A novel hybrid approach based on Particle Swarm ...

Energy Conversion and Management 53 (2012) 75–83

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

A novel hybrid approach based on Particle Swarm Optimization and Ant Colony Algorithm to forecast energy demand of Turkey Mustafa Servet Kıran a, Eren Özceylan b,⇑, Mesut Gündüz a, Turan Paksoy b a b

Selcuk University, Computer Engineering Department, 42075 Konya, Turkey Selcuk University, Industrial Engineering Department, 42075 Konya, Turkey

a r t i c l e

i n f o

Article history: Received 21 May 2011 Received in revised form 25 July 2011 Accepted 2 August 2011 Available online 22 September 2011 Keywords: Ant Colony Optimization Energy demand Estimation Hybrid meta-heuristic Particle Swarm Optimization Turkey

a b s t r a c t This paper proposes a new hybrid method (HAP) for estimating energy demand of Turkey using Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO). Proposed energy demand model (HAPE) is the first model which integrates two mentioned meta-heuristic techniques. While, PSO, developed for solving continuous optimization problems, is a population based stochastic technique; ACO, simulating behaviors between nest and food source of real ants, is generally used for discrete optimizations. Hybrid method based PSO and ACO is developed to estimate energy demand using gross domestic product (GDP), population, import and export. HAPE is developed in two forms which are linear (HAPEL) and quadratic (HAPEQ). The future energy demand is estimated under different scenarios. In order to show the accuracy of the algorithm, a comparison is made with ACO and PSO which are developed for the same problem. According to obtained results, relative estimation errors of the HAPE model are the lowest of them and quadratic form (HAPEQ) provides better-fit solutions due to fluctuations of the socio-economic indicators. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction Energy, as a resource of many things, with its ever growing role in world economy, and its multi-purpose application in production and consumption, has gained special attention. Through the development of societies and growth of economic activities, energy becomes more effective on countries and their sectors [1]. Hence, carrying an idea about energy demand and energy policy is a problem which has a serious importance. Turkey, which is a Eurasian country that stretches across the Anatolian peninsula in western Asia and Thrace in the Balkan region of southeastern Europe, has been one of the fastest growing power markets in the world with its young and growing population, rapid urbanization, strong economic growth and low per-capita electricity consumption for two decades [2,3]. Fig. 1 shows energy demand growth rates of ENTSOE (European Network of Transmission System Operators for Electricity) members and Turkey. High growth potential of Turkey could be seen clearly besides other European countries. Turkey’s primary energy consumption sources are mostly lignite coal, hard coal, hydropower, oil, natural gas, geothermal, solar energy, wood, as well as animal and plant wastes. However, the level of energy production in Turkey is very low. Fig. 2 shows the each primary energy source ratio of production to consumption of Turkey. In Turkey’s primary energy sources, except coal, lignite, ⇑ Corresponding author. Tel.: +90 332 2232075; fax: +90 332 2410635. E-mail address: [email protected] (E. Özceylan). 0196-8904/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2011.08.004

oil and natural gas, other source’s (hydraulic, spa water, wind, wood, solar, etc.) production and consumption values are balanced (see others in Fig. 2). While the proportion of primary energy consumption covered by production is totally 38.26% in 1999, this ratio has been decreased with 27.43% in 2008. At present, around 26% of the total energy demand is being met by domestic energy sources, while the rest originates from a diversified import-portfolio [5]. Coal, natural gas and oil consumptions are very close and have 84.74% in total primary energy consumption, while their production is 19.75% in total primary energy production in 2008. In other words, only a small percentage of total primary consumption was provided by domestic production. It is expected that by the year 2020, domestic energy consumption will reach 222 MTOE (million tons of oil equivalents), while domestic production will be at 70 MTOE, or 30% of national demand [6]. Aforementioned situations show that Turkey is forced to increase its dependence on foreign energy supplies. Thus, the accurate estimating of energy demand is very critical factor for Turkey’s energy policy. Estimation energy demand is usually dependent on many socio-economic factors such as GDP, population, import, export, growth rate and availability energy resources. Considering all parameters in energy demand modeling is a difficult task since it requires much detailed study and also much data, for which many of the data are unavailable. Therefore, it would be better to model energy demand forecasting with simplified forms of mathematical expressions using available data [8]. The goal of

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M.S. Kıran et al. / Energy Conversion and Management 53 (2012) 75–83

