ARTICLE IN PRESS
Energy Policy 35 (2007) 3984–3990
www.elsevier.com/locate/enpol
Ant colony optimization approach to estimate energy
demand of Turkey
M. Duran Toksarı
Engineering Faculty, Industrial Engineering Department, Erciyes University, 38039 Kayseri, Turkey
Received 29 November 2006; accepted 30 January 2007
Available online 23 March 2007
Abstract
This paper attempts to shed light on the determinants of energy demand in Turkey. Energy demand model is first proposed using the
ant colony optimization (ACO) approach. It is multi-agent systems in which the behavior of each ant is inspired by the foraging behavior
of real ants to solve optimization problem. ACO energy demand estimation (ACOEDE) model is developed using population, gross
domestic product (GDP), import and export. All equations proposed here are linear and quadratic. Quadratic_ACOEDE provided
better-fit solution due to fluctuations of the economic indicators. The ACOEDE model plans the energy demand of Turkey until 2025
according to three scenarios. The relative estimation errors of the ACOEDE model are the lowest when they are compared with the
Ministry of Energy and Natural Resources (MENR) projection.
r 2007 Elsevier Ltd. All rights reserved.
Keywords: Ant colony optimization; Energy demand; Turkey
1. Introduction
Energy plays a critically significant role in the economic
and social development of a country. Therefore, identification and analysis of energy issues and development of
energy policy options are of prime importance (Dincer and
Dost, 1996; Utlu and Hepbasli, 2006a). Energy demand
estimation is one of the most important policy tools used
by the decision makers for a developing country. Turkey,
which is a Eurasian country that stretches from the
Anatolian peninsula in Southwestern Asia to the Balkan
region of Southeastern Europe, is a developing country.
The importance of energy as an essential ingredient in
economic growth as well as in any strategy for improving
the quality of human life is well established. The energy
policy agenda has changed significantly since the days of
1973 and 1979 oil crises (Utlu and Hepbasli, 2006a, b).
When average annual gross domestic product (GDP) of the
Turkish in last decade is 4.02 its population increased by
Tel.: +90 352 4374901; fax: +90 352 4375784.
E-mail address: [email protected].
0301-4215/$ - see front matter r 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.enpol.2007.01.028
about 50% in the last two decades. Proportion of imports
covered by exports in last decades is 62.3%. In the long
term, the Turkish economy is slated for robust, albeit
sometime erratic growth and persistent inflation, which will
need to be supported by steadily increasing energy supplies
(Haldenbilen and Ceylan, 2005).
According to collected data the Ministry of Energy and
Natural Resources (MENR, 2006), the energy import ratio of
Turkey in 2005 is about 72%, and the majority of this import
is based on petroleum and natural gas (Sayin et al., 2005).
Countries like Turkey should plan carefully about their energy
demand for critical periods, such as economic crises that
usually hit Turkey. Economic crisis hit Turkey three times in
the last decade, once in 1994 and the others in 2000 and 2001.
These periods showed that energy consumption fluctuates and
indicated a decreasing trend. After the economic crises, the
consumption of energy showed the same trend as before the
economical crises (Ceylan and Ozturk, 2004).
Turkey has been experiencing substantial demand
growth in all segments of the energy sector. The primary
energy need of Turkey has been growing by some 6% per
annum for decades. Recent forecasts indicate that this
ARTICLE IN PRESS
M. Duran Toksarı / Energy Policy 35 (2007) 3984–3990
trend will continue as a result of rapid urbanization and
industrialization (Hepbasli et al., 2007).
In future, a very large growth in energy demand in
Turkey is expected for primary energy types such as
electricity, natural gas and oil because of limited resources.
Table 1 shows Turkey’s primary energy production and
consumption in 2000–2005 according to the data collected
from MENR in detail. When productions of coal, lignite
and oil natural gas are less than their respective consumptions of eating these, for hydraulic, electric, heat and wood,
each production is equal to its consumption, respectively.
