorithm and simulated annealing is proposed for the objective of forecasting the natural gas demand with a smaller error rate. The main aim of this study is to show general natural gas demand forecasting model of the breeder hybrid algorithm based nonlinear regression. The most important difference that distinguishes this natural gas demand forecasting model from other models in the literature is that the proposed model evolves continuously with the best solutions in both the breeder genetic algorithm and simulated annealing parts. It is applied to Turkey natural gas demand forecasting to show its superiority and applicability. The consumption amount of natural gas has between 1985 and 2000 is determined as dependent variable whereas the independent variables are determined as the gross national product, population and the growth rate. Then, the consumption amounts of natural gas between 2001 and 2014 are forecasted with significantly small MAPE values that are obtained 0.0188 and 0.0143 for year 2014 using the proposed algorithms and compared to different solutions in the literature. The proposed algorithms are superior to the comparable algorithms in the literature. Then, two scenarios are applied for the years between 2015 and 2030 for future projection. © 2017 Elsevier Ltd. All rights reserved.

Keywords: Natural gas demand forecasting Nonlinear forecasting model Breeder genetic algorithm Simulated annealing Breeder hybrid algorithm

1. Introduction 1.1. Motivation One of the main needs of humankind, energy continues and enlarges together with the history of humanity. The types of energy sources during the civilization periods varied according to requirements. The usage of solid/fossil based energy resources or their derivatives forced the humankind to find alternative energy resources due to rise of the consumptions of these kinds of energy resources day by day. When the nature is damaged by energy wastes, such as gases harmful to the environment, new energy resources mainly clean and/or green are gained importance not only by a small part of the world but also by industrialized countries. Increasing global energy consumption and the environmental impacts of fossil fuels in traditional power plants have boosted the

* Corresponding author. Suleyman Demirel University, Engineering Faculty, Department of Industrial Engineering, 32260, Isparta, Turkey. E-mail addresses: [email protected] (Y. Karadede), gultekinozdemir@ sdu.edu.tr (G. Ozdemir), [email protected] (E. Aydemir). https://doi.org/10.1016/j.energy.2017.09.130 0360-5442/© 2017 Elsevier Ltd. All rights reserved.

tendency towards renewable energy sources [1]. Today, one of such energy resources is natural gas. It is widely used as environmentally friendly energy resource for cooking, heating, transportation and industrial production. It is generally considered as a clean and efficient fossil fuel, making it attractive as an energy source [2]. Energy consumption/demand forecasting has been always playing a vital role in planning and power system management [3]. Demand for natural gas raises everyday by most of the countries of the world. For this reason, accurate forecasts of natural gas demand can be important for utilities, energy traders, regulatory authorities, decision makers and others [4]. Therefore, forecasting of natural gas usage constitutes an important part of any country's energy policy and planning, especially for developing countries. Forecasting of natural gas demand/consumption is of vital importance for its economic planning, energy investment and environment protection. Inaccurate forecasting of natural gas consumption/demand can cause to economic losses by means of the domestic production of countries. Hence, natural gas forecasting models have a large amount of interest by researchers both for today and for the near future with the objective of conducting the projections as much as accurate belonging to the future. The natural gas demand/

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Y. Karadede et al. / Energy 141 (2017) 1269e1284

Nomenclature

b

y x1 x2 x3

Ps

the amount of natural gas consumption gross national product population growth rate b coefficients of the independent variables/parameters T% the best individuals taking place in the upper ranks in the existent population or threshold energy N population size x and y chromosomes in extended intermediate recombination operator zi new offspring(s)/solution(s) n the number of the variables of an individual ai random selected a number within the range of [-0.25; 1.25] rangei the mutation range for each coefficient searchintervali the difference between the lower and upper limits of the coefficients that shall undergo mutation l generally chosen as 0.1 d the probability distribution that corresponds to a small value k random selected a number within the range of [-2; 2]

consumption equation/model parameters can be considered calendar (weekday, daytime, month, season) and weather-related (temperature, humidity, sunshine, wind speed) factors, as well as demographic (general population, number of adults and children in the household, birth rate), economic (Gross Domestic or National Product, the price of gas), etc. [5]. Modeling is becoming practically impossible as a result of the increasing complexity of problems which forced the development of many new research techniques such as Times Series Analysis, Nature-based Heuristics Search Algorithms, Artificial Neural Networks (ANNs), Fuzzy Logic Theory, and Grey System Theory [6]. In fact, there are many uncontrollable parameters (i.e. political turmoil, wars, climate change, etc.) which are affecting the forecasting results. This type of parameters must be evaluated by considering as qualitative criteria and require expert opinions and sector analyses alike expert and/or intelligent systems. If uncontrollable variables depend on expert opinions and sector analyses, then effect on the model of the variables can be measured via fuzzy logic theory by defining membership functions and can be added to as a part of the model. If effects caused by these variables have a trend, then time series analysis is used and may be added to as a part of the proposed model. If there are insufficient and incomplete information about uncontrollable variables, then grey system theory can be considered as a part of the proposed model. In addition, some research questions for a natural gas forecasting in the study are given as follows: A general purpose forecasting model: How can we find the best curve representing various parameters and great dataset used for natural gas consumption? Energy system behavior: Is it possible to determine simultaneously the best linear or nonlinear equation and their coefficients? Higher accuracy: What can be the model of the system to reduce mean absolute percentage error (MAPE) value? Robustness: Is it possible to create a smart new methodology that will select the best linear or nonlinear curve and their

Pf Ts Tf F p N m DeltaE

Ts na At Ft n

random selected a number within the range of [0; 1] in Eq. (5) probability of accepting bad solutions for simulated annealing the probability of accepting bad solutions at the end of the optimization for simulated annealing starting temperature for simulated annealing final temperature for simulated annealing amount of temperature decreasing for each cycle for simulated annealing acceptance function for simulated annealing the number of cycles for simulated annealing number of neighbor solutions to be produced in each temperature for simulated annealing the energy difference between the value of new objective function and the value of existent objective function value of existent temperature of the metal in the heat bath the number of the accepted solutions the amount of real usage at time-t in Eq. (11) the amount of forecasted usage at time-t in Eq. (11) the period (year) in Eq. (11)

coefficients from a generated pool which contains numerous linear or nonlinear equations and their coefficients? The purpose of this study is to develop a breeder hybrid algorithm as a natural gas demand (NGD) forecasting model. The breeder hybrid algorithm consists of three stages as follow: The first stage is constructing a Nonlinear Regression forecasting model (NGD_NLR) by using statistical software such as Minitab 15.0. The second stage is developing a Breeder Genetic Algorithm (BGA), which is a special type of real valued genetic algorithm and uses specific operators, to improve the coefficients of the regression equation of NGD_NLR in order to obtain the regression coefficients of the second model namely NGD-BGA. The third stage introduces Simulated Annealing (SA) algorithm to the system to reach the breeder hybrid algorithm (NGDBGA_SA). The best coefficients of the second stage (NGD-BGA) are selected as inputs of the simulated annealing part of the model. The MAPE is used as the objective functions of NGD-BGA and NGD-BGA_SA. The model NGD-BGA_SA is formed to forecast the amounts of natural gas consumptions between years 2001 and 2014 by using amount of natural gas consumption as dependent variable and gross national product (GNP), population (POP) and growth rate (GR) as independent variables. The natural gas consumptions of Turkey between years 2001 and 2014 are used to construct the regression equations. The performance of natural gas forecasting of the model is compared to the previous studies in the literature. Additionally, projections of consumption forecasts are presented for years between 2015 and 2030 over two different scenarios by using the proposed models. 1.2. Literature review According to the related literature, there are many studies