Fig. 1. Energy consumption growth rates 2010–2015 [4].

this study is to provide an accurate and a realistic estimation model for energy demand via using GDP, population, import and export figures of Turkey. The energy estimation model (HAPE) based on hybridized PSO and ACO is developed in two forms (linear and quadratic) and applied to forecast energy demand of Turkey. In the following section, a brief description of the problem and literature survey about the solution approaches to the problem is given. In Section 3, the concept of swarm intelligence and the basic PSO and ACO algorithms are given. Proposed hybrid PSO–ACO algorithm (HAP) is explained in Section 4. Energy demand forecasting model (HAPE), which is developed for Turkey case, is given and results obtained by proposed approach, comparisons with PSO and ACO and future projections are presented in Section 5. Finally, the study is concluded in Section 6 with suggestions for future researches. 2. Literature review Energy estimation modeling is a subject of widespread current interest among practitioners and academicians concerned with problems of energy production and consumption [2]. First applications on energy demand forecasting in Turkey have been implemented by State Planning Organization (SPO) via using of simple regression techniques [9]. Modern econometric techniques have been applied for energy planning and estimation of future energy demands of Turkey in 1984 first. One of these modern econometric

techniques, model for analysis of energy demand (MAED) which is a kind of simulation model and developed by International Atomic Energy Agency (IAEA) was started to be used by Ministry of Energy and Natural Resources of Turkey (MENR) [10]. MAED is used to estimate the medium and long term energy demand, considering the relationships between several factors that affect the social, economic and technologic system of the country [11]. In the overall assessment of Turkey energy demand forecasts, these studies always foresaw energy demand as being greater than it actually is. These policies lead Turkey to be import dependent and much more vulnerable to external shocks and prevent energy markets from liberalizing [12]. Hence, many models have been developed from many researches using various forms of mathematical formulations, which are directly or indirectly related to energy development models to find a relation between energy consumption and income [13–15]. For energy forecasting, statistical models are also considered by Ediger and Tatlıdil [11] which previous studies on energy forecasting of Turkey are summarized, Yumurtacı and Asmaz [30], Ediger and Akar [27], Mucuk and Uysal [35], Akkurt et al. [36] and Dilaver and Hunt [12]. In the energy estimation literature, meta-heuristic methods, which are used to solve combinatorial optimization problem, have been rarely applied to estimate energy consumption [10]. A summary of techniques, used for Turkey’s energy demand forecasting is given in Table 1. Therefore, given the discussion above, ACO and PSO algorithms are applied to forecast energy demand of Turkey. But, there is no hybrid meta-heuristic model which is applied for energy demand estimation in literature. Hence, to the best knowledge or the authors, this study is the first application of a hybrid model which is combined PSO and ACO to estimate energy demand of Turkey.

3. Particle Swarm and Ant Colony Optimization Algorithms 3.1. Particle Swarm Optimization Particle Swarm Optimization is one of the recent meta-heuristic techniques proposed by Kennedy and Eberhart [37] based on natural flocking and swarming behavior of birds and insects. It is initialized with a population of random solutions and searches for optimal by updating generations. In PSO, the potential solutions called as particles, move through the problem space by following the current optimum particles [38]. The individuals in a PSO have a position and a velocity. The PSO algorithm works by attracting the particles to search space positions of high fitness. Each particle has a memory function, and adjusts its trajectory according to two pieces of information, the best position that it has so far visited, and the global best position attained by the whole swarm [38]. Each particle keeps a memory of its previous best position, pbest, and a particle takes all the population as its topological neighbors, the best value is a global best and is called gbest. The

Fig. 2. Proportion (%) of primary energy consumption covered by production [7].

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M.S. Kıran et al. / Energy Conversion and Management 53 (2012) 75–83 Table 1 Summary of Turkish energy demand estimation studies. Method used

Author(s)

Forecasting for

Genetic Algorithm (GA)

Canyurt et al. [16] Ceylan and Öztürk [17] Öztürk et al. [18] Ceylan et al. [19] Haldenbilen and Ceylan [20] Canyurt and Öztürk [3]

Energy demand Energy demand Energy demand Energy and exergy consumption Transport energy demand Oil demand

Artificial Neural Network (ANN)

Sözen et al. [2] Murat and Ceylan [21] Sözen and Arcaklıog˘lu [22] Hamzaçebi [23] Kavaklıog˘lu et al. [24] Kankal et al. [25]

