Research ArticleForecasting Iranrsquos Energy Demand Using CuckooOptimization Algorithm

Sayyed Abdolmajid Jalaee 1 Amin GhasemiNejad 2 Mehrdad Lashkary 3

and Maryam Rezaee Jafari4

1Professor of Economics Shahid Bahonar University of Kerman Kerman Iran2PhD Student of Economics Shahid Bahonar University of Kerman Kerman Iran3BSc Economics Shahid Bahonar University of Kerman Kerman Iran4MSc Economics Shahid Bahonar University of Kerman Kerman Iran

Correspondence should be addressed to Amin GhasemiNejad aminghasemiecogmailcom

Received 18 April 2019 Revised 6 July 2019 Accepted 10 July 2019 Published 2 September 2019

Academic Editor Vyacheslav Kalashnikov

Copyright copy 2019 Sayyed Abdolmajid Jalaee et al +is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

+is study deals with the modeling of the energy consumption in Iran to forecast future projections based on socioeconomic anddemographic variables (GDP population import and export amounts and employment) using the cuckoo optimization al-gorithm For this purpose four diverse models including different indicators were used in the analyses Linear and power forms ofequations are developed for each model +e related data between 1972 and 2013 were used partly for installing the models +eresult of the models shows that the obtained demand estimation linear models are in closer agreement with the observed dataparticularly the linear model with five independent variables including GDP population import export and employment whichoutperformed other linear models Finally the future energy demand of Iran is forecasted up to the year 2030 using these modelsunder three scenarios

1 Introduction

Energy is a foundation element of the modern industrialeconomy Over the past few decades energy has become avery critical element in industries and also a fundamentalproduct and factor in the growth of the economy in differentworld regions Ever-increasing dependence of human life onenergy hasmade this factor play a critically crucial role eitherpotentially or actively in the functions of various economicsectors of countries

In spite of the fact that Iran has the richest sources ofenergy squandering and despicable utilization of them causeirrecoverable harm to the national annual financial plan+ecost is evaluated proportionally to the whole national annualdevelopment financial plan (around 5 billion $) As in-dicated by approximately settled raw petroleum generationincrease in the measure of domestic utilization will promptto diminish in oil fares and therefore will diminish proceeds

from the offer of oil incomes In this manner energy ad-ministration issue has specific significance regardingmaintaining oil export capacity diminishing energy in-tensity and sporadic development in utilization ecologicalinsurance and monetary limitations for interest in theenergy sector

+erefore Iranian authorities have to forecast moreexactly the energy consumption in the correct arranging anddirection utilization so that to manage the way they soughtenergy demand and supply parameters So energy demandexpectation is vital to auspicious supply Hence regulationson the raised issues result in focusing on energy security

+e Ministry of Energy which assessed the amount ofenergy consumption in Iran during 1972ndash2013 also preparedthe detailed breakdown of energy consumption For ex-ample in 2013 Iran consumed about 13207 million barrelsof oil equivalents (Mboe) which consisted of 4825Mtoe ofpetroleum 6967Mboe of natural gas 3Mboe of coal

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 2041756 8 pageshttpsdoiorg10115520192041756

84Mtoe of biofuel energy and 1302Mboe of electricalenergy

Distinctive techniques acquainted with energy consump-tion expectation According to the increasing demand forenergy the assessment of energy is necessary +is assessmentcan be done based on socioeconomic indicators using differentmethods of mathematical demonstration +e energy demandequations can be expressed in linear or nonlinear forms In-telligent optimization technique entities eg birds bats andfireflies are appropriate to forecast these models

+is article focuses on forecasting the energy demand inIran based on socioeconomic factors using the COA (cuckoooptimization algorithm) technique Different models arestudied to determine the best possible approach in modelingenergy demand as a function of various indicators +is studyexamines the relationship between energy demand and diverseindependent variables in four models utilizing linear andpower types of equations Results arising from this studyprovide important reference information for the utility com-panies in assessing energy consumption patterns and selectinga more accurate approach to estimate future energy demand

Several studies that propose several models for energydemand policy management with different techniques areintroduced Pao [1] developed linear and nonlinear statis-tical models including ANN methods to forecast Taiwanrsquoselectricity consumption based on the national incomepopulation GDP and consumer price index For furtherdetails on employing ANN to estimate energy consumptionrefer Assareh et al [2] and Azadeh et als [3] study Biancoet al [4] employed the HoltndashWinters exponential smoothingmethod and the trigonometric grey model with rollingmechanism (TGMRM) to estimate electricity consumptionin Italy Ceylan et al [5] used the harmony search (HS)technique to forecast Turkish transport energy demand intree forms (linear exponential and quadratic) and based onpopulation GDP and vehicle kilometers driven Mohamedand Bodger [6] estimated the electricity demand of NewZealand based on economic indicators including GDPelectricity price and population by multiple linear re-gression analysis Amjadi et al [7] presented two forms(exponential and linear) of energy demand equations toforecast the electricity demand for future projections basedon PSO and GA techniques (see also Sadeghi et al [8]) +eyused population GDP number of customerrsquos electricity andaverage price electricity as independent variables+e energyconsumption in Iran is also determined using the bees al-gorithm technique by Behrang et al [9] with independentvariables such as population GDP import and exportKıran et al [10] applied artificial bee colony (ABC) andparticle swarm optimization (PSO) techniques to forecastelectricity energy demand in Turkey in two forms linear andquadratic by using selected economic and demographicvariables that include the gross domestic product (GDP)population import and export

+e paper is organized as follows In the next section weexplain the specification of the cuckoo optimization algo-rithm Section 3 presents problem definition In Section 4 themodel estimations and forecasting results are done and fi-nally in Section 5 the conclusions will be stated

2 Cuckoo Optimization Algorithm

+e cuckoo algorithm has been proposed by Yang and Deb[11] It was developed by Rajabioun [12]+is algorithm runslike other evolutionary algorithms +e cuckoos used in thismodeling are considered in two forms namely adultcuckoos and eggs +us the COA begins with an initialpopulation of cuckoos Each adult cuckoo lays only one eggat a time and dumps it in a randomly selected nest Some ofthese eggs grow up and turn into adult birds which are moresimilar to the host birdrsquos eggs and other eggs are recognizedand thrown out by host birds+erefore an egg whose profitfunction value is smaller is removed More profit is gained inhabitats in which more eggs survive In fact the nests(position) in which more eggs remain will be the term thatthe COA is going to optimize On the contrary theremaining eggs grow and turn into adult cuckoos+ey formsome groups in all different regions of the environment+en they migrate to better regions where eggs have highersurvival chances +us the group with the best position ischosen as the goal point for all other groups to immigrate

+erefore it is necessary that problem values be convenedas an array called ldquohabitatrdquo for solving an optimization problemwith COA In a Nvar dimensional optimization problem ahabitat presents the current living place of a cuckoo and is anarray of 1timesNvar +e array is indicated as follows

habitat x1 x2 xNvar1113858 1113859 (1)

+e suitability of a habitat is estimated by the assessmentof profit function fb at a habitat of (x1 x2 xNvar) where

profit fb( habitat) fb x1 x2 xNvar( 1113857 (2)