Many researchers (Uri, 1980; Kavrakoglu, 1983; Yu and
Been, 1984; Ebohon, 1996; Cheng and Lai, 1997; Ceylan
and Ozturk, 2004; Canyurt and Öztürk, 2006; Say and
Yücel, 2006) have studied on the relationship between
energy consumption and income. In the energy literature,
meta-heuristic methods, which are used to solve combinatorial optimization problem, have been narrowly applied to
estimate energy consumption. Ceylan and Ozturk (2004)
used genetic algorithm (GA) for estimating energy demand,
and Canyurt and Öztürk (2006) proposed three applications of GA techniques on oil demand estimation. Canyurt
et al. (2006) developed GA approaches for the transport
energy demand estimation. Ozcelik and Hepbasli (2006)
applied another meta-heuristic, which simulated annealing,
to estimate petroleum energy production and consumption.
However, ant colony optimization (ACO) has never been
applied to estimate energy demand in the literature.
In this paper, models obtained by using ACO-based
algorithm are suggested to forecast energy demand of
Turkey. The estimation of energy demand based on
economic indicators uses various forms of equations. These
forms are linear and quadratic. The economic indicators
that were used during the model development are GDP,
population and import and export data of Turkey.
The paper is organized as follows. First, ACO are be
explained. The proposed ACO algorithm to estimate
3985
energy demand are detailed in Section 3. In Section 4,
models for energy demand of Turkey are developed by
using algorithm proposed in Section 3. Finally, proposed
models are discussed Turkey’s energy demand in years
2006–2025 and uses three scenarios.
2. ACO
ACO belongs to the class of biologically inspired
heuristics. The basic idea of ACO is to imitate the
cooperative behavior of ant colonies. ACO for solving
combinatorial optimization problems was initiated by
Dorigo (1992). The principle of these methods is based on
the way ants search for food and find their way back to the
nest. During trips of ants a chemical trail called pheromone
is left on the ground. The role of pheromone is to guide the
other ants towards the target point. For one ant, the path is
chosen according to the quantity of pheromone.
As illustrated in Fig. 1, when facing an obstacle, there is
an equal probability for every ant to choose the left or right
path. As the left trail is shorter than the left one it required
less travel time, and it will end up with higher level of
pheromone. More the ants take the right path, higher the
pheromone trail is. This fact will be increased in the
evaporation stage.
The general ACO algorithm is illustrated in Fig. 2. The
procedure of the ACO algorithm manages the scheduling
of three activities (Talbi et al., 2001; Dorigo and Di Caro,
1999): The first step consists mainly of the initialization of
the pheromone trail. In the iteration (second) step, each ant
constructs a complete solution to the problem according to
a probabilistic state transition rule. The state transition
rule depends mainly on the state of the pheromone. The
third step updates the quantity of pheromone; a global
pheromone updating rule is applied in the two phases.
First, a fraction of the pheromone evaporates, and then
each ant deposits an amount of pheromone which is
Table 1
Turkey’s primary energy production and consumption in 2000–2005
Years
Coal
(MTOE)a
Lignite
(MTOE)
Oil
(MTOE)
Natural gas
(106m3)
Hydraulic
(GWh)
Electric
(GWh)
Heat
(GWh)
Wood
(MTOE)
Energy production
2000
2392
2001
2494
2002
2319
2003
2059
2004
1946
2005
2170
60,854
59,572
51,660
46,168
43,709
55,282
2749
2551
2420
2375
2276
2281
639
312
378
561
708
980
30,879
24,010
33,684
35,330
46,084
39,561
76
90
105
89
93
94
648
687
730
784
811
926
16,938
16,263
15,614
14,991
14,393
13,819
Energy consumption
2000
15,525
2001
11,176
2002
18,830
2003
17,535
2004
18,904
2005
19,421
64,384
61,010
52,039
46,051
44,823
56,577
31,072
29,661
29,776
30,669
31,729
30,016
15,086
16,339
17,694
21,374
22,446
27,314
30,879
24,010
33,684
35,330
46,084
39,561
76
90
105
89
93
94
648
687
730
784
811
926
16,938
16,263
15,614
14,991
14,393
13,819
a
MTOE: million tons of oil equivalents.
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Fig. 1. Ants finding the shortest path around an obstacle.
Step 1. Initialization
- Initialize pheromone trail
Step 2. Solution construction
- For each ant Repeat
Solution construction using the pheromone trail
Step 3. Update the pheromone trail
Until stopping criteria
Fig. 2. A generic ACO algorithm
proportional to the fitness of its solution. This process is
iterated until a stopping criterion (Toksarı, 2006).
vectors. For example, if the number of coefficients of the
design parameters
of an ant is three
is three, initial vector
ðk ¼ 1; 2; . . . ; mÞ
dimensions vk ¼ xkinitial ; ykinitial ; zkinitial
(see Fig. 3(a) for parameters (x, y, z) are bounded by
ð1ox; y; zo1ÞÞ.