searching the forecasting of the consumption level of natural gas. Some studies which are related to the natural gas consumption level are summarized from the scientific literature in Table 1. Sarak and Satman [7] are examining the consumption level made by the households have foreseen that there would be a consumption of 14.92 Gm3 in Turkey in 2003 in their forecasting based on the daily weather temperatures, population and consumption data. Aras [8] has conducted a similar study for the city of Eskisehir in Turkey. In the study conducted by Ceylan and Ozturk [9] with the use of macroeconomic indicators, a model based on the genetic algorithm has been suggested for the objective of finding the values of regression coefficients taking place in the forecasting equation. In the suggested model; forecasting has been made for the years between 2020 and 2025 based on the data of gross national product, population, import and export. The results occurred in smaller error level when compared to the forecasting of the related ministry of Turkey. In a similar study; linear and quadratic regression forecasting equations and the ant colony algorithm have been taken into consideration for the years between 1979 and 2005. It has been determined that the quadratic regression has a better forecasting precision [10]. Unler [11] applied the particle swarm optimization to the data belonging to the study of Toksarı [10] and reached a smaller forecasting error. Then, Toksari [12] presented a study using SA until the year of 2025. In addition, Box-Jenkins method [13] which is mostly used in the forecasting literature applies with the short and long term income and price flexibility as the independent variables. Consequently; if there is an increase in the prices of the alternative energy resources, a significant decrease is observed in terms of the flexibility of demand [14]. Melikoglu [15] aimed to generate accurate forecasts for Turkey's natural gas demand between 2013 and 2030. For this purpose, two semi-empirical models based on econometrics, gross domestic product (GDP) at purchasing power parity (PPP) per capita, and demographics, population change, have been developed. Ozdemir et al. [16] developed a hybrid genetic-simulated annealing (GA-SA) algorithm, which is a regional model for natural gas forecasting model, based on linear regression to forecast natural gas demand of Turkey. The linear models which was constructed by using the amounts of natural gas consumption for years between 1985 and 2000 as dependent variable, and gross national product, population, and growth rate as independent variables used to forecast the amount of natural gas consumption for years between 2001 and 2009. Then, the forecasts are compared with amounts of consumptions and analyzed statistically. Forouzanfar et al. [17] proposed a logistic approach to forecast the natural gas consumption for residential as well as commercial sectors in Iran. They presented two different methods to estimate the logistic parameters. The first method is based on the concept of the Nonlinear Programming (NLP) and the second one is based on Genetic Algorithm (GA). The forecast implemented in this study is based on yearly and seasonal consumption. Two parameters are estimated of logistic model in this study. However, the proposed breeder hybrid algorithm

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estimates ten parameters. The proposed algorithm in this paper contains different operators in both BGA and SA parts. It does not stick to local optimum point(s)/solution(s). This feature makes the breeder hybrid algorithm superior and global to search the best point/solution. Salehnia et al. [18] illustrated the use of the Gamma test in selecting irregular embeddings for time series data and the goal is to form a good predictive model for natural gas spot price time series. They considered three modeling techniques which are Local Linear Regression (LLR), Dynamic LLR (DLLR) and ANNs trained by using MATLAB software since it has a high flexibility in neurons and layers variations. Taspinar et al. [19] considered two different types of ANN for day-ahead forecasts in a providence of Turkey. Yu and Xu [20] proposed an appropriate combinational approach that is based on improved BP neural network for shortterm gas load forecasting, and the network is optimized by the real-coded genetic algorithm to avoid partial dinky and achieve the global minimum. The simulation results of several different combinational algorithms demonstrated that the CCMGA-Im_MBP model is ideal for gas short-term load forecasting of Shanghai as it can give more satisfactory prediction accuracy and relatively few iteration number. Similarly, Karimi and Dastranj [21] presented the Genetic algorithm is incorporated in order to define the optimal number of layers, the weights and bias of an Artificial Neural Networks. The proposed model predicts daily gas consumption as a function of degree-day, relative humidity, rainfall, and wind speed and is applied on a city in Iran. Szoplik [5] proposed a comparison between various ANNs takes place in order to derive the most effective topology for the natural gas demand prognosis of a city in Poland. Khan [22] examined both the short and long-term dynamics of natural gas consumption in Pakistan through an econometric model, sector-specific income, price and cross price elasticities of natural gas demand are estimated over the period of 1978 thru 2011. Wu et al. [23] presented a novel grey forecasting model that integrates the principle of new information priority into accumulated generation. This Grey Model (GM) could better reflect the priority of the new information theoretically. The results of two practical examples have been demonstrated that this grey model provides very remarkable short-term prediction performance compared with traditional grey forecasting model for limited data set forecasting. It is applied to Chinese gas consumption forecasting to show its superiority and applicability. Cheng et al. [24] proposed a multi-region optimization model that can deliver insights into how planning of the long term development of China's power sector could minimize the total cost of China's power sector by considering regional variations in availabilities of resources and inter-region power transmission line capacity. They considered a case study that how investment decisions to expand and alter the existing generation mix could be optimized across a timeframe from 2011 to 2050. Yuan et al. [25] proposed two univariate models, ARIMA (Autoregressive Integrated Moving Average) model and GM(1,1) model are used to forecast China's primary energy consumption. The results of the two models are in line with

Table 1 Literature for natural gas forecasting studies. Forecasting Methods

Related Literature

Time Series Models

an Box-Jenkins (1976), Sarak and Satman (2003), Erdogdu (2010), Melikoglu (2013), Salehnia et al. (2013), Khan (2015), Dog (2015), Shaikh and Ji (2016), Yuan et al. (2016), Boroojeni et al. (2017) Bianco et al. (2010), Meng et al. (2011), Pao and Tsai (2011), Li et al. (2013), Niu et al. (2013), and Wang et al. (2014). Wu et al. (2015), Boran (2015), Wang et al. (2016), Yuan et al. (2016), Bo (2017). Salehnia et al. (2013), Taspinar et al. (2013), Hong et al. (2013), Karimi and Dastranj (2014), Ou and Hong (2014), Szoplik (2015), Pino-Mejias et al. (2017) Ceylan and Ozturk (2004), Toksari (2007), Unler (2008), Aras (2008), Forouzanfar et al. (2010), Toksari (2010), Karimi and Dastranj (2014), Ozdemir et al. (2016), Ou et al. (2016) Lin et al. (2011), Yu and Xu (2014), Cheng et al. (2015), Ozdemir et al. (2016), Panapakidis and Dagoumas (2017).