To begin the COA a primary habitat matrix of sizeNpop timesNvar is introduced

Due to the number of eggs each cuckoo has and thecuckoorsquos distance to the best habitat (the current optimalarea) an egg-laying radius (ELR) is assigned to it +en thecuckoo begins to lay eggs randomly in several nests insideher ELR +is process reiterates until the best position isobtained

ELR α timesnumber of current cuckoorsquos eggs

total number of eggstimes varhi minus varlow( 1113857

(3)

where α is an integer that adjusts the maximum value ofELR varhi and varlow are the upper and lower bound for thevariables respectively Since adult cuckoos exist all over theenvironment it is a problem to discover which group eachcuckoo is dependent on Grouping of birds is done by usingthe K-means clustering method to solve this problem Nowthat the grouprsquos cuckoos are determined their mean profitvalue is calculated +en other groups migrate to the regionwith the greatest mean profit All cuckoos do not migrate theentire path in the movement to the goal point they just goacross a part of the total distance

To keep the balance between the cuckoo and otherbirds the maximum number of cuckoos that may live in aregion is finite (Nmax) After iteration all cuckoos arrive in an

2 Mathematical Problems in Engineering

optimized region with the most similarity of their eggs to theeggs of the host bird In this location the number of theremoved eggs will be minimal and will gain the greatestobjective function +e repeated algorithm to more than 95of all the cuckoos converges toward a single point Relation(4) shows the migration function in the COA

XNext habitat XCurrent habitat + F times XGoal point minus XCurrent habitat1113872 1113873

(4)

where F is a parameter of cause deflection +e cuckoooptimization algorithm (COA) is classified as follows

Step 1 forming initial cuckoorsquos habitats by using severalrandom pointsStep 2 allocating several eggs to each cuckoo and givingdefinition ELR for each cuckooStep 3 allowing cuckoos to lay eggs inside their cor-responding ELRStep 4 allowing eggs similar to the host birdrsquos eggs tohatch grow and remove other eggs that are recognizedby the host birdsStep 5 evaluating the habitat of each newly grown cuckooStep 6 limiting themaximum number of cuckoos in theenvironment and ignoring those who exist in the worsthabitatsStep 7 clustering cuckoos determining the best groupand selecting goal habitat and then allowing newcuckoo population immigrates toward a goal habitatStep 8 checking the convergence and then if the stopcriterion is satisfied stop If not go to step 2

To check cuckoo optimization algorithm in detail referMellal et al [13] Shadkam and Bijari [14] and Mellal et alrsquos[15] study

21 Multiple Linear Cuckoo Optimization Algorithm(COAlinear) +e present study uses population GDP (grossdomestic product) import export and employment todevelop energy consumption models For estimating theenergy consumption themodels have been developed in twoforms (linear and power) as follows

Multiple linear cuckoo optimization algorithm (COA) isused for modeling the energy consumption in Iran +e fourmodels taking different socioeconomic variables into con-sideration are as follows

Model 1 y a1x1 + b1x2 + f1

Model 2 y a2x1 + b2x2 + c2x3 + d2x4 + f2

Model 3 y a3x1 + b3x2 + e3x5 + f3

Model 4 y a4x1 + b4x2 + c4x3 + d4x4 + e4x5 + f4

(5)

where y represents the estimated energy consumption anda1 a4 b1 b4 f1 f4 c2 c4 d2 d4 e3 and e4values are the algorithm coefficients +e xi values representthe five independent variables used as the predictors of y (x1

is population x2 is GDP x3 is import amount x4 is exportamount and x5 is employment)

22 Power Cuckoo Optimization Algorithm (COApower)Power cuckoo optimization algorithm (COA) for estimatingenergy consumption is used as follows

Model 1 y a1xb11 x

c12

Model 2 y a2xb21 x

c22 x

d23 x

e24

Model 3 y a3xb31 x

c32 x

f35

Model 4 y a4xb41 x

c42 x

d43 x

e44 x

f45

(6)

where a1 a4 b1 b4 c1 c4 d2 d4 e2 e4 f3and f4 are the algorithm coefficients x1 is population x2 isGDP x3 is import amount x4 is export amount and x5 isemployment

+e fitness function for selecting candidates for optimalcoefficients is defined as

minF(x) 1113944k

j1Yobserved minus Ypredicted1113872 1113873

2 (7)

where Yobserved and Ypredicted are the observed and predictedenergy consumption respectively and k is the number ofobservations

3 Estimation

Energy consumption in Iran from 1972 to 2013 is consideredas a case in point in this paper +e available data are partlyused for finding the optimal or near-optimal values of theweighting parameters (1972ndash2008) and partly for testing themodels (2009ndash2013)

+e following steps are conducted for forecasting energyconsumption in Iran between 2014 and 2030

Step 1 population GDP import export employmentand energy consumption need normalizing accordingto equation (8)

XN XR minus Xmin( 1113857

Xmax minus Xmin( 1113857 (8)

where XN is the normalized value XR is the value to be nor-malized Xmin is the minimum value in all the values for therelated variable andXmax is themaximum value in all the valuesfor the related variable +e Xmin and Xmax values for eachvariable are selected between 1972 and 2008 and are shown inTable 1

Table 1 Values for normalization

Xmin Xmax

GDP (billion Iranian rials) 162557 555436Population (thousand persons) 30284 76911Import (Mboe) 01440 1349738Export (Mboe) 3263281 21090781Employment (thousand persons) 8188 21324Energy consumption (Mboe) 948216 12297495

Mathematical Problems in Engineering 3

Step 2 the proposed algorithm is used in order todetermine corresponding weighting factors (Ci) foreach model according to the lowest objective functions

Step 3 in the second step the best results of step 1 for eachmodel and less average relative errors in the testing periodare chosen (ie the related data from 2009 to 2013)

Table 2 COA-linear model coefficients

a b c d e f

Model 1 09451 minus 00347 00783 mdash mdash mdashModel 2 08151 minus03325 minus02272 05819 04416 mdashModel 3 07312 00344 03379 minus01104 mdash mdashModel 4 10659 04089 minus03118 08644 04744 minus02153

Table 3 COA-linear model coefficients

a b c d e f

Model 1 09913 12568 minus01195 mdash mdash mdashModel 2 10408 10660 minus06527 minus00990 01338 mdashModel 3 10665 minus00045 06311 19404 mdash mdashModel 4 11164 10714 05894 minus00769 00693 minus01325

Actual dataCuckoo-linearCuckoo-power

EstimationModeling

0

200

400

600

800

1000

1200

1400

Ener

gy co

nsum

ptio

n (M

toe)

20121980 1984 1988 1992 1996 2000 2004 200819761972Years

Figure 1 Comparison of the actual data and cuckoo-linear and cuckoo-power results for Model 1

Actual dataCuckoo-linearCuckoo-power

EstimationModeling

0

200

400

600

800

1000

1200

1400

Ener

gy co

nsum

ptio

n (M

toe)

20121980 1984 1988 1992 1996 2000 2004 200819761972Years

Figure 2 Comparison of the actual data and cuckoo-linear and cuckoo-power results for Model 2