Then, modifications based on the pheromone trail are
then applied to each vector. In the proposed ant colonybased algorithm, quantity of pheromone (tt) only intensifies around the best objective function value obtained from
the previous iteration and all ants turn towards there to
search a solution (Fig. 3b). The solution vector of each ant
is updated at beginning of the each iteration using the
formula
xkt ¼ xbest
t1 dx;
ðt ¼ 1; 2; . . . ; I Þ,
(3)
3. ACO energy demand estimation (ACOEDE)
ykt ¼ ybest
t1 dy;
ðt ¼ 1; 2; . . . ; I Þ,
(4)
ACOEDE was developed from ACO algorithm used to
find global minimum (Toksarı, 2006). Models which are
obtained using ACO include four economic parameters:
population, GDP, import and export. The estimation of
energy demand based on economic indicators was modeled
by using various forms, e.g. linear and quadratic. For
example, quadratic form can be expressed as
zkt ¼ zbest
t1 dy;
ðt ¼ 1; 2; . . . ; I Þ,
(5)
E ACEDE
¼ w1 þ w2 X 1 þ w3 X 2 þ w4 X 3 þ w5 X 4
quad
þ w6 X 1 X 2 þ w7 X 1 X 3 þ w8 X 1 X 4
þ w9 X 2 X 3 þ w10 X 2 X 4 þ w11 X 3 X 4
þ w12 X 21 þ w13 X 22 þ w14 X 23 þ w15 X 24 .
ð1Þ
ACO optimizes coefficients (wi) of the design parameters
(Xi), which are included by models, concurrently. Objective
function of model, f(v) takes the following form:
n
2
X
Min f ðvÞ ¼
si E observed
E predicted
.
(2)
i
i
i¼1
ACO algorithm searches the best set of coefficients for the
design parameters. In the proposed ACO algorithm, first m
number of ants are associated with m random initial
where xkt ; ykt and zkt are solution values of the kth ant at
best best
iteration t, xbest
t1 ; yt1 ; zt1 is the best solution obtained at
the iteration t1 and dx, dy and dz are vectors generated
randomly from [a, a] range to determine the length of jump.
At the end of the each iteration, quantity of pheromone (tt) is
updated in two phases. First, the quantity of pheromone (tt)
is reduced to simulate the evaporation process by the formula
(6). In a second phase, the pheromone is only reinforced
around the best objective function value obtained from the
previous iteration (formula (7)):
tt ¼ 0:1 tt1 ,
(6)
best best
tt ¼ tt1 þ 0:01 f xbest
t1 ; yt1 ; zt1 .
(7)
This process is iterated until number of maximum
iteration (I).
In formulas (3), (+) sign is used when point vkt is on the
left of global minimum on the x-coordinate axis and ()
sign is used when point xkt is to the right of global minimum
on the x-coordinate axis. This condition is valid for all
dimensions. The direction of movement is defined by
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M. Duran Toksarı / Energy Policy 35 (2007) 3984–3990
a
3987
z=1
y
x= –1
z
x=1
y=1
1
Ant 2
B
Ant 1
A
z= –1
1
Ant 5
E
-–3
–2
x
Ant 3
C
Global
Optimum
–1
1
2
Ant 4
D
–1
3
y=–1
–1
b
Global
Optimum
x
Ant 4
D1
Ant 1
Ant 2
A1
B1
Ant 3
C1
Ant 5
E1
z
C
y
Fig. 3. (a) Five ants being associated with five random initial vectors (the best vector is on the C point. So, quantity of pheromone intensifies only between
optimum and C point). (b) The first iteration (searching was only done between optimum and C point. At the end of the iteration 1, the best vector is on
the D1 point and so, quantity of pheromone only intensifies between optimum and D1 point).
4. Development of ACOEDE models for Turkey
Institute (TSI, 2006) and the MENR. When GDP, import,
export and population are obtained from TSI and
WECTNC, the observed data for energy were collected
from MENR. Table 2 shows the observed data between
1979 and 2005.