Grey System Theory Artificial Neural Networks Nature-Based Heuristics Algorithms Hybrid Optimization Studies

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requirements. Through comparing, it is found that the fitted values of ARIMA model respond less to the fluctuations because they are bounded by its long-term trend while those of GM(1,1) model respond more due to the usage of the latest four data. A large number of studies on energy consumption forecasting using grey models have been developed, such as Meng et al. [26], Bianco et al. [27], Li et al. [28], Niu et al. [29], Pao and Tsai [30] and Wang et al. [31]. Future projection for the country has been drawn in the study developing a grey forecasting model adaptive to this limited data and investigating the change in natural gas consumption which has shown increase in recent years and can obtain electric energy apart an [33] reconsidered the relafrom heating in Turkey [32]. Dog tionship between economic growth and natural gas consumption over the data of the last period. It has been seen that variables such as daily air temperatures, population, the amount of consumption, levels of imports and exports, income, rate of economic growth and national income have been utilized in the studies on the forecasting of the level of natural gas consumption in the scientific literature. Shaikh and Ji [34] developed the logistic and logistic-population model based approach to forecast the medium-(2020) to long(2035) term natural gas demand in China. Wang et al. [35] employed the multi-cycle Hubbert model to forecast China's annual nature gas production and to determine the peak year and the future production trends based on several different Ultimate Recoverable Reserves (URR) scenarios. Moreover, a small-sample effective rolling GM(1,1) model has been proposed for the first time to forecast exponential natural gas consumption with different lengths of data sets. Then, the grey relationship analysis has been used to select the best consumption curve in correspond with different URR scenarios. Bo [36] proposed a novel grey model called TPGM(1,1) to simulate and forecast the supply and demand of natural gas in China. Firstly, the unbiased parameter estimation method of TPGM(1,1) was studied by Cramer's rule; secondly the optimal method of the initial value of TPGM(1,1) was deduced; thirdly, the TPGM(1,1) for the output and consumption of natural gas in China was then built, and simulated and predicted results were compared with those of other models using known data. Pino-Mejias et al. [37] attempted to develop linear regression models using with ANN to predict the energy demand/consumption and CO2 emissions of office buildings in Chile. In addition to the above, natural gas can play an essential role in the global energy market through generating electricity in largescaled gas plants and small-scaled CHP (Combined Heat and Power) systems [38]. The CHP device couples the three energy systems at the same time that produces electricity, heat and cooling from natural gas [39]. One of the popular topics for natural gas demand variations in todays' market is the integration of natural gas network with electricity network (e.g., by using CHP systems, micro-turbines in commercial sectors). Especially, the recent advances in technologies such as CHP and power systems has accelerated the integration of energy resources in energy hubs. Furthermore the advances in smart grid technologies motivate the electricity utility companies toward developing demand response programs to influence the electricity usage behavior of the customers [40]. The electric power generation or natural gas accurate demand forecast will improve the real-time and long-term performance of power systems based on the available historical data [41]. In recent years, smart grids and microgrids are becoming important topics for energy demand. The microgrid causes to effectively integrate various sources of Distributed Generation (DG), especially renewable energy sources, and thus reduce CO2 emissions [42]. Moreover, both Offshore Wind Farms (OWFs) and Seashore Wave Power Farms (SWPFs) have been evaluated and are now in commercial operation [43]. Combined OWFs and SWPFs are

evaluated and developed in the seas around Western Europe and the United Kingdom [44]. When OWFs and SWPFs deliver or trip a large amount of electric power via the grid simultaneously, the inherent power fluctuations that occur can have adverse impacts on the power quality of the systems to which they are connected. For this reason, Ou et al. [42] introduce a Novel Intelligent Damping Controller (NIDC) for the Static Synchronous Compensator (STATCOM) to reduce the power fluctuations, voltage support and damping in a hybrid power multi-system. The proposed NIDC consists of a designed ProportionaleIntegraleDerivative (PID) linear controller, an adaptive critic network and a proposed Functional Link-based Novel Recurrent Fuzzy Neural Network (FLNRFNN). An FLNRFNN is adopted to implement the function expansion for the Functional Link (FL)-based NRFNN, to improve the accuracy of the function approximation. The adaptive critic network is applied in order to provide suitable training signals for the FLNRFNN controller. The FLNRFNN produces the variation gains values DKPID (DKP, DK1 and DKD) of the PID controller. Therefore, the proposed NIDC is added to the voltage reference Vdc*, reference signals for dc link voltage, of the STATCOM and it is capable of providing near optimal results for complex and hybrid power multi-system connected the integration of the OWF and SWPF systems in order to mitigate the power oscillations and to improve stability. Lin et al. [45] proposed a recurrent FL-based fuzzy neuralnetwork (FNN) controller with improved particle swarm optimization (IPSO) to control a three-phase induction-generator (IG) system for stand-alone power application. Thus, IPSO is adopted to adjust the learning rates to improve the online learning capability of the recurrent FL-based FNNs. Tang et al. [46] presented the model of Wind Turbine (WT) with doubly-fed induction generators (DFIG) system is a high-dimensional multivariate time-varying system. They choose particle swarm optimization (PSO) to search the optimal parameters for the controller of the WT system. Similarly, Hong and Luo [47] proposed a method using wind generator voltages, static compensators, and transformer taps as controllers to regulate the voltage profile for operation planning in a distribution system. Wind power generations and bus loads are modeled with random variables. Through grey-based genetic algorithms (GAs), the megawatt (MW) loss in the system is minimized and the operational constraints are fulfilled. Ou and Hong [48] examined dynamic operation and control strategies for a microgrid hybrid windephotovoltaic (PV) e fuel cell (FC) based power supply system. The system consists of the PV power, wind power, FC power, static var compensator (SVC) and an intelligent power controller. An SVC was used to supply reactive power and regulate the voltage of the hybrid system. A general regression neural network (GRNN) with an improved particle swarm optimization (PSO) algorithm, which has a nonlinear characteristic, was applied to analyze the performance of the PV generation system. Then, the proposed algorithms, NGD-BGA and NGD-BGA_SA, are given to improve and optimize these control parameters and learning rates in the backpropagatioan learning method of the above-presented soft models. The maximum and minimum values of each parameter for the intelligent damping controller system or the problem involved are described to ranges which indicate the possible solutions for the desired parameters, and also no complicated mathematical operations are required in proposed algorithms, so it is independent of the derivative information. Similar studies for wind hybrid power systems demand forecast and developed approaches for different connections of transformers can be found in Refs. [49,50], and [51]. Our proposed algorithms, NGD-BGA and NGD-BGA_SA, can use different horizons when day-ahead, week-ahead forecasting structures are wanted to be predicted, at this phase, due to the annually historical data, the proposed algorithm is not suitable for