4 Mathematical Problems in Engineering

Actual dataCuckoo-linearCuckoo-power

Modeling Estimation

0

200

400

600

800

1000

1200

1400

Ener

gy co

nsum

ptio

n (M

toe)

20121980 1984 1988 1992 1996 2000 2004 200819761972Years

Figure 3 Comparison of the actual data and cuckoo-linear and cuckoo-power results for Model 3

Actual dataCuckoo-linearCuckoo-power

Modeling Estimation

0

200

400

600

800

1000

1200

1400

Ener

gy co

nsum

ptio

n (M

toe)

20121980 1984 1988 1992 1996 2000 2004 200819761972Years

Figure 4 Comparison of the actual data and cuckoo-linear and cuckoo-power results for Model 4

Table 4 Comparison of the COA estimation models for energy consumption in the testing period (2009ndash2013)

Years 2009 2010 2011 2012 2013 AverageActual dataa 1158311 1134874 1184621 1182055 122975 mdashCOA-linear model 1 1146673 1167896 1175386 1199447 1221124 mdashRelative error () minus 101495 28275 minus 078565 14499 minus 07063 13568COA-linear model 2 1152347 1140204 1175386 1185487 119207Relative error () minus 05175 04674 minus 07856 02894 minus 31608 10441COA-linear model 3 1150078 1161654 116608 1198539 1217719Relative error () minus 07159 23053 minus 15900 13753 minus 09879 13948COA-linear model 4 1160292 1134983 1179132 1196383 1208753Relative error () 01707 00096 minus 04655 11975 minus 17370 0716COA-power model 1 113748 115893 1165626 12041 1235424Relative error () minus 18313 20757 minus 16295 18308 04593 15653COA-power model 2 1152574 1125201 1124201 1174252 1195248Relative error () minus 049772 minus 09493 minus 53744 minus 06645 minus 28865 20745COA-power model 3 116199 1160065 1163924 1217379 122067Relative error () 03169 21715 minus 17782 29015 minus 07438 15824COA-power model 4 1129422 120898 1265613 1230657 121613Relative error () minus 25578 61296 63994 39492 minus 11198 40311aActual data are in million barrel oil equivalent (Mboe)

Mathematical Problems in Engineering 5

Step 4 to use the obtained models for future pro-jections each indicator should be forecasted in thefuture time domain

In this section COA models are coded with MATLAB2013 software Note that all data include 41 annual data(1972ndash2013) +ey are used for finding optimal values ofweighting factors regarding actual data (1972ndash2008) Fol-lowing COA demand estimationmodels have been obtainedfor energy consumption in Iran +e best-obtainedweighting factors by the COA for linear and power modelsare shown in Tables 2 and 3

It can be seen that there is a good agreement between theresults obtained from COA estimation models (COAlinearand COApower) but COA-linear models outperformedCOApower models

Figures 1ndash4 for the modeling and the testing data show theperformance of the linear cuckoo optimization algorithm andthe power cuckoo optimization algorithm for all models +efindings proved that the recommended linear models weremore appropriate tools for effective energy consumptionprediction in Iran For more clarification Table 4 reports actualand estimated values of testing data by utilizing all models

Using the COAlinear models which was determined abovethe energy consumption predictions are forecasted until 2030 forIran For different scenarios differently forecasted data of GDPpopulation employment and export and import volumes areconsidered +e following three scenarios are used for fore-casting each socioeconomic indicator in the years 2014ndash2030

Scenario 1 it is assumed that the average growth ratesof population GDP import export and employment

Model 1Model 2

Model 3Model 4

2016 2018 2020 2022 2024 2026 2028 20302014Years

0

500

1000

1500

2000

2500

3000

Ener

gy co

nsum

ptio

n (M

boe)

Figure 5 Forecasted values for energy demand in Iran (2014ndash2030) under scenario 1

Model 1Model 2

Model 3Model 4

2016 2018 2020 2022 2024 2026 2028 20302014Years

0

500

1000

1500

2000

2500

3000

Ener

gy co

nsum

ptio

n (M

boe)

Figure 6 Forecasted values for energy demand in Iran (2014ndash2030) under scenario 2

6 Mathematical Problems in Engineering

are 2 5 3 3 and 6 respectively during2014ndash2030Scenario 2 it is assumed that the average growth ratesof population GDP import export and employmentare 22 67 33 33 and 65 respectivelyduring 2014ndash2030Scenario 3 it is assumed that the average growth ratesof population GDP import export and employmentare 25 8 35 35 and 75 respectively during2014ndash2030

4 Conclusion

+e point of this study is to demonstrate to the authoritiesthe significance of utilizing option estimating strategies

+erefore in this study the COA (cuckoo optimizationalgorithm) has been successfully used to estimate Iranrsquosenergy demand based on the structure of the Iranrsquos socio-economic conditions In the first model energy consump-tion is estimated based on population and GDP In thesecond model population GDP import and export areused to forecast energy consumption In model 3 pop-ulation GDP and employment are used to estimate energyconsumption Finally in the fourth model energy con-sumption is modeled based on population GDP exportimport and employment +e proposed linear models an-ticipated the energy demand superior to anything the powermodels in terms of relative errors and RMSEs In additionapproval of models demonstrates that acquired demandestimation linear models are in great concurrence with thewatched information yet the COAlinear model 4 outflankedother introduced models +us three scenarios are designedto estimate Iranrsquos energy demand during 2014ndash2030 usingCOA-linear models and the results are shown inFigures 5ndash7

In conclusion this paper presented helpful suggestionsand novel insights into experts and policy planners Itrecommended a strong tool for developing energy programsForecasting energy demand can as well be studied by neuralnetworks or other new metaheuristics including harmonysearch and simulated annealing +e results of differentmethods may be compared with the COA method Furtherstudies should concentrate on the comparison of methodsexplained in this study with the rest of the available toolsForecasting energy demand may as well be investigated byusing electromagnetism mechanism algorithm krill herdoptimization algorithm and the rest of intelligent optimi-zation techniques +e results of using different methodscould be put into analogy with the COA method

Data Availability

All data are available in the World Bank depository CentralBank of the Islamic Republic of Iran and Irans Ministry ofEnergy

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] H Pao ldquoComparing linear and nonlinear forecasts for Tai-wanrsquos electricity consumptionrdquo Energy vol 31 no 12pp 2129ndash2141 2006

[2] E Assareh M A Behrang and A Ghanbarzadeh ldquoIn-tegration of artificial neural network and intelligent optimi-zation techniques on world electricity consumptionestimationrdquo World Academy of Science Engineering andTechnology vol 73 pp 690ndash694 2011

[3] A Azadeh S F Ghaderi and S Sohrabkhani ldquoA simulated-based neural network algorithm for forecasting electrical

Model 1Model 2

Model 3Model 4

2016 2018 2020 2022 2024 2026 2028 20302014Years

0

500

1000

1500

2000

2500

3000

3500

4000

Ener

gy co

nsum

ptio

n (M

boe)

Figure 7 Forecasted values for energy demand in Iran (2014ndash2030) under scenario 3