Two models for energy demand for Turkey are developed by using proposed ACOEDE algorithm. These are
linear_ACOEDE (Ylinear), the linear form of ACOEDE,
and _ACOEDE (Yquadratic) is the quadratic form of
ACOEDE. Common parameters for ACOEDE models
are that the number of ants (m) are 500, and maximum
iteration (I) is 1000. Twenty-seven data (1979–2005) were
used to determine the weighting parameters of ACOEDE
models:
Turkey’s energy demand models are developed by using
the ACO-based algorithm and observed data between 1970
and 2005. The data are collected from Turkish Statistical
Y linear ¼ 51:3046 þ 0:0124X 1 þ 1:8102X 2
þ 0:3524X 3 0:4439X 4 ,
following three equations:
best
best
x̄best
initial ¼ xinitial þ xinitial 0:01 ,
(8)
best
best
ȳbest
initial ¼ yinitial þ yinitial 0:01 ,
(9)
best
best
z̄best
initail ¼ zinitial þ zinitial 0:01 .
(10)
pffiffiffi
Setting a ¼ 0.1 a at end of the each iteration I to not
pass over global minimum (I is number of maximum
iteration). Thus, the length of jumping will gradually
decrease.
Steps of the proposed algorithm are as in Fig. 4.
ð11Þ
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M. Duran Toksarı / Energy Policy 35 (2007) 3984–3990
3988
Initialization
Set the initial values:
Stopping criterion: maximum iteration n X I ,
The interval dx vector is to be generated initial ,
Generate m random initial vectors (x kinitial , y kinitial , z kinitial (k = 1,2,...,m)) (or all of them may
be set to the same value), each one associated to an ant and assign this as current
solution( f (v)kinitial ) ,
Determine (x initial , y initial , z initial ),
best
best
best
Define the direction of movement by equations (8), (9) and (10).
Solution Manipulation
FOR k = 1 TO n
FOR i =1 TO k X I
FOR all ants
Generate dx random vector within
[a,b]
range,
Calculate new solution of each ant by equations (3), (4) and (5),
IF f (vt
) ≤ f (vbest
t−1 )
best
ELSE v
globalmin
THEN
best
v globalmin = vt
best
= vt−1
Update of the Number of Pheromone
Generate it by equations (6) and (7).
END
END
END
Fig. 4. Ant colony optimization for estimating energy demand.
f ðvÞlinear ¼ 45:7239; R2linear ¼ 99:52%,
Y quadratic ¼ 96:4418 0:4820X 1 þ 4:7370X 2 þ 1:0937X 3
2:8935X 4 þ 0:0188X 1 X 2 þ 0:0230X 1 X 3
0:0255X 1 X 4 0:0625X 2 X 3
þ 0:1014X 2 X 4 þ 0:0915X 3 X 4 0:0027X 21
0:0466X 22 0:0389X 23 0:0651X 24 ,
ð12Þ
f ðvÞquadratic ¼ 27:9470; R2quadratic ¼ 99:70%,
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 3
shows relative errors between estimated and observed data.
Table 3 shows that ACOEDE models for energy demand
estimation are very robust and successful. Although the
biggest deviation is 3.87% from linear_ACOEDE, it is a
quite acceptable level.
5. ACOEDE models for future estimation of Turkey’s
energy demand
Three scenarios are used to estimate Turkey’s energy
demand in the years 2006–2025. They are compared with
the MENR projection.
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. Fig. 5 shows that the estimated values for two
forms of ACOEDE and MENR for the Scenario 1. The
linear_ACOEDE gives lower estimates of the energy demand
than the quadratic_ACOEDE and the MENR projections.
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. When Fig. 6
presents that the estimated values for two forms of
ACOEDE and MENR for the Scenario 2, the linear_ACOEDE gives the lowest estimates of the energy demand.
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. As can be seen from Fig. 7, two
forms of ACOEDE give nearly the same estimation and
they are better than the MENR projections.
The low and very high estimations of energy demand are
unlikely to be realized in Turkey in the long term (Ceylan
and Ozturk, 2004). Hence, lowest and highest values for the
energy demand of Turkey should be determined. These
values can be obtained from ACOEDE models.
