Estimating Transport Energy Demand Using Ant Colony Optimization

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1Department of Civil Engineering, Pamukkale University, Denizli, Turkey. Abstract This study proposes a heuristic algorithm based on ant colony optimization.
Energy Sources, Part B, 7:188–199, 2012 Copyright © Taylor & Francis Group, LLC ISSN: 1556-7249 print/1556-7257 online DOI: 10.1080/15567240903030513

Estimating Transport Energy Demand Using Ant Colony Optimization O. BASKAN,1 S. HALDENBILEN,1 H. CEYLAN,1 AND H. CEYLAN1 1

Department of Civil Engineering, Pamukkale University, Denizli, Turkey Abstract This study proposes a heuristic algorithm based on ant colony optimization for estimating the transport energy demand (TED) of Turkey using gross domestic product, population, and vehicle-km. Three forms of the improved ant colony optimization transport energy demand estimation (IACOTEDE) models are used for improving estimating capabilities of TED models. Performance of IACOTEDE is compared with the Ministry of Energy and Natural Resources (MENR) projections. Sensitivity analysis is also carried out for testing the effects of the parameters. The quadratic form provided a better-fit solution to the observed data, and it underestimates Turkey’s TED by about 28% less than the MENR projection in year 2025. Thus, it may be used with a highest correlation coefficient and considerably lower relative error according as the MENR projection in the testing period. It is also expected that this study will be helpful in developing highly applicable and productive planning for transport energy policies. Keywords ant colony optimization, energy demand modeling, transport

1. Introduction Energy demand has rapidly been increasing all over the world because of developments in the industrial, agricultural, transportation, commercial, and housing sectors. Population rise and improved lifestyle are other reasons for the increase in energy demand. The fast growth on the gross domestic product (GDP) leads to an increase in the number of vehicle owners and hence to and increase in energy demand in the transportation sector (Murat and Ceylan, 2006). The transport sector is one of the major consumers of primary energy production in the world. It consumes about one-fifth of the primary energy in the world (Asmann and Sieber, 2005). Furthermore, strong population growth and rapid urbanization in Turkey have played an important role in energy consumption. In the long term, the Turkish economy is slated for robust, albeit sometimes erratic growth, and persistent inflation, which will need to be supported by steadily increasing energy supplies. Therefore, estimating the future energy demand is an important issue for a sustainable plan for the transport sector (Haldenbilen and Ceylan, 2005). The transportation sector takes one of the biggest shares in energy use in Turkey— about 21% of total energy consumption according to the World Energy Council-Turkish Address correspondence to Ozgur Baskan, Department of Civil Engineering, Transportation Division, Pamukkale University, Kinikli Campus, Denizli 20017 Turkey. E-mail: obaskan@pau. edu.tr

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National Committee (WEC-TNC, 2006). Transport energy demand (TED), GDP, population and vehicle-km, in the last 35 years, have increased about 4.3, 17, 2, and 9 times, respectively (Murat and Ceylan, 2006). It may be well known that the modeling of energy consumption in the transport sector depends on many factors such as vehicular usage, income, type of car, housing size, and many other socioeconomic factors. Including all the parameters in sectoral energy modeling previously mentioned, it is a difficult task since it requires much detailed study and also much data, many of which isunavailable. Therefore, it would be better to model transport energy consumption with simplified forms of mathematical expressions with available data. In this study, a heuristic algorithm is used that is proposed by Baskan et al. (2009) based on ant colony optimization (ACO), for estimating the transport energy demand of Turkey. Among improved ant colony optimization transport energy demand estimation (IACOTEDE) models, the best-fit model to the observed data is investigated and is selected for the future projection of Turkey’s transport energy demand. The reason for using the IACOTEDE is its flexible nature to solve the exponential and the quadratic equations. The available data are partly used for finding the optimal or near-optimal values of IACOTEDE parameters and partly used for testing of the IACOTEDE model for each form. The results are compared with the Ministry of Energy and Natural Resources (MENR) projections in Turkey. In this paper, three forms of the IACOTEDE models are developed for estimating Turkey’s future transport energy demand based on GDP, population and total annual vehicle-km. The objective function for the IACOTEDE model solution is to minimize the sum of squared error between the observed and predicted values for each form. This article is organized as follows. In the next section, some relevant literature review is given. Section 3 deals with the shortly general ACO approach and heuristic algorithm based on ACO that is used for estimating Turkey’s TED in this study. Section 4 deals with the IACOTEDE models application for estimating Turkey’s transport energy demand and problem formulation. Sensitivity analyses (SAs) on IACOTEDE parameters are given in Section 5. Forecasting the future energy consumption in Turkey’s transport sector is given in Section 6. Finally, in the last section, proposed models are discussed for estimating of Turkey’s transport energy demand in years 2006–2025.