Energy consumption Transport energy demand Energy consumption Electricity consumption Electricity consumption Energy consumption

Ant Colony Optimization (ACO)

Toksarı [10] Toksarı [26]

Energy demand Electricity demand

Autoregressive Integrated Moving Average (ARIMA) Seasonal Autoregressive Integrated Moving Average (SARIMA)

Ediger and Akar [27] Erdog˘du [28]

Primary energy demand Electricity demand

Grey Prediction with Rolling Mechanism (GPRM)

Akay and Atak [29]

Electricity demand

Linear Regression (LR)

Yumurtacı and Asmaz [30]

Electricity demand

Winters’ Exponential Smoothing Method and Cycle Analysis

Ediger and Tatlıdil [11]

Primary energy demand

Modeling Based on Degree-day Concept

Sarak and Satman [31]

Natural gas demand

Multivariable Regression Model

Görücü and Gümrah [32]

Gas consumption

First order Autoregressive Time Series Model

Aras and Aras [33]

Natural gas demand

Harmony Search Algorithm (HSA)

Ceylan et al. [8]

Transport energy demand

Simulated Annealing (SA)

Özçelik and Hepbasßlı [34]

Petroleum energy consumption

Particle Swarm Optimization (PSO)

Ünler [9]

Energy demand

PSO algorithm operates iteration by iteration and solution produced in each iteration is compared self-local best and global best of swarm. V velocity of particle, X particle vector and N number of particle, the new position of particle is computed according to the following equations:

v i ðt þ 1Þ ¼ w v i ðtÞ þ c1 rand1 ðpbseti ðtÞ xi ðtÞÞ þ c2 rand2 ðgbesti ðtÞ xi ðtÞÞ

ð1Þ

xi ðt þ 1Þ ¼ xi ðtÞ þ v i ðt þ 1Þ ði ¼ 1 NÞ

ð2Þ

where c1 and c2 determine the relative influence of the social and cognitive components (learning factors), rand1 and rand2 note two random numbers uniformly distributed in the interval [0, 1]. w is a parameter called inertia weight [39] used to control the impact of the previous velocities on the current one. In proposed PSO, inertia value of the equation changes on the each iteration (Eq. (3)). This change is based on the logic of decreasing from the value determined to minimum value according to inertia function. The objective is to converge the created speed by diminishing on the further iterations; hence more similar results can be obtained [40]. Inertia function is obtained and used as follow:

w ¼ t i=t

ð3Þ

where t is the maximum iteration number and i is the current iteration index. The particles try to achieve to global minimum by using global and local best information. According to the above explanations and equations, generic PSO algorithm is given in Table 2. 3.2. Ant Colony Optimization Ant Colony Optimization algorithm based on the foraging behavior of ants has been first introduced by Dorigo and Gambardella [41]. The basic idea of ACO is to imitate the cooperative behavior of ant colonies. As soon as an ant finds a food source, it

evaluates it and carries some food back to the nest. During the return trip, the ant deposits a pheromone trail on the ground. The pheromone deposited, the amount of which may depend on the quantity and quality of the food, guides other ants to the food source [42]. Quantity of pheromone on the arc is decreased in time due to evaporating. Each ant decides to a path or way according to the quantity of pheromone. More pheromone trail consists in short path than long path. The technique is based on updating pheromone trail of good solutions and there are many ant models in this way [41,43]. Continuous ACO algorithm has been introduced and used for optimization of benchmark functions [10,44] and energy and electricity demand estimating of Turkey [10,26]. In continuous ACO algorithm, quantity of pheromone (st) is only intensified around the best objective value obtained from the previous iteration and all ants are closed towards that value to search a solution. t is iteration index and i is number of iterations and new positions of the ants (k) are updated using the following equation [10]:

xktþ1 ¼ xgbest @x ðt ¼ 1; 2; 3; . . . IÞ t

ð4Þ

ox is a vector generated randomly from [a, a] range to determine the length of jumps. The length ofpffiffijump is set by using at+1 = 0.1 at equation at the end of I iterations. xgbset is the t parameter of the best solution found by ants and equals to dimension of ox. ± is the direction operator of movement in Eq. (4). To be (+) or () is decided by using the following equation:

xbest ¼ xgbest þ ðxgbest 0:01Þ

ð5Þ

If f ð xbest Þ 6 f ðxgbest Þ, (+) sign is used, otherwise () is used in Eq. (5). Quantity of pheromone is reduced to simulate the evaporation process as in the following equation:

st ¼ 0:1 st1

ð6Þ

Pheromone is only increased around the best objective value obtained from the previous iteration (Eq. (7)).