Mathematical Problems in Engineering 7

energy consumption in Iranrdquo Energy Policy vol 36 no 7pp 2637ndash2644 2008

[4] V Bianco O Manca S Nardini and A A Minea ldquoAnalysisand forecasting of nonresidential electricity consumption inRomaniardquo Applied Energy vol 87 no 11 pp 3584ndash35902010

[5] H Ceylan H Ceylan S Haldenbilen and O BaskanldquoTransport energy modeling with meta-heuristic harmonysearch algorithm an application to Turkeyrdquo Energy Policyvol 36 no 7 pp 2527ndash2535 2008

[6] Z Mohamed and P Bodger ldquoForecasting electricity con-sumption in New Zealand using economic and demographicvariablesrdquo Energy vol 30 no 10 pp 1833ndash1843 2005

[7] M H Amjadi H Nezamabadi-pour and M M FarsangildquoEstimation of electricity demand of Iran using two heuristicalgorithmsrdquo Energy Conversion and Management vol 51no 3 pp 493ndash497 2010

[8] H Sadeghi M Zolfaghari and M Heydarizade ldquoEstimationof electricity demand in residential sector using genetic al-gorithm approachrdquo International Journal of Industrial Engi-neering vol 22 no 1 2011

[9] M A Behrang E Assareh M R Assari andA Ghanbarzadeh ldquoTotal energy demand estimation in Iranusing bees algorithmrdquo Energy Sources Part B EconomicsPlanning and Policy vol 6 no 3 pp 294ndash303 2011

[10] M S Kıran E Ozceylan M Gunduz and T Paksoy ldquoSwarmintelligence approaches to estimate electricity energy demandin Turkeyrdquo Knowledge-Based Systems vol 36 pp 93ndash1032012

[11] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing IEEE Coimbatore India December2009

[12] R Rajabioun ldquoCuckoo optimization algorithmrdquo Applied SoftComputing vol 11 no 8 pp 5508ndash5518 2011

[13] M A Mellal S Adjerida and E J Williams ldquoOptimal se-lection of obsolete tools in manufacturing systems usingcuckoo optimization algorithmrdquo Chemical Engineeringvol 33 no 1 pp 355ndash360 2013

[14] E Shadkam andM Bijari ldquoEvaluation the efficiency of cuckoooptimization algorithmrdquo 2014 httparxivorgabs14052168

[15] M A Mellal S Adjerid E J Williams and D BenazzouzldquoOptimal replacement policy for obsolete components usingcuckoo optimization algorithm based-approach de-pendability contextrdquo Journal of Scientific and Industrial Re-search vol 71 no 11 pp 715ndash721 2012

8 Mathematical Problems in Engineering

optimized region with the most similarity of their eggs to theeggs of the host bird In this location the number of theremoved eggs will be minimal and will gain the greatestobjective function +e repeated algorithm to more than 95of all the cuckoos converges toward a single point Relation(4) shows the migration function in the COA

XNext habitat XCurrent habitat + F times XGoal point minus XCurrent habitat1113872 1113873

(4)

where F is a parameter of cause deflection +e cuckoooptimization algorithm (COA) is classified as follows

Step 1 forming initial cuckoorsquos habitats by using severalrandom pointsStep 2 allocating several eggs to each cuckoo and givingdefinition ELR for each cuckooStep 3 allowing cuckoos to lay eggs inside their cor-responding ELRStep 4 allowing eggs similar to the host birdrsquos eggs tohatch grow and remove other eggs that are recognizedby the host birdsStep 5 evaluating the habitat of each newly grown cuckooStep 6 limiting themaximum number of cuckoos in theenvironment and ignoring those who exist in the worsthabitatsStep 7 clustering cuckoos determining the best groupand selecting goal habitat and then allowing newcuckoo population immigrates toward a goal habitatStep 8 checking the convergence and then if the stopcriterion is satisfied stop If not go to step 2

To check cuckoo optimization algorithm in detail referMellal et al [13] Shadkam and Bijari [14] and Mellal et alrsquos[15] study

21 Multiple Linear Cuckoo Optimization Algorithm(COAlinear) +e present study uses population GDP (grossdomestic product) import export and employment todevelop energy consumption models For estimating theenergy consumption themodels have been developed in twoforms (linear and power) as follows

Multiple linear cuckoo optimization algorithm (COA) isused for modeling the energy consumption in Iran +e fourmodels taking different socioeconomic variables into con-sideration are as follows

Model 1 y a1x1 + b1x2 + f1

Model 2 y a2x1 + b2x2 + c2x3 + d2x4 + f2

Model 3 y a3x1 + b3x2 + e3x5 + f3

Model 4 y a4x1 + b4x2 + c4x3 + d4x4 + e4x5 + f4

(5)

where y represents the estimated energy consumption anda1 a4 b1 b4 f1 f4 c2 c4 d2 d4 e3 and e4values are the algorithm coefficients +e xi values representthe five independent variables used as the predictors of y (x1

is population x2 is GDP x3 is import amount x4 is exportamount and x5 is employment)

22 Power Cuckoo Optimization Algorithm (COApower)Power cuckoo optimization algorithm (COA) for estimatingenergy consumption is used as follows

Model 1 y a1xb11 x

c12

Model 2 y a2xb21 x

c22 x

d23 x

e24

Model 3 y a3xb31 x

c32 x

f35

Model 4 y a4xb41 x

c42 x

d43 x

e44 x

f45

(6)

where a1 a4 b1 b4 c1 c4 d2 d4 e2 e4 f3and f4 are the algorithm coefficients x1 is population x2 isGDP x3 is import amount x4 is export amount and x5 isemployment

+e fitness function for selecting candidates for optimalcoefficients is defined as

minF(x) 1113944k

j1Yobserved minus Ypredicted1113872 1113873

2 (7)

where Yobserved and Ypredicted are the observed and predictedenergy consumption respectively and k is the number ofobservations

3 Estimation

Energy consumption in Iran from 1972 to 2013 is consideredas a case in point in this paper +e available data are partlyused for finding the optimal or near-optimal values of theweighting parameters (1972ndash2008) and partly for testing themodels (2009ndash2013)

+e following steps are conducted for forecasting energyconsumption in Iran between 2014 and 2030

Step 1 population GDP import export employmentand energy consumption need normalizing accordingto equation (8)

XN XR minus Xmin( 1113857

Xmax minus Xmin( 1113857 (8)

where XN is the normalized value XR is the value to be nor-malized Xmin is the minimum value in all the values for therelated variable andXmax is themaximum value in all the valuesfor the related variable +e Xmin and Xmax values for eachvariable are selected between 1972 and 2008 and are shown inTable 1

Table 1 Values for normalization

Xmin Xmax

GDP (billion Iranian rials) 162557 555436Population (thousand persons) 30284 76911Import (Mboe) 01440 1349738Export (Mboe) 3263281 21090781Employment (thousand persons) 8188 21324Energy consumption (Mboe) 948216 12297495

Mathematical Problems in Engineering 3

Step 2 the proposed algorithm is used in order todetermine corresponding weighting factors (Ci) foreach model according to the lowest objective functions

Step 3 in the second step the best results of step 1 for eachmodel and less average relative errors in the testing periodare chosen (ie the related data from 2009 to 2013)