2. Literature Review Turkey expects steadily-increasing growth in energy demand in the future as its economy expands, especially for gas in the transportation sector. Because of its limited energy resources, Turkey is greatly dependent on imported oil and gas, which is the most important fuel in Turkey, contributing 55% of total primary energy supply and importing 90% of its energy needs in 2004 (WEC-TNC, 2006). Passenger transport in Turkey increased by 2.5 times and goods transport increased by 4 times in the last two decades. The population increased by about 50% in the same time as well. Transportation demand increased more than GDP in Turkey when national economic parameters are compared to the transportation sector (Ceylan et al., 2008). Energy planning and future forecasting in Turkey are carried out by the MENR and it uses the Model for Analysis of Energy Demand model that requires a very detailed and large number of data for the total and sectoral energy consumption estimations. On the other hand, many models have been developed from many studies using various forms of mathematical formulations, which are related to energy development models (Ebohan, 1996; Say and Yucel, 2006). Gilland (1988) developed an energy demand projection

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of the world primary energy demand for the years 2000 and 2020. Ediger and Tatlidil (2002) proposed an approach that uses the analysis of cyclic patterns in historical curves to forecast the primary energy demand in Turkey. Ceylan and Ozturk (2004) developed a genetic algorithm (GA) for estimating the energy demand using GDP, population, and import and export figures. Yumurtaci and Asmaz (2004) proposed an approach to calculate the future energy demand of Turkey for the period of 1980 and 2050, based on the population and energy consumption increase rates per capita. Haldenbilen and Ceylan (2005) developed three forms of energy demand equations in order to forecast the transport energy consumption for future projections based on the GA notion. Ceylan et al. (2005a; 2005b) developed new models for estimating energy and exergy production and consumption values using the GA approach. Similarly, Murat and Ceylan (2006) obtained that modeling the energy consumption may be carried out with artificial neural networks (ANN) with a lack of future estimation because ANN is good at solving current data, but is not good for forecasting. Canyurt et al. (2007) proposed GA approaches for the modeling and development of the energy input estimation equations in order to make future projections. Toksari (2007) developed an ant colony energy demand estimation model for Turkey. In addition Sozen and Arcaklioglu (2007) developed the energy sources estimation equations in order to estimate the future projections and make correct investments in Turkey using the ANN approach. Saidur et al. (2007) applied the useful energy and exergy analysis models for different modes of transport in Malaysia and compared the result with a few countries. Ceylan et al. (2008) proposed a new method for estimating transport energy demand using the harmony search approach. Unler (2008) used the particle swarm optimization technique for Turkey’s energy demand estimation. Although there are many studies in literature ranging from GA to ANN to estimate energy demand, there is little application of ACO to energy modeling. In addition, there is no study to improve the ACO estimation capabilities by reducing the feasible search space (FSS). Thus this study illustrates IACOTEDE models to estimate transport energy demand.

3. Ant Colony Optimization ACO belongs to the class of biologically inspired heuristics. The procedure of the ACO algorithms simulates the decision-making processes of ant colonies as they forage for food and is similar to other artificial intelligent techniques. The ACO is the one of the most recent techniques for approximate optimization methods and was initiated by Dorigo (1992). The main idea is that it is indirect local communication among the individuals of a population of artificial ants. The core of the ants’ behavior is the communication between the ants by means of chemical pheromone trails, which enables them to find the shortest paths between their nest and food sources. The role of pheromones is to guide the other ants towards the target points. This behavior of real ant colonies is exploited to solve optimization problems. 3.1.