real time energy demand forecasting operations. However, when the daily and weekly data are obtained, the structure of the model can be easily adapted and applicable. Panapakidis and Dagoumas [4] proposed a novel hybrid computational intelligence model for day-ahead natural gas demand predictions. Their model combines the Wavelet Transform (WT), Genetic Algorithm (GA), Adaptive Neuro-Fuzzy Inference System (ANFIS) and Feed-Forward Neural Network (FFNN). The WT is used to decompose the original signal in a set of subseries and then a GA optimized ANFIS is employed to provide the forecast for each subseries. ANFIS output is fed into a FFNN to refine the initial forecast and upgrade the overall forecasting accuracy. A similar study related to time-series technique, Boroojeni et al. [41] presented a generalized technique for modeling historical load data in the form of time-series with different cycles of seasonality (e.g., daily, weekly, quarterly, annually) in a given power network from short-term to medium-term horizon. The appropriate coefficient estimate of our proposed model for natural gas demand forecasting model can be easily made as long as the various input/independent variables (the gross national product, population and the growth rate or the inputs according to the structure of the problem) are determined for daily, monthly and annually. Because, it is a powerful search technique that finds the best coefficients within the appropriate ranges defined for the parameters. 1.3. Our contributions Some contributions of this study are summarized as follows: This study shows the best parameters estimation independent of the model structure by using heuristic algorithms for natural gas demand forecasting methods and the proposed hybrid algorithm has more precise results than known methods such as ANNs, Evolutionary Algorithms and Grey forecasting models. This work proposes the best coefficients prediction for the uncontrollable or controllable variables included in the proposed model for natural gas demand/consumption forecasting. Whether the structure of the proposed model is a linear/ nonlinear or a stochastic differential model, it is very important to make the best parameter settings for these models. This work suggests a solution to this situation where a breeder hybrid algorithm uses in order to obtain the best parameter estimation for these models. No matter how the model is structured or no matter what type of model is used, it is possible to estimate the best coefficients for the model by using the proposed algorithm. The distribution of the data is important for some prediction models, for example a grey forecasting model works with constantly exponential increasing data, whereas the breeder hybrid algorithm works independent of data type because of the ability to quickly search the solution space. The proposed algorithm has always evolved with the best solutions in the genetic and simulated annealing algorithms parts, it does not stick to local optimum point(s)/solution(s). This feature makes the breeder hybrid algorithm superior and global the best point/solution finder. Thus, natural gas demand/consumption can be estimated with error close to zero for daily, monthly and annually data. The proposed breeder hybrid algorithm can estimate natural gas demand variations in market for the integration of natural gas network with electricity network (e.g., by using CHP systems in commercial buildings, energy hubs, micro turbines, etc.). The proposed algorithms, NGD-BGA and NGD-BGA_SA, can propose the use of a STATCOM in order to reduce the power fluctuations, voltage support and damping, and thus improve

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the transient stability of a multiple-bus hybrid power multisystem connected for the integration of wind farms and wave power farms to improve and optimize these control parameters. Thus, the maximum and minimum values of each control parameter for the intelligent damping controller system or the problem involved are described to ranges which indicate the possible solutions for the desired parameters, and also no complicated mathematical operations are required in the proposed algorithms, so it is independent of the derivative information.

1.4. Organization of the paper The rest of this paper is organized as follows: The solution approaches, nonlinear regression, breeder genetic algorithms and simulated annealing are given in Section 2. Then, the proposed forecasting models and results are given in Section 3 with modeling. The scenario based results as the future projections are given in Section 4. Section 5 concludes the paper and outlooks the further researches. 2. Solution approaches The known solution methods, nonlinear regression, breeder genetic algorithms and simulated annealing algorithm, which will be used to construct the hybrid algorithm are described in this section of the study briefly. The nonlinear regression models, NGD_NLR, NGD-BGA and NGD-BGA_SA, are constructed by using the amount of natural gas demand (NGD) as dependent variable and gross national product (GNP), population (POP) and growth rate (GR) as independent variables. The general form of the nonlinear models are given as:

y ¼ b0 þ b1 x1 þ b2 x2 þ b3 x3 þ b4 x1 x2 þ b5 x1 x3 þ b6 x2 x3 þ b7 x21 þ b8 x22 þ b9 x23 (1) where, y: the amount of natural gas consumption, x1: gross national product, x2: population x3: growth rate. bi: coefficients of the independent variables or parameters (i¼0,1,2,…,9). The general structure of the solution methods proposed in this study is given as follows in Fig. 1. The initial trial vectors which indicate the possible solutions for the coefficients of the independent variables or parameters (bi: i ¼ 0,1,2,…,9) are randomly generated for each model, NGD-BGA and NGD-BGA_SA. Each parameter is searched in very large range intervals, bi 2 ½biðminÞ ; biðmaxÞ , and the parameters having the smallest MAPE value are selected. Fig. 1 gives general working mechanism of the proposed algorithms in this study. 2.1. Nonlinear regression The regression analysis is used to measure the relationship between two or more variables in this study. If there is a relationship between variables in the regression analysis, it gives information about its strength. Then, it is possible to make comments about natural gas consumption/demand by using independent variables

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Fig. 1. The working mechanism of the solution methods.

and the relationships between them. The nonlinear regression is strengthened via the breeder hybrid algorithms in order to make more clear comments about natural gas consumption/demand. 2.2. Breeder genetic algorithms Genetic algorithms developed by John Holland [52] are classified in the meta-heuristic algorithms that are imitating the process style of biological evolution and modeling some natural events [53]. The most distinct difference to distinguish a genetic algorithm from other optimization techniques is that it evolves with a mechanism called population (solution space). Each solution in the population is named a chromosome. The most important feature of a genetic algorithm to contribute to the solution and scan the solution space quickly is the coding of coefficients of the independent variables or parameters correctly. The representation of parameters is the first key stage in processing of genetic algorithms because genetic algorithms work with coded chromosomes representing problem [54]. Genetic algorithms consist of various coding techniques such as binary coding or real coding. In this study, the real coded genetic algorithm has been used since some difficulties are faced when dealing with representation of binary coding requires big numeric accuracy and continuous research spaces with large sizes [55]. Especially, when the size of the problem enlarges (increasing of bit numbers of chromosomes, that is, increasing the number of parameters), the susceptibility of the binary coding becomes limited. Instead, using the real coded genetic algorithm being able to code with real numbers is more advantageous. Real coded genetic algorithm is more accurate (in terms of approaching the real value of the related parameter) and also it occupies less space in the memory of the computer that it is run [56]. Therefore, the accuracy of numbers plays an important role in the solution of any problem. Another disadvantage of binary coding is that the values fall apart when they are converted to binary code although the original values are close to each other. For example, even though 30 and 32 original two close values, when they are converted to binary code, the number 30 corresponds to 11110 and the number 32 corresponds to 100000. In order to move 30 to 32 within genetic algorithm structure, lots of bits should change place

consisting of 0 and 1's [57]. To handle with the above disadvantage, a very versatile and effective function optimizer called Breeder Genetic Algorithm (BGA) was recently proposed [58]. BGA uses a selection strategy based on the behavior of animals breeding instead of natural selection. The logic of the selection strategy is that mating two individuals with high fitness values is more likely to breeding an offspring of high fitness than mating two randomly selected individuals [59]. Breeder hybrid algorithm proposed in this study is an algorithm comprising of the combination of real valued breeder genetic algorithm and simulated annealing. The first part of the proposed hybrid algorithm comprises of real valued breeder genetic algorithm. The best result obtained from breeder genetic algorithm has been chosen the starting point of simulated annealing. Especially, during the process of coding the algorithm, an inaccurate coding can cause misunderstandings and diversions. It will lead to undesirable results in genetic algorithm. It should be remembered that the result might be unexpected if genetic algorithm is leaded to search the solution space in wrong direction since it searches the solution space in many directions [6]. Accurate coding of the genetic algorithm will provide opportunities for the model to produce results within the desired scope since the stage two will produce the starting point for simulated annealing which is the last stage of the breeder hybrid algorithm. Otherwise, it is expected undesirable results that will emerge for economic losses in solutions of real life problems. Breeder genetic algorithm (BGA) which is a special type of real valued genetic algorithm uses specific operators. Selection method in BGA should be truncation selection since BGA always works with the best chromosomes and recombine them and eliminates others. Some properties of breeder genetic algorithm presented in the study are follows [60]: Bredeer genetic algorithm uses real-valued code representation contrary to binary representation used in classical genetic algorithm. Bredeer genetic algorithm requires only a few parameters to be chosen by the user. It always uses truncation selection as the selection method. This method takes T % of the available population in order to choose


the best individuals ranking at the top. These individuals experience recombination and mutation for the next generation. Remainders of the individuals are thrown. Pseudo code of breeder genetic algorithm developed in the study is given as follows [60]:

begin randomly initialize form a random initial population that includes N pieces of individuals. while (if the stopping criterion has not been met). evaluate the fitness of each individual. save the best individuals in the new population. select the best individuals as much as T % of the total population. for conduct from i¼1 for N-1. randomly select the two individuals among the best individuals as much as T % of the total population. recombine crossbreed two individuals to attain an offspring. perform mutation apply the process of mutation on the occurring offspring. update the variable if the stopping condition has been met (satisfying result with small error). end

A population in the size of N is formed in breeder genetic algorithm in the first step. All chromosomes are ranked according to the best fitness values, then T % of these chromosomes are selected and exposed to recombination. Then, obtained offspring are applied to the mutation process. If the results are satisfactory, algorithm is stopped. Otherwise, algorithm continues until the satisfactory result is obtained.