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Table 2 Generic algorithm of PSO. 1. Initialization Generate random initial solutions for particles Determine gbest of swarm and pbest of particles 2. For all particles Generate new solutions using Eqs. (1) and (2) 3. Update global pbest and local gbest 4. Not stopping criterion go to Step 2 5. Stop Fig. 3. Interaction between swarm and colony.

st ¼ st1 þ ð0:01 f ðxgbest ÞÞ

ð7Þ

The generic algorithm of ACO is shown in Table 3. 4. Hybrid method based on PSO and ACO (HAP) The best solution is assigned global best solution of the system according to comparing best solutions which are found by PSO and ACO. Solution parameters are transferred to the global best of PSO and ACO. Thus, they are motivated generating new solutions by using the system solution parameters. While pheromone trail is only updated around of the best solution obtained in ACO, the pheromone trail is updated around of the best solution of system in HAP. Initially, ants and particles are randomly distributed to the search space or may be set same values in HAP algorithm. While colony and swarm exhibit individual behaviors at the beginning, they begin to be affected from the global best of system during any iteration. Also, while the ants try to close to the global minimum with Eqs. (4)–(7); the particles use Eqs. (1)–(3) for closing to the global minimum. The best solutions found by particles and ants are compared during any iteration. Where xgbest and pgbest are the best solutions of colony and swarm, interaction between swarm and colony is shown as follows (Fig. 3). Search ability of PSO and continuous ACO around the global best is improved by using technique in Fig. 3. This improvement leads to better results in optimization problems. If the best solution of ants is affected from the best solution of particles, movement direction operator must be updated. Therefore, the direction operator must be kept up to date during the iterations by being used Eq. (5). The algorithm of HAP is shown in Table 4 (initialization phase) and Table 5 (solution manipulation phase) according to explanations and equations given above. 5. Estimation of Turkey energy demand with HAPE HAPE was developed from HAP algorithm used to find global minimum. Four indicators (GDP, population, import and export) were used in energy demand estimating model which are proposed based on HAP. These indicators are commonly used in

Table 3 Generic algorithm of ACO. 1. Initialization Assign to each ant initial solution Update pheromone trail 2. Solution For all ants Create the solution using pheromone trail 3. Updating pheromone Evaporate the pheromone trails of all solutions a certain amount of Update pheromone trails according to solutions created 4. Not stopping criterion go to Step 2 5. Stop

literature [9,10,26,46] and believed that energy demand of a country is mostly affected by them. Table 6 shows four indicators and energy demand of Turkey between 1979 and 2005. The data are collected from Turkish Statistical Institute (TSI) and the MENR. Data until 2005 is used to make a comparison with other models which are developed by PSO and ACO for the same problem. It is clear that there is a linear relationship between four indicators and energy demand (Table 6). For example, while GDP, population, import and export of Turkey increased 3.4; 0.63; 22 and 31.5 times respectively, energy consumption of Turkey has increased 1.98 times between 1979 and 2005 years. In this study, the estimation of energy demand based on economic indicators was modeled by using various forms, e.g. linear (Eq. (8)) and quadratic (Eq. (9)). Linear form (HAPEL) can be expressed as,

Elinear ¼ w1 X 1 þ w2 X 2 þ w3 X 3 þ w4 X 4 þ w5

ð8Þ

and quadratic form (HAPEQ) can be expressed as,

Equadratic ¼ w1 X 1 þ w2 X 2 þ w3 X 3 þ w4 X 4 þ w5 X 1 X 2 þ w6 X 1 X 3 þ w7 X 1 X 4 þ w8 X 2 X 3 þ w9 X 2 X 4 þ w10 X 3 X 4 þ w11 X 21 þ w12 X 22 þ w13 X 23 þ w14 X 24 þ w15

ð9Þ

HAPE model optimizes coefficients (wi) of the design parameters (Xi), which are included by models, concurrently. In energy demand estimating, the aim is to find the fittest model to the data. The fitness function of the model is given by (Eq. (10)),

min f ðv Þ ¼

R X

ðErobserv ed Epredicted Þ2 r

ð10Þ

r¼1

where Eobserved and Epredicted are the actual and predicted energy demand, respectively, r is the number of observations. Turkey’s energy Table 4 Initialization of HAP. Initialize

pffiffi Stopping criteria: n I Generate ox vector with aintial For all ants Generate xkinitial values)