Improved Solution Algorithm for ACO

The heuristic algorithm that is used for estimating TED is based on each ant’s search only around the best solution of the previous iteration with ˇ. The heuristic algorithm differs from other ACOs in that its FSS is reduced with ˇ and its best solution obtained using information on the previous iteration. At the core of the algorithm, ants search

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randomly for the solution within the FSS to reach optimum or near-optimum values. At the end of the each iteration, only one of the ants is near to global optimum. After the first iteration, when global optimum is searched around the best solution of the previous iteration using ˇ, the algorithm will quickly reach to the global optimum. The algorithm consists of three main phases: initialization, pheromone update, and solution. All of these phases build a complete search to the global optimum as can be seen in Figure 1. At the beginning of the first iteration, all ants search randomly for the best solution of a given problem within the FSS, and an old ant colony is created at the initialization phase. After that, the quantity of pheromone is updated. In the solution phase, a new ant colony is created based on the best solution from the old ant colony using Eqs. (1) and (2). Then, the best solutions of two colonies are compared. At the end of the first iteration, FSS is reduced by ˇ and the best solution obtained from the

Figure 1. Steps of heuristic algorithm based on ACO.

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previous iteration is kept. ˇ guides the bounds of search space during the algorithm process, where ˇ is a vector, ˇ D .ˇ1 ; ˇ2 ; : : : ; ˇn /, and n is the number of variables. The range of the ˇ may be chosen between minimum and maximum bounds of any given problem. The optimum solution is then searched for in the reduced search space during the algorithm progress. Let number of m ants being associated with m random initial vectors .x k ; k D 1; 2; 3; : : : ; m/. The solution vector of the each ant is updated using the expression: k.new/

xt

k.ol d /

D xt

˙˛

(1)

.t D 1; 2; : : : ; I /

k.new/

k.ol d /

where xt is the solution vector of the kth ant at iteration t, xt is the solution obtained from the previous step at iteration t, and ˛ is a vector generated randomly to determine the length of jump. ˛ controls the global optimum search direction not being k.new/ trapped at bad local optimum. Ant vector xt obtained at tth iteration in Eq. (1) is determined using the value of the same ant obtained from the previous step. Furthermore, in Eq. (1), (C) sign is used when point xtk is on the left of the best solution on the x coordinate axis. ( ) sign is used when point xtk is on the right of the best solution on the same axis. The direction of search is defined by expression (2). x best D xtbest C .xtbest  0:01/ t

(2)

/  f .xtbest /, (C) sign is used in Eq. (1). Otherwise, the ( ) sign is used. If f .x best t .˙/ sign defines the search direction to reach to the global optimum. ˛ value is used to define the length of jump, and it will be gradually decreased in order not to pass over the global optimum, as shown in Figure 1. At the end of the each iteration, a new ant colony (see Figure 1, second loop) is developed as the number of colony size that is generated at the beginning of the each iteration. The quantity of pheromone .t / is reduced to simulate the evaporation process of real ant colonies using Eq. (3) in the pheromone update phase. After reducing of the number of pheromones, it is updated using Eq. (4). The quantity of pheromone only intensifies around the best objective function value. This process is repeated until the given number of iteration, I , is completed. t D 0:1  t t D t

1

1

C 0:01  f .xtbest1 /

(3) (4)

where initial pheromone intensity is set to 100. Consider a problem of 5 ants representing the formulation of the problem. For example, as shown in Figure 2, 5 ants being associated 5 random initial vectors. At the beginning of the first epoch (Figure 2a), the old ant colony is randomly created within the FSS for any given problem. After the pheromone update phase, a new ant colony is created at the last phase of the first epoch according to the old ant colony using Eqs. (1) and (2). After that, the best values of the two colonies are compared .E1 $ E10 ; E2 $ E20 ; : : : ; EI $ EI0 / where I is the iteration number, i D 1; 2; : : : ; I . According to the best value obtained so far by comparing the old and new colonies and ˇ, the FSS is reduced at the beginning of the second epoch and once again the old ant colony is created, as can be seen in Figure 2b. The new ant colony is created at the last phase of the second epoch according to a randomly generated ˛ value using Eq. (1). Any of the newly created solution vectors

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Figure 2. Main idea of heuristic algorithm based on ACO.

may be outside the reduced search space that is created at the beginning of the second epoch. Therefore, the created new ant colony prevents being trapped in a bad local optimum.