Table 2 COA-linear model coefficients

a b c d e f

Model 1 09451 minus 00347 00783 mdash mdash mdashModel 2 08151 minus03325 minus02272 05819 04416 mdashModel 3 07312 00344 03379 minus01104 mdash mdashModel 4 10659 04089 minus03118 08644 04744 minus02153

Table 3 COA-linear model coefficients

a b c d e f

Model 1 09913 12568 minus01195 mdash mdash mdashModel 2 10408 10660 minus06527 minus00990 01338 mdashModel 3 10665 minus00045 06311 19404 mdash mdashModel 4 11164 10714 05894 minus00769 00693 minus01325

Actual dataCuckoo-linearCuckoo-power

EstimationModeling

0

200

400

600

800

1000

1200

1400

Ener

gy co

nsum

ptio

n (M

toe)

20121980 1984 1988 1992 1996 2000 2004 200819761972Years

Figure 1 Comparison of the actual data and cuckoo-linear and cuckoo-power results for Model 1

Actual dataCuckoo-linearCuckoo-power

EstimationModeling

0

200

400

600

800

1000

1200

1400

Ener

gy co

nsum

ptio

n (M

toe)

20121980 1984 1988 1992 1996 2000 2004 200819761972Years

Figure 2 Comparison of the actual data and cuckoo-linear and cuckoo-power results for Model 2

4 Mathematical Problems in Engineering

Actual dataCuckoo-linearCuckoo-power

Modeling Estimation

0

200

400

600

800

1000

1200

1400

Ener

gy co

nsum

ptio

n (M

toe)

20121980 1984 1988 1992 1996 2000 2004 200819761972Years

Figure 3 Comparison of the actual data and cuckoo-linear and cuckoo-power results for Model 3

Actual dataCuckoo-linearCuckoo-power

Modeling Estimation

0

200

400

600

800

1000

1200

1400

Ener

gy co

nsum

ptio

n (M

toe)

20121980 1984 1988 1992 1996 2000 2004 200819761972Years

Figure 4 Comparison of the actual data and cuckoo-linear and cuckoo-power results for Model 4

Table 4 Comparison of the COA estimation models for energy consumption in the testing period (2009ndash2013)

Years 2009 2010 2011 2012 2013 AverageActual dataa 1158311 1134874 1184621 1182055 122975 mdashCOA-linear model 1 1146673 1167896 1175386 1199447 1221124 mdashRelative error () minus 101495 28275 minus 078565 14499 minus 07063 13568COA-linear model 2 1152347 1140204 1175386 1185487 119207Relative error () minus 05175 04674 minus 07856 02894 minus 31608 10441COA-linear model 3 1150078 1161654 116608 1198539 1217719Relative error () minus 07159 23053 minus 15900 13753 minus 09879 13948COA-linear model 4 1160292 1134983 1179132 1196383 1208753Relative error () 01707 00096 minus 04655 11975 minus 17370 0716COA-power model 1 113748 115893 1165626 12041 1235424Relative error () minus 18313 20757 minus 16295 18308 04593 15653COA-power model 2 1152574 1125201 1124201 1174252 1195248Relative error () minus 049772 minus 09493 minus 53744 minus 06645 minus 28865 20745COA-power model 3 116199 1160065 1163924 1217379 122067Relative error () 03169 21715 minus 17782 29015 minus 07438 15824COA-power model 4 1129422 120898 1265613 1230657 121613Relative error () minus 25578 61296 63994 39492 minus 11198 40311aActual data are in million barrel oil equivalent (Mboe)

Mathematical Problems in Engineering 5

Step 4 to use the obtained models for future pro-jections each indicator should be forecasted in thefuture time domain

In this section COA models are coded with MATLAB2013 software Note that all data include 41 annual data(1972ndash2013) +ey are used for finding optimal values ofweighting factors regarding actual data (1972ndash2008) Fol-lowing COA demand estimationmodels have been obtainedfor energy consumption in Iran +e best-obtainedweighting factors by the COA for linear and power modelsare shown in Tables 2 and 3

It can be seen that there is a good agreement between theresults obtained from COA estimation models (COAlinearand COApower) but COA-linear models outperformedCOApower models

Figures 1ndash4 for the modeling and the testing data show theperformance of the linear cuckoo optimization algorithm andthe power cuckoo optimization algorithm for all models +efindings proved that the recommended linear models weremore appropriate tools for effective energy consumptionprediction in Iran For more clarification Table 4 reports actualand estimated values of testing data by utilizing all models

Using the COAlinear models which was determined abovethe energy consumption predictions are forecasted until 2030 forIran For different scenarios differently forecasted data of GDPpopulation employment and export and import volumes areconsidered +e following three scenarios are used for fore-casting each socioeconomic indicator in the years 2014ndash2030

Scenario 1 it is assumed that the average growth ratesof population GDP import export and employment

Model 1Model 2

Model 3Model 4

2016 2018 2020 2022 2024 2026 2028 20302014Years

0

500

1000

1500

2000

2500

3000

Ener

gy co

nsum

ptio

n (M

boe)

Figure 5 Forecasted values for energy demand in Iran (2014ndash2030) under scenario 1

Model 1Model 2

Model 3Model 4

2016 2018 2020 2022 2024 2026 2028 20302014Years

0

500

1000

1500

2000

2500

3000

Ener

gy co

nsum

ptio

n (M

boe)

Figure 6 Forecasted values for energy demand in Iran (2014ndash2030) under scenario 2

6 Mathematical Problems in Engineering

are 2 5 3 3 and 6 respectively during2014ndash2030Scenario 2 it is assumed that the average growth ratesof population GDP import export and employmentare 22 67 33 33 and 65 respectivelyduring 2014ndash2030Scenario 3 it is assumed that the average growth ratesof population GDP import export and employmentare 25 8 35 35 and 75 respectively during2014ndash2030

4 Conclusion

+e point of this study is to demonstrate to the authoritiesthe significance of utilizing option estimating strategies

+erefore in this study the COA (cuckoo optimizationalgorithm) has been successfully used to estimate Iranrsquosenergy demand based on the structure of the Iranrsquos socio-economic conditions In the first model energy consump-tion is estimated based on population and GDP In thesecond model population GDP import and export areused to forecast energy consumption In model 3 pop-ulation GDP and employment are used to estimate energyconsumption Finally in the fourth model energy con-sumption is modeled based on population GDP exportimport and employment +e proposed linear models an-ticipated the energy demand superior to anything the powermodels in terms of relative errors and RMSEs In additionapproval of models demonstrates that acquired demandestimation linear models are in great concurrence with thewatched information yet the COAlinear model 4 outflankedother introduced models +us three scenarios are designedto estimate Iranrsquos energy demand during 2014ndash2030 usingCOA-linear models and the results are shown inFigures 5ndash7

In conclusion this paper presented helpful suggestionsand novel insights into experts and policy planners Itrecommended a strong tool for developing energy programsForecasting energy demand can as well be studied by neuralnetworks or other new metaheuristics including harmonysearch and simulated annealing +e results of differentmethods may be compared with the COA method Furtherstudies should concentrate on the comparison of methodsexplained in this study with the rest of the available toolsForecasting energy demand may as well be investigated byusing electromagnetism mechanism algorithm krill herdoptimization algorithm and the rest of intelligent optimi-zation techniques +e results of using different methodscould be put into analogy with the COA method