ðk ¼ 1; 2; . . . ; mÞ vectors (or all of them may be set same

Associate each ant to f ðxÞkinitial

ðk ¼ 1; 2; . . . ; mÞ solutions

Determine the xgbest according to f ðxÞkinitial solutions For all particles Generate pkinitial values)

ðk ¼ 1; 2; . . . ; mÞ vectors (or all of them may be set same

Associate each particle to f ðpÞkinitial ðk ¼ 1; 2; . . . ; mÞ solutions Determine the self-local best solutions according to f ðpÞkinitial LBEST kinitial

ðk ¼ 1; 2; . . . ; mÞ ðk ¼ 1; 2; . . . ; mÞ

Determine pgbest vector according to f ðpÞkinitial solutions (GBEST) Apply the technique (Fig. 2) to the best solutions between colony and swarm Determine the movement direction of ants using Eq. (5) Update pheromone using Eqs. (6) and (7) around of the best solution

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parameters of HAPE models. HAPEL and HAPEQ models with aforementioned parameters and data were tested 20 times and best results were considered. Following HAPE (linear and quadratic) equations have been obtained for energy forecasting. In the linear form, coefficients obtained are given below:

Table 5 Solution manipulation of HAP. For k = 1 to n

pffiffi For i = 1 to k I For all ants Generate ox random vector within [a, a] range Calculate new position of each ant by Eq. (4) End Determine

Elinear ¼ 0:003762X 1 þ 1:912553X 2 þ 0:373362X 3 þ 0:483252X 4 55:909111

vector xbest i gbest

If f ðX best Þ 6 f ðx Þ then xgbest ¼ xi best i For all particles Calculate new position of each particle using Eqs. (1) and (2) End For all particles Determine parameters of local best solutions LBESTk (k = 1, 2, . . ., m) End Determine pbest vector i Þ f ðpgbest Þthen pgbest ¼ pbest If f ðpbest i i Apply technique (Fig. 2) to the best solutions between colony and swarm Update pheromone by using Eqs. (6) and (7) around of the best solution End at = 0.1 at1 End

ð11Þ

f ðv Þlinear ¼ 41:702954 In the quadratic form of the proposed model, coefficients obtained are given below:

Equadratic ¼ 0:103937X 1 þ 1:811010X 2 1:477769X 3 þ 1:117386X 4 þ 0:002523X 1 X 2 þ 0:011235X 1 X 3 0:007423X 1 X 4 þ 0:012079X 2 X 3 0:002990X 2 X 4 þ 0:015805X 3 X 4 0:001414X 21 0:006979X 22 0:017030X 23 0:010368X 24 43:309577 ð12Þ

f ðv Þquadratic ¼ 20:539297 Table 6 Energy demand, GDP, population, import and export data of Turkey [7,47]. Year

Energy demand (MTOE)

GDP ($109)

Population (106)

Import ($109)

Export ($109)

1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

30.71 31.97 32.05 34.39 35.70 37.43 39.40 42.47 46.88 47.91 50.71 52.98 54.27 56.68 60.26 59.12 63.68 69.86 73.78 74.71 76.77 80.50 75.40 78.33 83.84 87.82 91.58

82.00 68.00 72.00 64.00 60.00 59.00 67.00 75.00 86.00 90.00 108.00 151.00 150.00 158.00 179.00 132.00 170.00 184.00 192.00 207.00 187.00 200.00 146.00 181.00 239.00 299.00 361.00

43.53 44.44 45.54 46.69 47.86 49.07 50.31 51.43 52.56 53.72 54.89 56.10 57.19 58.25 59.32 60.42 61.53 62.67 63.82 65.00 66.43 67.42 68.37 69.30 70.23 71.15 72.97

5.07 7.91 8.93 8.84 9.24 10.76 11.34 11.10 14.16 14.34 15.79 22.30 21.05 22.87 29.43 23.27 35.71 43.63 48.56 45.92 40.67 54.50 41.40 51.55 69.34 97.54 116.77