4. The Application of Heuristic Algorithm for the Estimation of Turkey’s TED Models which are obtained using IACOTEDE include three parameters: GDP, population, and total annual vehicle-km. The estimation of Turkey’s TED using three mathematical forms is given as shown. (5)

f .x/l i near D w1 X1 C w2 X2 C w3 X3 C w4 f .x/exp D w1 X1w2 C w3 X2w4 C w5 X3w6 C w7

(6)

f .x/quad D w1 X1 C w2 X2 C w3 X3 C w4 X1 X2 C w5 X1 X3 C w6 X2 X3 C w7

(7)

where f .x/l i near , f .x/exp , and f .x/quad are linear, exponential and quadratic forms of IACOTEDE models, respectively, and X1 , X2 and X3 are the GDP(109 US$), population (106 ) and total annual vehicle-km (109 ), respectively, wi 2 Wi .i D 1; 2; 3; : : : ; n/ are the corresponding weighting factors and n is the number of decision variables that changes from one model to another. The objective function, F , to be minimized is Min F D

m X .TEDobserved

TEDpredicted /2

(8)

i D1

where TEDobserved and TEDpredicted are the observed and predicted TED, m is the number of observations. 4.1.

Data for IACOTEDE

The GDP and the TED are collected from the Central Bank of Turkey (2007) and the WEC-TNC (2006). Observed vehicle-km and population are taken from the General

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Directorate of Turkish Highways (GDTH, 2005) and National Statistics (NS, 2006). During the IACOTEDE modeling process, each form of the model is validated using the available data partly for use in estimating the weighting factors and partly for the testing purposes. The first 26 years observed data from 1970 to 1995 are used for estimating the weighting factors and the 10 years data from 1996 to 2005 are used for testing. The testing procedure is carried out to obtain the minimum relative errors between the observed and estimated values in the period of testing. 4.2.

The Solution of IACOTEDE Models

The model parameters such as colony size (CS) and ˇ are chosen according to lowest relative errors in testing period of each form of proposed IACOTEDE models. The linear form of the IACOTEDE model is: f .x/linear D 0:0087X1 C 0:1131X2 C 0:0921X3

1:3210 (9)

R2 D 0:94

F D 6:42

The exponential form of the IACOTEDE model is: f .x/exp D 8:7402X1 F D 6:48

0:0956

C 0:8576X2

13:2746

C 0:5962X30:7471 C 7:1921

R2 D 0:94

(10)

The quadratic form of the IACOTEDE model is: f .x/quad D 0:0170X1 C 0:1075X2 C 0:0122X3 0:0002X1 X2 C 0:0002X1 X3 C 0:0011X2 X3 F D 5:99

0:7433

(11)

R2 D 0:95

where F is the final values of objective function given in Eq. (8) and R2 is the correlation coefficient for each equation. The comparisons of IACOTEDE outputs and their relative errors in the testing period are given for the period of 1996 to 2005 in Table 1. The relative errors based on the observed values for each IACOTEDE and WEC-TNC (2006) are compared. The relative errors obtained, for example, in 2000 are about 5%, 7%, 9%, and 45% for linear, exponential, quadratic forms of the IACOTEDE models, and MENR, respectively. Although the highest relative error in the testing period is in the quadratic form of the IACOTEDE model, the quadratic form gives lowest F and highest R2 values in the observation period as shown in Eq. (11).

5. Sensitivity Analysis SA is carried out for testing the effects of the solution parameters of IACOTEDE models. The choosing of the CS and ˇ that it is chosen differently for each weighting factor is a very important step for the algorithm to find optimum or near-optimum results in IACOTEDE models. Six different cases chosen for the SA for each IACOTEDE model are given in Table 2. Best fit values and mean absolute relative errors of each case for IACOTEDE models in the testing period are given in Table 3.