Data Availability

All data are available in the World Bank depository CentralBank of the Islamic Republic of Iran and Irans Ministry ofEnergy

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] H Pao ldquoComparing linear and nonlinear forecasts for Tai-wanrsquos electricity consumptionrdquo Energy vol 31 no 12pp 2129ndash2141 2006

[2] E Assareh M A Behrang and A Ghanbarzadeh ldquoIn-tegration of artificial neural network and intelligent optimi-zation techniques on world electricity consumptionestimationrdquo World Academy of Science Engineering andTechnology vol 73 pp 690ndash694 2011

[3] A Azadeh S F Ghaderi and S Sohrabkhani ldquoA simulated-based neural network algorithm for forecasting electrical

Model 1Model 2

Model 3Model 4

2016 2018 2020 2022 2024 2026 2028 20302014Years

0

500

1000

1500

2000

2500

3000

3500

4000

Ener

gy co

nsum

ptio

n (M

boe)

Figure 7 Forecasted values for energy demand in Iran (2014ndash2030) under scenario 3

Mathematical Problems in Engineering 7

energy consumption in Iranrdquo Energy Policy vol 36 no 7pp 2637ndash2644 2008

[4] V Bianco O Manca S Nardini and A A Minea ldquoAnalysisand forecasting of nonresidential electricity consumption inRomaniardquo Applied Energy vol 87 no 11 pp 3584ndash35902010

[5] H Ceylan H Ceylan S Haldenbilen and O BaskanldquoTransport energy modeling with meta-heuristic harmonysearch algorithm an application to Turkeyrdquo Energy Policyvol 36 no 7 pp 2527ndash2535 2008

[6] Z Mohamed and P Bodger ldquoForecasting electricity con-sumption in New Zealand using economic and demographicvariablesrdquo Energy vol 30 no 10 pp 1833ndash1843 2005

[7] M H Amjadi H Nezamabadi-pour and M M FarsangildquoEstimation of electricity demand of Iran using two heuristicalgorithmsrdquo Energy Conversion and Management vol 51no 3 pp 493ndash497 2010

[8] H Sadeghi M Zolfaghari and M Heydarizade ldquoEstimationof electricity demand in residential sector using genetic al-gorithm approachrdquo International Journal of Industrial Engi-neering vol 22 no 1 2011

[9] M A Behrang E Assareh M R Assari andA Ghanbarzadeh ldquoTotal energy demand estimation in Iranusing bees algorithmrdquo Energy Sources Part B EconomicsPlanning and Policy vol 6 no 3 pp 294ndash303 2011

[10] M S Kıran E Ozceylan M Gunduz and T Paksoy ldquoSwarmintelligence approaches to estimate electricity energy demandin Turkeyrdquo Knowledge-Based Systems vol 36 pp 93ndash1032012

[11] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing IEEE Coimbatore India December2009

[12] R Rajabioun ldquoCuckoo optimization algorithmrdquo Applied SoftComputing vol 11 no 8 pp 5508ndash5518 2011

[13] M A Mellal S Adjerida and E J Williams ldquoOptimal se-lection of obsolete tools in manufacturing systems usingcuckoo optimization algorithmrdquo Chemical Engineeringvol 33 no 1 pp 355ndash360 2013

[14] E Shadkam andM Bijari ldquoEvaluation the efficiency of cuckoooptimization algorithmrdquo 2014 httparxivorgabs14052168

[15] M A Mellal S Adjerid E J Williams and D BenazzouzldquoOptimal replacement policy for obsolete components usingcuckoo optimization algorithm based-approach de-pendability contextrdquo Journal of Scientific and Industrial Re-search vol 71 no 11 pp 715ndash721 2012

8 Mathematical Problems in Engineering

Step 2 the proposed algorithm is used in order todetermine corresponding weighting factors (Ci) foreach model according to the lowest objective functions

Step 3 in the second step the best results of step 1 for eachmodel and less average relative errors in the testing periodare chosen (ie the related data from 2009 to 2013)

Table 2 COA-linear model coefficients

a b c d e f

Model 1 09451 minus 00347 00783 mdash mdash mdashModel 2 08151 minus03325 minus02272 05819 04416 mdashModel 3 07312 00344 03379 minus01104 mdash mdashModel 4 10659 04089 minus03118 08644 04744 minus02153

Table 3 COA-linear model coefficients

a b c d e f

Model 1 09913 12568 minus01195 mdash mdash mdashModel 2 10408 10660 minus06527 minus00990 01338 mdashModel 3 10665 minus00045 06311 19404 mdash mdashModel 4 11164 10714 05894 minus00769 00693 minus01325

Actual dataCuckoo-linearCuckoo-power

EstimationModeling

0

200

400

600

800

1000

1200

1400

Ener

gy co

nsum

ptio

n (M

toe)

20121980 1984 1988 1992 1996 2000 2004 200819761972Years

Figure 1 Comparison of the actual data and cuckoo-linear and cuckoo-power results for Model 1

Actual dataCuckoo-linearCuckoo-power

EstimationModeling

0

200

400

600

800

1000

1200

1400

Ener

gy co

nsum

ptio

n (M

toe)

20121980 1984 1988 1992 1996 2000 2004 200819761972Years

Figure 2 Comparison of the actual data and cuckoo-linear and cuckoo-power results for Model 2

4 Mathematical Problems in Engineering

Actual dataCuckoo-linearCuckoo-power

Modeling Estimation

0

200

400

600

800

1000

1200

1400

Ener

gy co

nsum

ptio

n (M

toe)

20121980 1984 1988 1992 1996 2000 2004 200819761972Years

Figure 3 Comparison of the actual data and cuckoo-linear and cuckoo-power results for Model 3

Actual dataCuckoo-linearCuckoo-power

Modeling Estimation

0

200

400

600

800

1000

1200

1400

Ener

gy co

nsum

ptio

n (M

toe)

20121980 1984 1988 1992 1996 2000 2004 200819761972Years

Figure 4 Comparison of the actual data and cuckoo-linear and cuckoo-power results for Model 4

Table 4 Comparison of the COA estimation models for energy consumption in the testing period (2009ndash2013)

Years 2009 2010 2011 2012 2013 AverageActual dataa 1158311 1134874 1184621 1182055 122975 mdashCOA-linear model 1 1146673 1167896 1175386 1199447 1221124 mdashRelative error () minus 101495 28275 minus 078565 14499 minus 07063 13568COA-linear model 2 1152347 1140204 1175386 1185487 119207Relative error () minus 05175 04674 minus 07856 02894 minus 31608 10441COA-linear model 3 1150078 1161654 116608 1198539 1217719Relative error () minus 07159 23053 minus 15900 13753 minus 09879 13948COA-linear model 4 1160292 1134983 1179132 1196383 1208753Relative error () 01707 00096 minus 04655 11975 minus 17370 0716COA-power model 1 113748 115893 1165626 12041 1235424Relative error () minus 18313 20757 minus 16295 18308 04593 15653COA-power model 2 1152574 1125201 1124201 1174252 1195248Relative error () minus 049772 minus 09493 minus 53744 minus 06645 minus 28865 20745COA-power model 3 116199 1160065 1163924 1217379 122067Relative error () 03169 21715 minus 17782 29015 minus 07438 15824COA-power model 4 1129422 120898 1265613 1230657 121613Relative error () minus 25578 61296 63994 39492 minus 11198 40311aActual data are in million barrel oil equivalent (Mboe)