2.26 2.91 4.70 5.75 5.73 7.13 7.95 7.46 10.19 11.66 11.62 12.96 13.59 14.72 15.35 18.11 21.64 23.22 26.26 26.97 26.59 27.78 31.33 36.06 47.25 63.17 73.48

demand by using the structure of the Turkey socio-economic conditions is the main objective of this study. HAPE models (linear (HAPEL) and quadratic (HAPEQ)) are developed to estimate the future energy demand values based on population, GDP (gross domestic product), import and export figures (Table 6). The HAPE model was coded with MATLAB 2009 and run on a Pentium IV, 1.66 GHz, 2 GB RAM notebook computer. One of the important problems is setting the best parameters of PSO and ACO. According to Shi and Eberhart [39] c1 and c2 have a fixed value as 2. Hence, in this study these fixed values are also used. Except mentioned parameters, the other parameters are considered as; inertia weight (w): 1; number of maximum iteration (I): 100,000; number of particles and ants (m): 20; n: 40. Twenty-seven data (1979–2005) were used to determine the weighting

where X1 is GDP, X2 is population, X3 is import, X4 is export and f(v) is sum of squared errors. Ten data (1996–2005) were used to validate the models. Table 7 shows relative errors between estimated and observed data. According to Table 7, proposed HAPE approach for energy demand estimation is very robust and successful. Although the largest deviation is 3.37% for linear form and 2.77% for quadratic form, they are quite acceptable levels. The largest deviations are obtained in 1999 because of the decrease in GDP, import and export in that year (Table 6). Results show that quadratic form provided better fit estimation than the linear form due to the fluctuations of the economic indicators. Figs. 4 and 5 show the comparisons between proposed HAPE model, PSO and ACO. While compared ACO is proposed by Toksarı [10]; PSO is developed by Ünler [9]. It is observed that while proposed HAPEL approach is providing better fit estimation than ACO and PSO in linear form (Fig. 4), HAPEQ model has better estimation than ACO and a bit worse estimation than PSO because PSO gave importance to 1996–2005 data more (Fig. 5). When 27 data is considered (1979–2005), proposed approach finds less relative error than the other studies in both of linear and quadratic forms. Tables 8 and 9 give coefficients and forecasting relative errors of each study in linear and quadratic forms, respectively. In order to show the accuracy of proposed models, three scenarios are used for forecasting Turkey’s energy demand in the years

Table 7 Energy demand estimation of proposed models between 1996 and 2005 years. Years

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Observed energy demand (MTOE)

69.86 73.78 74.71 76.77 80.50 75.40 78.33 83.84 87.82 91.58

Estimated energy demand (MTOE)

Relative errors (%)

Linear (HAPEL)

Quadratic (HAPEQ)

Linear (HAPEL)

Quadratic (HAPEQ)

69.71 72.32 73.30 74.18 80.71 75.71 79.14 82.37 87.19 93.10

69.76 72.79 74.43 74.64 81.17 74.71 79.59 84.32 87.12 92.49

0.21 1.98 1.88 3.37 0.26 0.41 1.03 1.75 0.72 1.66

0.14 1.34 0.37 2.77 0.83 0.91 1.61 0.57 0.79 0.99

80


94 92 90 88 86 84 82 80 78 76 74 72 70 68 1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2004

2005

Fig. 4. Comparisons of energy demand in linear form.

94 92 90 88 86 84 82 80 78 76 74 72 70 68

1996

1997

1998

1999

2000

2001

2002

2003

Fig. 5. Comparisons of energy demand in quadratic form.

2006–2025 and they are compared with Toksari’s [10] ACO, Ünler’s [9] PSO models and observed 4 years data. Since it is proven that ACO and PSO models already give better results than MENR projection, it is not mentioned in this study either. Each scenario is explained below [10]; Scenario 1: It is assumed that the average growth rate of GDP is 6%, population growth rate is 0.17%, import growth rate is 4.5%, and export growth rate is 2% during the period of 2006–2025. Scenario 2: It is assumed that the average growth rate of GDP is 5%, population growth rate is 0.15%, import growth rate is 5%, and proportion of import covered by export is 45% during the period of 2006–2025. Scenario 3: It is assumed that the average growth rate of GDP is 4%, population growth rate is 0.18%, import growth rate is 4.5%, and export growth rate 3.5% during the period of 2006–2025. Table 10 and Fig. 6 show the estimated values for two forms of proposed approach for the Scenario 1. According to Fig. 6, proposed HAPEQ form gives lower forecasts of the energy demand than ACO and PSO linear models. For quadratic form, HAPEL gives lower estimates of the energy demand than ACO quadratic, but it gives a bit higher estimation values than PSO linear model. When all methods are compared with observed data according to Scenario 1, it is seen that all methods give similar estimations. Table 11 and Fig. 7 present that the forecasted values for two forms of HAPE, PSO and ACO for the Scenario 2. As can be seen from Fig. 7, HAPEL form has lower estimations than ACO linear and a bit higher than PSO linear forms. Proposed HAPEQ form gives lower forecasts of the energy demand than PSO and ACO quadratic forms. When all methods are compared with observed data according to Scenario 2, it is seen that while linear models give closer estimations, quadratic models produce much higher results. Estimated values for two forms of proposed approach for the Scenario 3 could be seen in Table 12 and Fig. 8. Fig. 8 presents that