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Table 1 The comparison of the IACOTEDE models an MENR projection for the testing period between 1996–2005

Years

TED (observed), MTOE

1996 11.78 1997 11.34 1998 10.76 1999 13.32 2000 12.12 2001 12.00 2002 11.32 2003 12.40 2004 13.80 2005 13.78 Mean absolute error

f .x/li near , Relative MTOE error, % 10.90 11.49 11.99 11.97 12.68 12.04 12.32 12.90 13.94 14.55

7.47 1.32 11.45 10.17 4.65 0.33 8.79 4.09 1.04 5.62 5.49

f .x/exp , Relative MTOE error, % 10.82 11.63 12.16 12.11 12.98 12.39 12.23 12.36 13.20 13.53

8.11 2.55 13.01 9.06 7.14 3.22 8.00 0.33 4.34 1.81 5.76

f .x/quad , Relative MTOE error, % 11.05 11.75 12.35 12.28 13.16 12.31 12.65 13.35 14.67 15.45

6.14 3.62 14.76 7.82 8.57 2.62 11.77 7.72 6.37 12.11 8.15

MENR, Relative MTOE error, % — 13.11 14.46 15.96 17.61 17.58 18.06 18.55 19.06 19.58

— 15.63 34.39 19.80 45.33 46.50 59.54 49.65 38.17 42.11 39.01

According to SA results, Cases 1, 4, and 2 are chosen to obtain best values of parameters for the each form of IACOTEDE models since they provided lowest relative errors in testing period.

6. Forecasting Turkey’s Transport Energy Demand 6.1.

Estimation of IACOTEDE Parameters

For estimating Turkey’s transport energy demand in the future using the IACOTEDE model, the GDP, population and total annual vehicle-km needs to be estimated. Then, the future transport energy demand can be forecasted. The estimation of socioeconomic and transport related indicators is performed in the as shown. For the annual GDP: y D 0:1418x 2 C 1:6654x C 25:045

R2 D 0:90

(12)

where y is the GDP in 109 US$/yr, and x is the time series .1970 D 1; 1981 D 2 : : : 2005 D 36/. For the population: y D 1:0975x C 3318

R2 D 0:99

(13)

where y is the population in 106 /yr, and x is the time series .1970 D 1; 1981 D 2 : : : 2005 D 36/. For the total annual vehicle-km: y D 0:0219x 2 C 0:5239x C 6:5904

R2 D 0:98

(14)

where y is the total annual vehicle-km in 109 /year, and x is the time series .1970 D 1; 1981 D 2 : : : 2005 D 36/.

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O. Baskan et al. Table 2 Solution parameters for IACOTEDE models Solution parameters for f .x/exp

Case

CS

ˇ1

ˇ2

ˇ3

ˇ4

ˇ5

ˇ6

ˇ7

1 2 3 4 5 6

10 10 20 20 30 30

1.5 3.0 1.5 3.0 1.5 3.0

0.4 0.8 0.4 0.8 0.4 0.8

0.4 0.8 0.4 0.8 0.4 0.8

0.8 1.6 0.8 1.6 0.8 1.6

0.8 1.6 0.8 1.6 0.8 1.6

0.8 1.6 0.8 1.6 0.8 1.6

0.1 0.2 0.1 0.2 0.1 0.2

Solution parameters for f .x/quad Case

CS

ˇ1

ˇ2

ˇ3

ˇ4

ˇ5

ˇ6

ˇ7

1 2 3 4 5 6

10 10 20 20 30 30

0.15 0.30 0.15 0.30 0.15 0.30

0.15 0.30 0.15 0.30 0.15 0.30

0.15 0.30 0.15 0.30 0.15 0.30

0.005 0.010 0.005 0.010 0.005 0.010

0.00015 0.00030 0.00015 0.00030 0.00015 0.00030

0.002 0.004 0.002 0.004 0.002 0.004

5 10 5 10 5 10

Solution parameters for f .x/l i near Case

CS

ˇ1

ˇ2

ˇ3

ˇ4

1 2 3 4 5 6

10 10 20 20 30 30

0.5 1.0 0.5 1.0 0.5 1.0

0.5 1.0 0.5 1.0 0.5 1.0

1.0 2.0 1.0 2.0 1.0 2.0

4.0 8.0 4.0 8.0 4.0 8.0

6.2.