Mathematical Problems in Engineering 5

Step 4 to use the obtained models for future pro-jections each indicator should be forecasted in thefuture time domain

In this section COA models are coded with MATLAB2013 software Note that all data include 41 annual data(1972ndash2013) +ey are used for finding optimal values ofweighting factors regarding actual data (1972ndash2008) Fol-lowing COA demand estimationmodels have been obtainedfor energy consumption in Iran +e best-obtainedweighting factors by the COA for linear and power modelsare shown in Tables 2 and 3

It can be seen that there is a good agreement between theresults obtained from COA estimation models (COAlinearand COApower) but COA-linear models outperformedCOApower models

Figures 1ndash4 for the modeling and the testing data show theperformance of the linear cuckoo optimization algorithm andthe power cuckoo optimization algorithm for all models +efindings proved that the recommended linear models weremore appropriate tools for effective energy consumptionprediction in Iran For more clarification Table 4 reports actualand estimated values of testing data by utilizing all models

Using the COAlinear models which was determined abovethe energy consumption predictions are forecasted until 2030 forIran For different scenarios differently forecasted data of GDPpopulation employment and export and import volumes areconsidered +e following three scenarios are used for fore-casting each socioeconomic indicator in the years 2014ndash2030

Scenario 1 it is assumed that the average growth ratesof population GDP import export and employment

Model 1Model 2

Model 3Model 4

2016 2018 2020 2022 2024 2026 2028 20302014Years

0

500

1000

1500

2000

2500

3000

Ener

gy co

nsum

ptio

n (M

boe)

Figure 5 Forecasted values for energy demand in Iran (2014ndash2030) under scenario 1

Model 1Model 2

Model 3Model 4

2016 2018 2020 2022 2024 2026 2028 20302014Years

0

500

1000

1500

2000

2500

3000

Ener

gy co

nsum

ptio

n (M

boe)

Figure 6 Forecasted values for energy demand in Iran (2014ndash2030) under scenario 2

6 Mathematical Problems in Engineering

are 2 5 3 3 and 6 respectively during2014ndash2030Scenario 2 it is assumed that the average growth ratesof population GDP import export and employmentare 22 67 33 33 and 65 respectivelyduring 2014ndash2030Scenario 3 it is assumed that the average growth ratesof population GDP import export and employmentare 25 8 35 35 and 75 respectively during2014ndash2030

4 Conclusion

+e point of this study is to demonstrate to the authoritiesthe significance of utilizing option estimating strategies

+erefore in this study the COA (cuckoo optimizationalgorithm) has been successfully used to estimate Iranrsquosenergy demand based on the structure of the Iranrsquos socio-economic conditions In the first model energy consump-tion is estimated based on population and GDP In thesecond model population GDP import and export areused to forecast energy consumption In model 3 pop-ulation GDP and employment are used to estimate energyconsumption Finally in the fourth model energy con-sumption is modeled based on population GDP exportimport and employment +e proposed linear models an-ticipated the energy demand superior to anything the powermodels in terms of relative errors and RMSEs In additionapproval of models demonstrates that acquired demandestimation linear models are in great concurrence with thewatched information yet the COAlinear model 4 outflankedother introduced models +us three scenarios are designedto estimate Iranrsquos energy demand during 2014ndash2030 usingCOA-linear models and the results are shown inFigures 5ndash7

In conclusion this paper presented helpful suggestionsand novel insights into experts and policy planners Itrecommended a strong tool for developing energy programsForecasting energy demand can as well be studied by neuralnetworks or other new metaheuristics including harmonysearch and simulated annealing +e results of differentmethods may be compared with the COA method Furtherstudies should concentrate on the comparison of methodsexplained in this study with the rest of the available toolsForecasting energy demand may as well be investigated byusing electromagnetism mechanism algorithm krill herdoptimization algorithm and the rest of intelligent optimi-zation techniques +e results of using different methodscould be put into analogy with the COA method

Data Availability

All data are available in the World Bank depository CentralBank of the Islamic Republic of Iran and Irans Ministry ofEnergy

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] H Pao ldquoComparing linear and nonlinear forecasts for Tai-wanrsquos electricity consumptionrdquo Energy vol 31 no 12pp 2129ndash2141 2006

[2] E Assareh M A Behrang and A Ghanbarzadeh ldquoIn-tegration of artificial neural network and intelligent optimi-zation techniques on world electricity consumptionestimationrdquo World Academy of Science Engineering andTechnology vol 73 pp 690ndash694 2011

[3] A Azadeh S F Ghaderi and S Sohrabkhani ldquoA simulated-based neural network algorithm for forecasting electrical

Model 1Model 2

Model 3Model 4

2016 2018 2020 2022 2024 2026 2028 20302014Years

0

500

1000

1500

2000

2500

3000

3500

4000

Ener

gy co

nsum

ptio

n (M

boe)

Figure 7 Forecasted values for energy demand in Iran (2014ndash2030) under scenario 3

Mathematical Problems in Engineering 7

energy consumption in Iranrdquo Energy Policy vol 36 no 7pp 2637ndash2644 2008

[4] V Bianco O Manca S Nardini and A A Minea ldquoAnalysisand forecasting of nonresidential electricity consumption inRomaniardquo Applied Energy vol 87 no 11 pp 3584ndash35902010

[5] H Ceylan H Ceylan S Haldenbilen and O BaskanldquoTransport energy modeling with meta-heuristic harmonysearch algorithm an application to Turkeyrdquo Energy Policyvol 36 no 7 pp 2527ndash2535 2008

[6] Z Mohamed and P Bodger ldquoForecasting electricity con-sumption in New Zealand using economic and demographicvariablesrdquo Energy vol 30 no 10 pp 1833ndash1843 2005

[7] M H Amjadi H Nezamabadi-pour and M M FarsangildquoEstimation of electricity demand of Iran using two heuristicalgorithmsrdquo Energy Conversion and Management vol 51no 3 pp 493ndash497 2010

[8] H Sadeghi M Zolfaghari and M Heydarizade ldquoEstimationof electricity demand in residential sector using genetic al-gorithm approachrdquo International Journal of Industrial Engi-neering vol 22 no 1 2011

[9] M A Behrang E Assareh M R Assari andA Ghanbarzadeh ldquoTotal energy demand estimation in Iranusing bees algorithmrdquo Energy Sources Part B EconomicsPlanning and Policy vol 6 no 3 pp 294ndash303 2011

[10] M S Kıran E Ozceylan M Gunduz and T Paksoy ldquoSwarmintelligence approaches to estimate electricity energy demandin Turkeyrdquo Knowledge-Based Systems vol 36 pp 93ndash1032012

[11] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing IEEE Coimbatore India December2009

[12] R Rajabioun ldquoCuckoo optimization algorithmrdquo Applied SoftComputing vol 11 no 8 pp 5508ndash5518 2011