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[-0.25; 1.25], it is called as extended intermediate recombination [64]. For example; x and y-chromosomes taking place in Fig. 2 (a) are taken into consideration. It is assumed that the values of a are selected for the first offspring are 1; 0.25; 1.2 and 0.3 and the values of a are randomly selected from the range for the second offspring are 0.25; 1.1; 0.2 and 1. The new offspring shall be as in Fig. 2 (b). 2.2.3. Discrete mutation A variable xi is selected with a small probability for the mutation of the real valued variables. The breeder genetic algorithm normally uses pm ¼ 1n and the n expresses the number of the variables of an individual/chromosome. At least one variable in a chromosome should be mutated. The mutation range for each variable is shown with rangei . The mutation range (rangei ) is calculated with l$searchintervali . The statement of searchintervali in the mutation range represents the difference between the lower and upper limits of the variable that shall undergo mutation. The value of l in this process is generally chosen as 0.1. The value of new offspring zi is calculated according to the statement of xi ±rangei $d. Here, þ and e are selected with the probability of 0.5 and d is calculated from the probability distribution that corresponds to a small value as expressed in Eq. (3). Also, ai in Eq. (3) determines the contribution of the d ¼ 2j to the mutation for c j ¼ 1; 2; ::: ; 15.

d¼

accur1 X

ai $2i ai 2f0; 1g

(3)

i¼0

The mutation range is determined with Eq. (4) [64]:

rangei ¼ 0:1*ðupper level lower levelÞ

(4)

2.2.1. Truncate selection This selection method has a deterministic structure not a stochastic method. The best individuals taken with only a percentage part of the total population are taken to the gene pool for the application of recombination and mutation processes. Therefore, the best individuals always find the chance of selection, others are eliminated [61]. Similarly, the individuals are firstly sequenced according to their fitness values and the best individuals are multiplied as 1/p times with a rate like p (p ¼ 1/2, 1/3, etc.). This random multiplication process is applied until the number of the individuals as much as the magnitude of the population is attained [62]. In other words, T % of the best individuals/solutions, namely solutions having small MAPE values, taking place in the upper ranks in the existent population is taken. These individuals undergo recombination and mutation for the next generation [63]. T threshold energy specified above is normally selected between 10% and 50% [64]. When these explanations are taken into consideration, the place of the best individual in the next generation is guaranteed. Other (T-1) percent taking place in the upper ranks evolve in the mechanism of recombination and mutating the remaining individuals for the objective of forming the next generation. The process is repeated until the optimal solution is attained or until the highest iteration number is reached [65].

provided, each ai is changed from zero (0) to one (1) with the 1 . Only when the a takes the value of 1, it probability of pd ¼ accur i contributes to the summation in Eq. (3). In this case, it could be given as d ¼ 2j . As it is clearly expressed above; the candidate variable that shall experience mutation in the real valued coding is subjected to mutation in the way of decreasing its value as much as the determined mutation steps or increasing with equal probability. The determination of this step is conducted in different ways that breeder genetic mutation is one of them [58].

2.2.2. Extended intermediate recombination operator In this recombination method; either the value of a taking place in Eq. (2) is selected as 0.5 fixed or it is randomly selected within the range of [0; 1]. In here, x and y are chromosomes. Then, new offspring is z for extended intermediate recombination. (Mühlenbein and Schlierkamp-Voosen [64]).

2.3. Simulated annealing algorithm

zi ¼ i þ ai $ðyi i Þ

i ¼ 1; 2; …; n

(2)

This recombination type is called as intermediate recombination. Similarly; if the values of ai are selected within the range of

The 'accur' in Eq. (3) expresses the precision of the steps of mutation and it is related to the precision of the computer; in other words, they are the bit numbers used in the computer to represent a real valued variable. In the studies, generally 8 and 16 bit values are used [66]. In the discrete mutation, generally the value of 'accur' is taken as 16. If the condition a i ¼ rand ðaccur; 1Þ < 1=accur is

2.2.4. Continuous mutation This mutation method has same operational principle with the discrete mutation; only Eq. (3) becomes Eq. (5).

d ¼ 2kb

(5)

A uniform distribution of a random variable is determined in a way that it shall be b2 ½0; 1 [61]. Similarly, the value of k in Eq. (5) is randomly produced within the range of [-2; 2] [67].

Simulated Annealing (SA) has firstly been proposed by Ref. [68]. Simulated Annealing is an algorithm that imitates the physical annealing process of the solids. The annealing process of the solids could be imitated for the objective of finding a close global solution for combinatorial optimization problems [69]. Simulated annealing is a search method with probability that provides a better solution

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chromosome 12

4

5

Offspring-I 6

9

3

2

1.4

17.7

Offspring-II

y chromosome 9

3.75

45

(a)

11.25

2.9

4.4

45

(b)

Fig. 2. New offspring z for the extended intermediate recombination.

of the combinatorial optimization problems [70]. Annealing could be defined as the process of passing from the high energy status in the heat bath to the low energy status for the objective of giving the desired properties to a solid. The thermo process could be explained with two items as follows: Keeping the heat bath temperature in the highest value in which the solid could melt. Decreasing the temperature of the heat bath regularly until the solid reaches the crystal (regular) structure. As a result; it is considered that the thermo process could be carried out successfully. Annealing is the process of heating the solid until its melting temperature and cooling it slowly until it has a regular crystal structure after that. While the atoms in metals have high energy in high temperatures, they have low energy in low temperatures. As the temperature is decreased slowly, regular crystal structure starts to occur. In this way; when it reaches the crystal structure, the energy starts to become minimum. In this process; decreasing the temperature parameter carefully is very significant. If the temperature is decreased fast, deficiencies/irregularities shall start to occur in the regular crystal structure. Cooling process should be carried out slowly in the thermo process for the objective of preventing this situation [11]. 2.4. The proposed breeder hybrid algorithm Nature-based algorithms have become popular in recent fifteen years and have been widely applied in various fields of science and engineering, such as robot control, cluster analysis, controller design, dynamic optimization, demand forecasting model and image processing [71]. The widely developed mathematical modeling approaches indeed help us to gain perspective and make reasonable accurate predictions for the targeted problems [72]. Our natural world veils many characteristics of living creatures such as animals, birds, plants, and all of them have some unique behavior or features to sustain them survive [53]. The vast majority of heuristic and metaheuristic algorithms, such as genetic algorithm and simulated annealing, were sprouted from the behavior of biological systems and/or physical systems in nature [73]. Those characteristics or behaviours also motivate researchers to develop natureinspired innovative computational intelligence algorithms for the solution of optimization problems. The proposed in this study breeder hybrid algorithm (NGD-BGA_SA) is formed with the common usage of the heuristics of real valued breeder genetic algorithm and simulated annealing. Breeder genetic algorithm is defined as a systematic process which consists of three methods which are truncate selection, extended intermediate recombination and continuous mutation, respectively. Simulated annealing