Table 8 Comparisons of coefficients and relative errors in linear form. Coefficients

HAPEL

ACO

PSO

w1 w2 w3 w4 w5 Relative error

0.0038 1.9126 0.3734 0.4833 55.9091 41.7029

0.0124 1.8102 0.3524 0.4439 51.3046 45.7239

0.0021 1.9126 0.3431 0.4240 55.9022 42.6139

Table 9 Comparisons of coefficients and relative errors in quadratic form. Coefficients

HAPEQ

ACO

PSO

w1 w2 w3 w4 w5 w6 w7 w8 w9 w10 w11 w12 w13 w14 w15 Relative error

0.1039 1.8110 1.4778 1.1174 0.0025 0.0112 0.0074 0.0121 0.0030 0.0158 0.0014 0.0070 0.0170 0.0104 43.3096 20.5393

0.4820 4.7370 1.0937 2.8935 0.0188 0.0230 0.0255 0.0625 0.1014 0.0915 0.0027 0.0466 0.0389 0.0651 96.4418 27.9470

0.4820 4.7370 1.0937 2.9350 0.0188 0.0230 0.0255 0.0625 0.1014 0.0915 0.0027 0.0466 0.0387 0.0651 96.4408 27.6640

the estimated values for linear form of proposed method (HAPEL) gives lower estimations than ACO and it also gives lower values than PSO model until 2011, and then it has similar estimations with PSO. In quadratic form, as it can be seen from Fig. 8, proposed

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M.S. Kıran et al. / Energy Conversion and Management 53 (2012) 75–83 Table 10 Future projections of total energy demand in MTOE according to Scenario 1. Year


2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025

99.59 107.63 106.34 106.14 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

Linear

Quadratic

HAPEL

ACO

PSO

HAPEQ

ACO

PSO

94.66 96.31 98.04 99.86 101.77 103.78 105.89 108.11 110.44 112.88 115.45 118.15 120.98 123.96 127.08 130.36 133.80 137.42 141.22 145.20

95.50 97.27 99.15 101.11 103.18 105.35 107.64 110.03 112.56 115.21 118.01 120.95 124.02 127.26 130.67 134.24 138.01 141.96 146.12 150.50

94.80 96.33 97.94 99.63 101.40 103.26 105.21 107.26 109.40 111.66 114.02 116.50 119.10 121.83 124.69 127.69 130.84 134.15 137.61 141.23

94.28 96.83 99.59 102.58 105.79 109.25 112.96 116.91 121.10 125.53 130.19 135.04 140.07 145.21 150.41 155.59 160.66 165.47 169.87 173.66

96.07 99.39 103.01 106.94 111.18 115.74 120.62 125.81 131.29 137.03 143.00 149.13 155.36 161.58 167.65 173.43 178.69 183.20 186.63 188.60

95.94 99.46 103.33 107.50 112.06 116.92 122.17 127.75 133.66 139.87 146.39 153.13 159.97 166.88 173.78 180.37 186.59 192.13 196.71 199.94

Fig. 6. Future projections of total energy demand in MTOE according to Scenario 1.