6. Conclusions
In this study, estimation of Turkey’s energy demand
based on ACO is studied based on GDP, population,
ARTICLE IN PRESS
M. Duran Toksarı / Energy Policy 35 (2007) 3984–3990
import and export. Two forms of the ACOEDE developed
using 27 data (1979–2005). Three scenarios are proposed to
estimate Turkey’s energy demand in the years 2006–2025
using the two forms of the ACOEDE. They are compared
with the MENR projection. The following main conclusions may be drawn from the results of the present study:
(a) Both linear_ACOEDE and quadratic_ACOEDE for
Three scenarios should be used to estimate the energy
demand of Turkey. Scenarios 1 and 3 have their estimations close. However, for Scenario 2, linear_ACOEDE
linear_ACOEDE
quadratic_ACOEDE
MENR
400
Energy Demand(MTOE)
350
Table 2
Energy demand, GDP, population, import and export data of Turkey
between 1979 and 2005 (TSI and MENR)
2022
2024
2022
2024
2020
2018
2016
Years
Fig. 5. Energy demand for Scenario 1.
linear_ACOEDE
quadratic_ACOEDE
MENR
400
350
300
250
200
150
100
50
2020
2018
0
2016
2.26
2.91
4.7
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
2014
5.07
7.91
8.93
8.84
9.24
10.76
11.34
11.1
14.16
14.34
15.79
22.3
21.05
22.87
29.43
23.27
35.71
43.63
48.56
45.92
40.67
54.5
41.4
51.55
69.34
97.54
116.77
2014
43.531
44.439
45.54
46.688
47.864
49.07
50.307
51.433
52.561
53.715
54.894
56.098
57.193
58.248
59.323
60.417
61.532
62.667
63.823
65.001
66.432
67.421
68.365
69.302
70.231
71.152
72.974
2012
82
68
72
64
60
59
67
75
86
90
108
151
150
158
179
132
170
184
192
207
187
200
146
181
239
299
361
2012
30.71
31.97
32.05
34.39
35.7
37.43
39.4
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
80.5
75.4
78.33
83.84
87.82
91.58
0
2010
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
50
2010
Export
($109)
100
2008
Import
($109)
150
2008
Population
(106)
200
2006
GDP
($109)
250
2006
Energy
demand
(MTOE)
300
Energy Demand (MTOE)
Years
3989
Years
Fig. 6. Energy demand for Scenario 2.
Table 3
Energy demand estimation of ACOEDE 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
80.5
75.4
78.33
83.84
87.82
91.58
Estimated energy demand (MTOE)
Relative errors (%)
Linear_ACOEDE
quadratic_ACOEDE
linear_ACOEDE
quadratic_ACOEDE
69.48
72.06
73.14
73.80
80.10
74.94
78.55
82.25
87.54
93.10
70.52
73.67
75.67
76.09
81.47
73.73
80.55
84.38
88.10
93.01
0.54
2.33
2.10
3.87
0.50
0.61
0.28
1.90
0.32
1.66
0.94
0.15
1.28
0.89
1.20
0.89
2.83
0.64
0.32
1.58
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M. Duran Toksarı / Energy Policy 35 (2007) 3984–3990
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References
linear_ACOEDE
quadratic_ACOEDE
MENR
400
Energy Demand (MTOE)
350
300
250
200
150
100
50
2024
2022
2020
2018
2016
2014
2012
2010
2008
2006
0
Years
Fig. 7. Energy demand for Scenario 3.
gives lower estimates of the energy demand than the
quadratic_ACOEDE.
(b) Although the largest deviation is 3.87% for
linear_ACOEDE, the largest deviation is 2.83% for
quadratic_ACOEDE. Then, we can say that quadratic_ACOEDE provided better fit solution due to the fluctuations
of the economic indicators.
(c) The estimation of energy demand of Turkey using the
ACOEDE forms is underestimated when the results are
compared to the MENR results. ACOEDE forms give
lower estimates of the energy demand than the MENR
results.
(d) The estimation of energy demand can also be
investigated with, neural networks or other metaheuristic
such as tabu search, genetic algorithm, simulated annealing, variable neighborhood search, etc. The results of the
different methods could be compared with the ACO
method to see the performance of the ACOEDE.
(e) The developed models based on the ACO approach
proved to be a successful energy estimation tool. The
results of the present study are also expected to give a new
direction to scientists and policy makers in implementing
energy planning studies and in dictating the energy
strategies as potential tool.
Acknowledgments
The authors is grateful for the support provided for the
present work by the Ministry of Energy and Natural
Resources of Turkey and Turkish Statistical Institute. The
authors also highly appreciate the constructive comments
of the reviewers.
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