consists of the probability of accepting bad solutions (Ps), the probability of accepting bad solutions at the end of the optimization (Pf), starting temperature (Ts), final Temperature (Tf), amount of temperature decreasing for each cycle (F), the number of solutions function to be produced in each temperature value, acceptance function (p), temperature decreasing function, the number of cycles (N) and the number of neighbor solutions to be produced in each temperature (m). The chromosomes, which refer to regression coefficients, of the breeder genetic algorithm part that forms the first stage of the breeder hybrid algorithm are coded as real codes. The truncation selection method suggested by Ref. [74] is used as the selection method in the breeder genetic algorithm. This selection method is a property that is peculiar to the breeder genetic algorithm [60]. In this method; T% of the best individuals taking place in the upper ranks in the existent population is chosen for recombination and mutation for the next generation [63]. T threshold energy specified above is normally selected between 10% and 50% [64]. In this study, the threshold energy is selected as 50%. In addition; the recombination and mutation operators used basically in the breeder hybrid algorithm are formed in the way that is used in the breeder genetic algorithms of [64]. The used recombination operator is extended intermediate recombination operator and ai values for two chromosomes, such as x and y, located in the operator shall get a random value within the range of [-0.25; 1.25] for the objective of forming offspring chromosome zi ¼ i þ ai $ðyi i Þ i ¼ 1; 2; …; n. Continuous mutation is applied to the variable xi randomly selected for the objective of providing variability between the chromosomes after performing of the recombination and the new offspring zi ¼ xi ±rangei $d is attained. The mutation range for each variable is shown within rangei and the mutation range is calculated with l$searchintervali . The statement of searchintervali in the mutation range represents the difference between the lower and upper limits of the variable that shall undergo mutation [64]. The value of l in this process is generally taken as 0.1 and the k in Eq. (4) is randomly produced within the range of [-2, 2] and the new offspring contributes to the value of zi ¼ xi ±rangei $d. In here, þ and e are selected with the probability of 0.5 and are selected with a uniform probability within the range of b2½0; 1 taking place in the d value for Eq. (5) [61]. The flow chart of the proposed breeder hybrid algorithm (NGD-BGA_SA) is given in Fig. 3. Regarding the simulated annealing that forms the second stage of the proposed breeder hybrid algorithm, the best chromosome attained from the breeder genetic algorithm is selected as the starting solution point of the simulated annealing and new trial points are formed by increasing or decreasing the neighbor searching technique in certain amounts. The energy of these neighbor solution points is calculated with the help of the objective function. If the value of attained objective function is better than


the value of objective function of the existent solution, it is accepted as the new solution. Similarly, if the value of objective function of the attained new solution is worse than the value of objective of the existent solution, the acceptance function is used with a certain pprobability value of

DeltaE exp DeltaEavg $Ts

(6)

([6,75]). Also, Eq. (6) is known as the Metropolis algorithm. It has been modeled by Ref. [76] based on Monte Carlo technique. Basically; this algorithm conducts the annealing of the changes occurring in the energy of a system undertaken to a cooling process until it becomes to a steady state status. After thirty years, Kirkpatrick et al. [68] have expressed that such kind of an annealing could find the convenient solution in the optimization problems [77]. If there has been a decrease in the system energy in Metropolis algorithm, this is accepted as new solution. If there is an increase in the system energy, a random number is produced and the new situation is accepted if this number is lower than the p-probability produced from the equation of the acceptance function. The p-probability value is calculated for each iteration in Eq. (6). Otherwise; the existent situation is accepted and no change occurs. DeltaE in the acceptance function taking place in Eq. (6) expresses the energy difference between the value of new objective function and the value of existent objective function. Ts shows the value of existent temperature of the metal in the heat bath. Similarly; DeltaE_avg taking place in Eq. (6) is accepted as zero in the beginning of the algorithm. As the number of the accepted solutions increases, DeltaE_avg is calculated with

DeltaE avg ¼

DeltaE avg *ðna 1Þ þ DeltaE na

(7)

In here, na-taking place in Eq. (7) shows the number of the accepted solutions. na is taken as zero at the beginning of the algorithm, but the first initial solution in the beginning of the algorithm is taken as accepted solution na ¼ na þ 1:0, then na equals to 1. That is, na 1. The accepted na increases as the iteration progresses; in this way, a numerical change occurs in the DeltaE_avg. The parameter values used in the simulated annealing are shown in Table 2. The changes in temperature for each cycle has been decreased for each iteration with Ts ¼ F:Ts ([6], [75]). The number of cycles in the simulated annealing is determined as 1000 and the number of neighbor solutions to be in each temperature is determined as 50. In this way; the simulated annealing is stopped in 1000 iterations. The result attained as a run of 1000 iterations in the breeder hybrid algorithm is accepted as satisfying result and if the desired result could not be reached, the algorithm is restarted and operated. Fig. 4 shows the MAPE values of forecasting equations for years between 1985 and 2000 as zero at the beginning of the (a) NGDBGA and (b) NGD-BGA_SA algorithms over iterations. When the iteration number is 50, the MAPE is reached to the least value of 0.0738 of (a) NGD-BGA. According to (b) NGD-BGA_SA, when iterations number is 995, the MAPE is reached to close the zero as 0.0043. Consequently, NGD-BGA_SA forecasting model provides the minimum MAPE values and is able to use the following years. 3. Forecasting models and results 3.1. Forecasting models Nonlinear regression forecasting model in Eq. (8) is used to forecast the natural gas consumption/demand in Turkey. Data TurkStat [78] for the period from 1985 to 2000 are attained for this

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nonlinear regression forecasting model (NGD_NLR) and the coefficient parameters in Eq. (8) are attained from Minitab 15.0 statistical software. Breeder genetic algorithm is applied to the coefficient parameters attained from Eq. (8) and the coefficient parameters in Eq. (9) are obtained. Simulated annealing is applied to the best coefficient parameters attained from Eq. (9) and the coefficient parameters in Eq. (10) are obtained. Nonlinear regression forecasting model

yNGD

¼ 131071 þ 63x1 þ 4095x2 þ 2047x3 þ 3x4 þ 7x5

NLR

þ 31x6 þ 1x7 þ 63x8 þ 31x9 (8) Nonlinear regression forecasting model for the breeder genetic algorithm

yNGDBGA ¼ 25070:69102 9:980219894x1 1333:787941x2 1333:78794x3 þ 0:076491106x1 x2 0:076491106x1 x3 þ 13:70639829x2 x3 þ 0:041331333x21 þ 16:64086721x22 16:64086721x23 (9) Nonlinear regression forecasting model for the breeder hybrid algorithm

yNGDBGA

SA

¼ 25070:6325 9:9174304x1 25070:632x2 25070:632x3 þ 0:03062801x1 x2 0:0306280x1 x3 þ 14:2525369x2 x3 þ 0:05876175x21 þ 16:6485551x22 16:648555x23 (10)

The MAPE is used for the breeder genetic algorithm and the simulated annealing part of the objective function of the breeder hybrid algorithm. The MAPE between the amounts of the real (NGD) and the estimated natural gas consumption is calculated with Eq. (11).