Table 11 Future projections of total energy demand in MTOE according to Scenario 2. Year

2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025



Linear

Quadratic

HAPEL

ACO

PSO

HAPEQ

ACO

PSO

104.40 105.63 106.92 108.27 109.66 111.13 112.65 114.23 115.89 117.62 119.43 121.31 123.28 125.34 127.49 129.74 132.09 134.54 137.11 139.80

104.40 105.77 107.20 108.69 110.24 111.86 113.56 115.32 117.19 119.12 121.14 123.24 125.45 127.75 130.15 132.69 135.32 138.07 140.96 143.98

103.34 104.52 105.75 107.04 108.37 109.77 111.22 112.74 114.32 115.97 117.69 119.49 121.37 123.33 125.38 127.52 129.76 132.10 134.55 137.10

120.77 123.69 126.66 129.69 132.78 135.90 139.07 142.25 145.44 148.63 151.80 154.92 157.97 160.93 163.76 166.44 168.91 171.14 173.07 174.65

145.96 152.71 159.75 167.10 174.74 182.70 190.97 199.56 208.47 217.71 227.27 237.16 247.37 257.90 268.74 279.88 291.30 302.99 314.92 327.07

146.67 153.62 160.87 168.46 176.40 184.65 193.28 202.25 211.66 221.42 231.55 242.04 252.97 264.26 275.98 288.13 300.63 313.53 326.82 340.47

HAPEQ model gives the lowest forecasts of the energy demand. When all methods are compared with observed data according to

Scenario 3, it is seen that all models produce lower estimation results than observed data.

82



Table 12 Future projections of total energy demand in MTOE according to Scenario 3. Year

2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025



Linear

Quadratic

HAPEL

ACO

PSO

HAPEQ

ACO

PSO

94.12 95.19 96.31 97.48 98.71 100.01 101.35 102.77 104.25 105.81 107.43 109.14 110.94 112.82 114.79 116.86 119.03 121.31 123.71 126.22

94.94 96.11 97.34 98.62 99.97 101.39 102.86 104.40 106.01 107.71 109.48 111.35 113.28 115.31 117.46 119.69 122.04 124.49 127.07 129.79

94.32 95.36 96.44 97.58 98.77 100.01 101.31 102.67 104.09 105.59 107.15 108.78 110.50 112.30 114.18 116.16 118.23 120.40 122.67 125.06

92.41 92.85 93.26 93.65 94.02 94.35 94.66 94.94 95.20 95.42 95.62 95.79 95.94 96.06 96.19 96.24 96.30 96.34 96.37 96.38

93.88 94.84 95.95 97.24 98.74 100.49 102.53 104.92 107.71 110.97 114.76 119.17 124.29 130.21 137.04 144.91 153.95 164.31 176.15 189.66

93.70 94.83 96.13 97.62 99.35 101.36 103.70 106.42 109.58 113.24 117.49 122.41 128.08 134.63 142.15 150.78 160.66 171.95 184.82 199.46


6. Conclusion Modeling and forecasting of energy demand has a significant importance for providing sustainable energy policy for countries. That’s why, in this study, estimation of Turkey’s energy demand with a hybrid model based on PSO and ACO is suggested via considering GDP, population, import and export socio-economic indicators.

Two forms (linear and quadratic) of the HAPE model are developed to meet the fluctuations of economic indicators. 27 years data (1979–2005) is used to show the availability and advantages of proposed approach. Three scenarios are proposed to estimate Turkey’s energy demand in the years 2006–2025 using the two forms of the HAPE. They are compared with ACO and PSO models. In addition, the following main conclusions may be drawn in this study:


While the largest deviation is 3.37% for linear form (HAPEL), the largest deviation is 2.77% for quadratic form (HAPEQ) in modeling with 27 years data (1979–2005). Then, it is observed that quadratic HAPEQ provided better fit solution than linear form due to the fluctuations of the economic indicators. While HAPEL gives lower relative error than ACO linear model with 8.79% and PSO linear model with 2.14%; HAPEQ gives lower relative error than ACO quadratic model with 26.51% and PSO quadratic model with 25.75%. According to results of modeling 1979–2005 years, proposed hybrid model is better than ACO and PSO. In scenario analysis 2006–2025 years, quadratic form of proposed hybrid model gives better forecasts than ACO and PSO; linear form of proposed hybrid model gives better forecasts than ACO and similar outputs with PSO. The estimation of energy demand of Turkey using HAPEQ form is underestimated and HAPEL form has close estimations when the results are compared with ACO and PSO linear and quadratic forms. So, it can be said that HAPE forms, especially HAPEQ is more realistic and acceptable in future scenarios. It is clear that the suggested models are satisfactory tools for successful energy demand forecasting and policy. Forecasting of energy demand can also be investigated with bee colony optimization, artificial bee colony, bacterial foraging optimization, fuzzy logic, artificial neural networks or other meta-heuristic such as tabu search and simulated annealing.

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