Forecasting Turkey’s Transport Energy Demand Using IACOTEDE Models

Future estimation of the three forms of the IACOTEDE and the MENR (WEC-TNC, 2006) projections are shown in Figure 3. All forms of the IACOTEDE model underestimates the energy demand when they are compared with the MENR projections, as can be seen in Figure 3. The MENR estimates transport sector energy consumption is about 38 MTOE in 2025. Linear, exponential, and quadratic forms of the IACOTEDE model estimate about a value of 24, 22, and 30 MTOE at the same year, respectively. The linear and exponential forms of models provide very close estimation results to each other and underestimate the energy demand when they are compared with the MENR projections. However, it can be seen that the MENR projections overestimate by about 18% the transport energy demand when the MENR (WEC-TNC, 2006) projections are compared with the observed transport energy demand between 2000 and 2005. Therefore, quadratic

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Table 3 Obtained results in the SA for each case F values and mean absolute relative errors in testing period for the IACOTEDE models Linear

Exponential

Quadratic

Case

F values

Relative errors, %

F values

Relative errors, %

F values

Relative errors, %

1 2 3 4 5 6

6.42 4.38 5.41 5.10 4.53 8.72

5.49 21.09 9.21 10.66 15.34 6.80

5.54 6.25 4.80 6.48 5.38 5.34

14.83 7.44 17.35 5.76 15.07 13.09

5.39 5.99 4.48 4.17 4.78 4.29

10.76 8.15 16.4 29.95 11.85 17.77

Figure 3. Future estimations of transport energy demand using IACOTEDE and MENR.

forms of the IACOTEDE model may be chosen as the best-fit model for forecasting transport energy demand. In the observation period, the quadratic form of IACOTEDE models gives lowest F and highest R2 values when three forms of IACOTEDE models are compared.

7. Conclusions This study seeks a way of possible application of the heuristic IACOTEDE algorithm to forecast Turkey’s transport energy demand for next 20 years. Transport energy demand is analyzed for the period 1970 to 2005 based on the GDP, population and vehicle-km as independent variables. The logic of the proposed IACOTEDE algorithm and the application to transport energy demand are described in detail. The SA on IACOTEDE algorithm parameters is carried out and best fit values of IACOTEDE parameters are obtained. The

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IACOTEDE models are compared with MENR projections. These conclusions can be drawn from this study: 1. Three forms of the IACOTEDE model may be used for estimating transport energy demand, but all forms of IACOTEDE model underestimate the energy demand when they are compared with the MENR projections although they provide minimum objective function values. Thus, quadratic forms of the models would be better to choose for energy modeling. In spite of the quadratic form of IACOTEDE models that underestimates transport sector energy consumption about 28% less than the MENR projections in year 2025, it can be used with a highest correlation coefficient and considerably lower relative error according to MENR projection in the testing period for Turkey’s future transport energy projections. 2. The linear and exponential form of the IACOTEDE models also may be used as alternative solutions and estimation techniques for transport energy demand. They will provide an alternative way of energy planning during the decision-making process and they also provide useful information for scientists. 3. The solution of the IACOTEDE models for each form showed a steady convergence toward an optimum as shown in Table 3. Although each of the SA cases may be used for model solution, the values of Cases 1, 4, and 2 are selected as a best-fit models for linear, exponential and quadratic forms of the IACOTEDE and then selected for future forecasting. 4. IACOTEDE models are flexible in nature to provide many near-optimal solutions to estimate the future trends of the transport energy demand. This advantage comes from the ACO approach itself, because the IACOTEDE starts the solution of the problem from a large search space. The model is actually a multi-parameter solution, which has many feasible solution points. Hence, the IACOTEDE can be used for estimating the energy demand in the future by optimizing the parameter values using available data. For future studies the transport demand management projects may be developed and the transportation systems may be planned for the future, accounting for these estimations on transport energy demand. As a developing country, Turkey needs a robust planning and/or approache to utilize energy sources for the future. The projections may help planners to plan their energy need for future. Future studies therefore should take into account the various parameters, such as import, export, and technological developments, and so on, to estimate the energy demand.

Acknowledgments The authors would like to thank the reviewers for their useful comments. Scientific & Technological Research Council of Turkey (TUBITAK), with the Project Number 104I119, is also acknowledged.

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