MAPE ¼

n 1X A t F t n t¼1 At

(11)

where; At expresses the amount of real usage at time-t, Ft expresses the amount of forecasted usage at time-t, n expresses the period (year) [25]. The nonlinear forecasting models in Eqs. 8e10 are formed to forecast the amounts of natural gas consumption between 2001 and 2014. These models use the amount of natural gas consumption (NGD) as dependent variable and gross national product (GNP), population (POP) and growth rate (GR) as independent variables. The natural gas consumption projection of Turkey between 2001 and 2014 of these models are given in Fig. 5. The natural gas consumption projection of Turkey between 2001 and 2014 of nonlinear regression forecasting model for the breeder hybrid algorithm (NGD-BGA_SA), nonlinear regression

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Assign to initial parameters from the coefficients obtaining the best result for NGD- BGA

Start to NGD-BGA_SA

Stop

Create randomly generated neighbour solutions No Yes

Comparison between initial solution and neighbour solutions

Stop Criteria?

Yes

If any solution from neighbour solution is better than initial solution No

Create a random number (Rnd)

Update the best solution

Yes Select to Initial Solution

Rnd Acceptance func. rate (p)

No

Fig. 3. Flow chart of the breeder hybrid algorithm (NGD-BGA_SA).

Reject the all solutions and Go to next generation


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Table 2 The values of parameter used in the simulated annealing. The probability of accepting bad solutions (Ps) The probability of accepting bad solutions at the end of the optimization (Pf) Starting temperature (Ts)

0.5 108

Final Temperature (Tf)

1:0 InðPf Þ N1

1:0 InðPsÞ

The amount of temperature decreasing for each cycle (F)

Tf Ts

The number of solution functions to be produced in each temperature value Acceptance function (p)

Steady exp

Temperature decreasing function The number of cycles (N) The number of neighbor solutions to be produced in each temperature (m)

DeltaE DeltaE avg$Ts

Geometric {1000} 50

values attained from Ref. [79] and the results are shown for NGD_NLR, NGD-BGA and NGD-BGA_SA models in sequence for the periods of 2006, 2009 and 2014 in Table 3. In addition; the proposed hybrid algorithm has been compared to the results of [12] having been conducted as the last study on the natural gas consumption of Turkey and the study of [62]. Table 4 shows previous results from Toksarı [12] and Ozdemir et al. [16]. The results of the MAPE are better than [16] as %48.08 and %51.60 and [12] as %66.25 and 68.54 for years 2001e2006 of NGD-BGA and NGD-BGA_SA, respectively. Similarly; Table 4 presents that the results are also better than [16] as %59.96 and %64.79 for years 2001e2009. Table 5 consists of the combination of Tables 3 and 4 NGD-BGA and NGD-BGA_SA present forecasts with significantly small MAPE values that are 0.0188 and 0.0143 for year 2014, respectively. NGDBGA_SA is the best forecasting model between Linear_SANGDE, NGD_GASA and proposed models in sequence for the periods of 2006, 2009 and 2014. MAPE values of the natural gas consumption projection of Turkey for the periods of 2006, 2009 and 2014 of NGD-BGA_SA, NGD-BGA, NGD_GASA and Linear_SANGDE models in Table 5 is visualized by Fig. 6.

forecasting model for the breeder genetic algorithm (NGD-BGA), and nonlinear regression forecasting model (NGD_NLR) in Table 3 is visualized by Fig. 5. The real amount of natural gas consumption of Turkey (NGD) is forecasted by NGD_NLR, NGD-BGA and NGDBGA_SA models. The best estimates of NGD are NGD-BGA_SA, NGD-BGA and NGD_NLR, respectively. Especially, NGD-BGA and NGD-BGA_SA models give forecasts with significantly small MAPE values that are 0.0188 and 0.0143 for year 2014, respectively. The natural gas consumption of Turkey attained in terms of MAPE and the real natural gas consumption are shown in Table 3 and Fig. 5 for the proposed algorithms. When the curves are examined, it could be clearly seen from Fig. 5 that the most convenient curve for natural gas demand forecasting model is firstly nonlinear regression forecasting model for the breeder hybrid algorithm (NGD-BGA_SA), secondly nonlinear regression forecasting model for the breeder genetic algorithm (NGD-BGA), and then, nonlinear regression forecasting model (NGD_NLR). The real curves of the natural gas consumption of Turkey (NGD) for NGD-BGA and NGD-BGA_SA curves have almost coincided. This shows that the models produce forecasts so close to the real value. The amount of forecasted consumption between 2001 and 2014 attained from the breeder hybrid model is compared to the real

(a) NGD-BGA 525

1:0

(b) NGD-BGA_SA 0.01 0.009

450

0.008

375

0.007

300

0.006 0.005

225

0.004 0.003

150

0.002

75

0.001

0

0 1

26

51

76 101 126 151 176

iterations

1

151

301

451 601 iterations

Fig. 4. MAPE values of (a) NGD-BGA and (b) NGD-BGA_SA algorithms over iterations.

751

901

1280


Fig. 5. Natural gas demand forecasting for years between 2001 and 2014.

Table 3 MAPE results for NGD-BGA and NGD-BGA_SA algorithms. Years

NGD

NGD_NLR

RE

NGD-BGA

RE

NGD-BGA_SA

RE

2001 2002 2003 2004 2005 2006

14868 16102 19450 20426 24726 28867

36523.242 41385.360 43083.695 45562.236 45953.271 46830.934

3.4565 3.5702 3.2151 3.2306 2.8585 2.6223

14511.17 15934.54 19158.25 20182.93 24327.91 28289.66

0.0240 0.0104 0.0150 0.0119 0.0161 0.0200

14509.68 15936.15 19166.03 20215.61 24392.20 28364.71

0.0241 0.0104 0.0146 0.0103 0.0135 0.0174

MAPE

3.1589

MAPE

0.0162

MAPE

0.0151

38412.612 38138.142 45943.725

2.0955 2.0138 2.3666

33906.89 36460.33 33020.58

0.0330 0.0308 0.0178

34012.08 36625.85 33269.36

0.0300 0.0264 0.0104

MAPE

2.8255

MAPE

0.0199

MAPE

0.0175

47829.964 47363.178 48204.286 49851.48 52819.2

2.2785 2.0839 2.0655 2.0473 2.1004

36782.50 42866.76 44422.14 46800.32 47337.6

0.0168 0.0190 0.0180 0.0168 0.0138

37081.78 43225.07 44797.63 47209.68 47769.6

0.0088 0.0108 0.0098 0.0082 0.0048

MAPE

2.5718

MAPE

0.0188

MAPE

0.0143

2007 2008 2009

35064 37619 33619

2010 2011 2012 2013 2014

37411 43697 45241 47600 48000

4. Scenarios for future forecasts of Turkey's natural gas demand

Table 4 Previous results from Toksarı [12] and Ozdemir et al. [16]. Years

NGD_GA

RE

NGD_GASA

RE

Linear_SANGDE

RE

2001 2002 2003 2004 2005 2006

17403.64 18089.68 20261.44 23062.40 25721.88 27406.32

0.1638 0.1234 0.0417 0.1297 0.0402 0.0506

14678.75 15482.58 18534.42 20870.35 23833.67 27964.92

0.0127 0.0385 0.0470 0.0218 0.0361 0.0313

14284.87 15718.12 18439.07 23231.75 25469.64 29562.87

0.040 0.020 0.050 0.130 0.030 0.020

MAPE

0.0312

MAPE

0.048

2007 2008 2009

25846.84 28167.04 31462.04

0.2628 0.2512 0.0641

32342.64 33876.29 36415.83

0.0776 0.0995 0.0832

MAPE

0.1253

MAPE

0.0497

Linear_SANGDE model was presented by Ref. [12]. NGD_GASA model was presented by Ref. [16].

In this section, Turkey's natural gas demand levels are forecasted under two different scenarios using the proposed nonlinearbased NGD-BGA and NGD-BGA_SA. The forecasts are carried out for

Table 5 Comparison of MAPE values with Linear_SANGDE Model and NGD_GASA. Years

NGD-BGA

NGD-BGA_SA

NGD_GASA

Linear_SANGDE

2006 2009 2014

0.0162 0.0199 0.0188

0.0151 0.0175 0.0143

0.0312 0.0497

0.048

Linear_SANGDE model was presented by Ref. [12]. NGD_GASA model was presented by Ref. [16].


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MAPE 0.06 0.05

0.0497

0.048

0.04 0.03 0.02 0.01

0.0312 0.0199

0.0162

0.0188 0.0143

0.0175

0.0151

0 2006

2009

NGD-BGA_SA

NGD-BGA

2014 NGD_GASA

Linear_SANGDE

Fig. 6. Comprasion of MAPE values for different models.

the years between 2015 and 2030. The results are shown in Figs. 7 and 8. The assumptions of the scenarios are as follows [16]: - Scenario 1: The mean increase rate of GDP is 4%, the mean increase rate of population (POP) is 0.5%, and the mean increase rate of economic growth rate (GR) is 4% during the period of 2015 and 2030. - Scenario 2: The mean increase rate of GDP is 2%, the mean increase rate of population (POP) is 0.25%, and the mean increase rate of economic growth rate (GR) is 2% during the period of 2015 and 2030.

According to Fig. 7 (Scenario 1), the maximum natural gas demand levels will reach between 125652 (NGD-BGA) e 160547 (NGD-BGA_SA) Gm3 respectively. Then, they will reach between 67535 (NGD-BGA) e 82494 (NGD-BGA_SA) Gm3 in Fig. 8 (Scenario 2). As a result, the future projections are seriously important for planning and managing of the natural gas consumption policy.

5. Conclusions and further research The aim of this study is to estimate the best coefficients for the uncontrollable or controllable variables/parameters included in the

170000 163000 156000 149000 142000 135000 128000 121000 114000 107000 100000 93000 86000 79000 72000 65000 58000 51000 44000 37000 30000 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 NGD-BGA

NGD-BGA_SA

Fig. 7. Forecasts of NGD-BGA and NGD-BGA_SA algorithms under Scenario-1 for years between 2015 and 2030.

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90000 86000 82000 78000 74000 70000 66000 62000 58000 54000 50000 46000 42000 38000 34000 30000 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 NGD-BGA

NGD-BGA_SA

Fig. 8. Forecasts of NGD-BGA and NGD-BGA_SA algorithms under Scenario-2 for years between 2015 and 2030.

proposed model for natural gas demand/consumption forecasting. As a result of this study, the three forecasting models are applied. The first model is nonlinear regression forecasting model (NGD_NLR) which is obtained by using Minitab 15.0 statistical software. The second model is breeder genetic algorithm which is applied to the first model, NGD_NLR, for finding the values of regression coefficients taking place in the nonlinear regression forecasting model for breeder genetic algorithm (NGD-BGA). The third model, breeder hybrid model (NGD-BGA_SA), uses the simulated annealing that starts to its initial solution with the best parameters of the second model. When the performance of the algorithms is considered, the results of the MAPE values are better than [16] as %48.08 and %51.60 and [12] as %66.25 and 68.54 for years 2001e2006 of NGD-BGA and NGD-BGA_SA models, respectively. Similarly; Table 4 shows that the results are also better than [16] as %59.96 and %64.79 for years 2001e2009. Table 5 shows that NGD-BGA and NGD-BGA_SA algorithms give forecasts with significantly small MAPE values that are 0.0188 and 0.0143 for year 2014, respectively. In addition, Turkey's natural gas demand levels are forecasted under two different scenarios using the proposed nonlinear-based NGD-BGA and NGDBGA_SA. The forecasts are carried out for the years between 2015 and 2030. The results are shown in Figs. 7 and 8. Then, it is seen that the breeder hybrid model (NGD-BGA_SA) is superior to other models and can be used as general natural gas demand forecasting model. New input variables can be easily added to the proposed model(s) and parameter estimation can be carried out when the parameters are specified by expert opinions, decision maker and sector analyses. Also, proposed model can estimate natural gas demand with daily, monthly and annually data with error close to zero. This study opens the way to develop on a smart model that contains varying linear or nonlinear equations and parameters. The smart model is composed of forms of random types of function, parameters and powers. It will be selected the best model when the parameters are specified by expert opinions, decision maker and sector analyses.

Compliance with ethical standards Conflict of Interest: The authors declare that they have no conflict of interest. Acknowledgements A part of the study reported in this paper was performed within projects funded by TUBITAK (Scientific and Technological Research Council of Turkey) 2210-C program with grand number of 1649B021303459 and by Suleyman Demirel University Scientific Research Projects Unit (BAP) with grant number of 3626-YL-13. Authors would like to thank to the editor and the anonyms referees for their valuable comments and criticisms. Their contributions lead to the improved version of this paper. References [1] Kamyab F, Bahrami S. Efficient operation of energy hubs in time-of-use and dynamic pricing electricity markets. Energy 2016;106:343e55. [2] Li J, Dong X, Shangguan J, Hook M. Forecasting the growth of China's natural gas consumption. Energy 2011;36:1380e5. [3] Kaboli S, Hr A, Selvaraj J, Rahim NA. Long-term electric energy consumption forecasting via artificial cooperative search algorithm. Energy 2016;115: 857e71. [4] Panapakidis LP, Dagoumas AS. Day-ahead natural gas demand forecasting based on the combination of wavelet transform and ANFIS/genetic algorithm/ neural network model. Energy 2017;118:231e45. [5] Szoplik J. Forecasting of natural gas consumption with artificial neural networks. Energy 2015;85:208e20. [6] Karadede Y. A hybrid algorithm approach to curve fitting problems. Isparta, Turkey: Graduate School of Applied and Natural Sciences; 2014. Department of Industrial Engineering, M.Sc. Thesis, 96 pages, Suleyman Demirel University. [7] Sarak H, Satman A. The degree-day method to estimate the residential heating natural gas consumption in Turkey: a case study. Energy 2003;28:929e39. [8] Aras N. Forecasting residential consumption of natural gas using genetic algorithms. Energy Explor Exploitation 2008;26(4):241e66. [9] Ceylan H, Ozturk HK. Estimating energy demand of Turkey based on economic indicators using genetic algorithm approach. Energy Convers Manag 2004;45: 2525e37. [10] Toksari MD. Ant colony optimization approach to estimate energy demand of

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