[13] M A Mellal S Adjerida and E J Williams ldquoOptimal se-lection of obsolete tools in manufacturing systems usingcuckoo optimization algorithmrdquo Chemical Engineeringvol 33 no 1 pp 355ndash360 2013

[14] E Shadkam andM Bijari ldquoEvaluation the efficiency of cuckoooptimization algorithmrdquo 2014 httparxivorgabs14052168

[15] M A Mellal S Adjerid E J Williams and D BenazzouzldquoOptimal replacement policy for obsolete components usingcuckoo optimization algorithm based-approach de-pendability contextrdquo Journal of Scientific and Industrial Re-search vol 71 no 11 pp 715ndash721 2012

8 Mathematical Problems in Engineering

Actual dataCuckoo-linearCuckoo-power

Modeling Estimation

0

200

400

600

800

1000

1200

1400

Ener

gy co

nsum

ptio

n (M

toe)

20121980 1984 1988 1992 1996 2000 2004 200819761972Years

Figure 3 Comparison of the actual data and cuckoo-linear and cuckoo-power results for Model 3

Actual dataCuckoo-linearCuckoo-power

Modeling Estimation

0

200

400

600

800

1000

1200

1400

Ener

gy co

nsum

ptio

n (M

toe)

20121980 1984 1988 1992 1996 2000 2004 200819761972Years

Figure 4 Comparison of the actual data and cuckoo-linear and cuckoo-power results for Model 4

Table 4 Comparison of the COA estimation models for energy consumption in the testing period (2009ndash2013)

Years 2009 2010 2011 2012 2013 AverageActual dataa 1158311 1134874 1184621 1182055 122975 mdashCOA-linear model 1 1146673 1167896 1175386 1199447 1221124 mdashRelative error () minus 101495 28275 minus 078565 14499 minus 07063 13568COA-linear model 2 1152347 1140204 1175386 1185487 119207Relative error () minus 05175 04674 minus 07856 02894 minus 31608 10441COA-linear model 3 1150078 1161654 116608 1198539 1217719Relative error () minus 07159 23053 minus 15900 13753 minus 09879 13948COA-linear model 4 1160292 1134983 1179132 1196383 1208753Relative error () 01707 00096 minus 04655 11975 minus 17370 0716COA-power model 1 113748 115893 1165626 12041 1235424Relative error () minus 18313 20757 minus 16295 18308 04593 15653COA-power model 2 1152574 1125201 1124201 1174252 1195248Relative error () minus 049772 minus 09493 minus 53744 minus 06645 minus 28865 20745COA-power model 3 116199 1160065 1163924 1217379 122067Relative error () 03169 21715 minus 17782 29015 minus 07438 15824COA-power model 4 1129422 120898 1265613 1230657 121613Relative error () minus 25578 61296 63994 39492 minus 11198 40311aActual data are in million barrel oil equivalent (Mboe)

Mathematical Problems in Engineering 5

Step 4 to use the obtained models for future pro-jections each indicator should be forecasted in thefuture time domain

In this section COA models are coded with MATLAB2013 software Note that all data include 41 annual data(1972ndash2013) +ey are used for finding optimal values ofweighting factors regarding actual data (1972ndash2008) Fol-lowing COA demand estimationmodels have been obtainedfor energy consumption in Iran +e best-obtainedweighting factors by the COA for linear and power modelsare shown in Tables 2 and 3

It can be seen that there is a good agreement between theresults obtained from COA estimation models (COAlinearand COApower) but COA-linear models outperformedCOApower models

Figures 1ndash4 for the modeling and the testing data show theperformance of the linear cuckoo optimization algorithm andthe power cuckoo optimization algorithm for all models +efindings proved that the recommended linear models weremore appropriate tools for effective energy consumptionprediction in Iran For more clarification Table 4 reports actualand estimated values of testing data by utilizing all models

Using the COAlinear models which was determined abovethe energy consumption predictions are forecasted until 2030 forIran For different scenarios differently forecasted data of GDPpopulation employment and export and import volumes areconsidered +e following three scenarios are used for fore-casting each socioeconomic indicator in the years 2014ndash2030

Scenario 1 it is assumed that the average growth ratesof population GDP import export and employment

Model 1Model 2

Model 3Model 4

2016 2018 2020 2022 2024 2026 2028 20302014Years

0

500

1000

1500

2000

2500

3000

Ener

gy co

nsum

ptio

n (M

boe)

Figure 5 Forecasted values for energy demand in Iran (2014ndash2030) under scenario 1

Model 1Model 2

Model 3Model 4

2016 2018 2020 2022 2024 2026 2028 20302014Years

0

500

1000

1500

2000

2500

3000

Ener

gy co

nsum

ptio

n (M

boe)

Figure 6 Forecasted values for energy demand in Iran (2014ndash2030) under scenario 2

6 Mathematical Problems in Engineering

are 2 5 3 3 and 6 respectively during2014ndash2030Scenario 2 it is assumed that the average growth ratesof population GDP import export and employmentare 22 67 33 33 and 65 respectivelyduring 2014ndash2030Scenario 3 it is assumed that the average growth ratesof population GDP import export and employmentare 25 8 35 35 and 75 respectively during2014ndash2030

4 Conclusion

+e point of this study is to demonstrate to the authoritiesthe significance of utilizing option estimating strategies

+erefore in this study the COA (cuckoo optimizationalgorithm) has been successfully used to estimate Iranrsquosenergy demand based on the structure of the Iranrsquos socio-economic conditions In the first model energy consump-tion is estimated based on population and GDP In thesecond model population GDP import and export areused to forecast energy consumption In model 3 pop-ulation GDP and employment are used to estimate energyconsumption Finally in the fourth model energy con-sumption is modeled based on population GDP exportimport and employment +e proposed linear models an-ticipated the energy demand superior to anything the powermodels in terms of relative errors and RMSEs In additionapproval of models demonstrates that acquired demandestimation linear models are in great concurrence with thewatched information yet the COAlinear model 4 outflankedother introduced models +us three scenarios are designedto estimate Iranrsquos energy demand during 2014ndash2030 usingCOA-linear models and the results are shown inFigures 5ndash7

In conclusion this paper presented helpful suggestionsand novel insights into experts and policy planners Itrecommended a strong tool for developing energy programsForecasting energy demand can as well be studied by neuralnetworks or other new metaheuristics including harmonysearch and simulated annealing +e results of differentmethods may be compared with the COA method Furtherstudies should concentrate on the comparison of methodsexplained in this study with the rest of the available toolsForecasting energy demand may as well be investigated byusing electromagnetism mechanism algorithm krill herdoptimization algorithm and the rest of intelligent optimi-zation techniques +e results of using different methodscould be put into analogy with the COA method

Data Availability

All data are available in the World Bank depository CentralBank of the Islamic Republic of Iran and Irans Ministry ofEnergy

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] H Pao ldquoComparing linear and nonlinear forecasts for Tai-wanrsquos electricity consumptionrdquo Energy vol 31 no 12pp 2129ndash2141 2006

[2] E Assareh M A Behrang and A Ghanbarzadeh ldquoIn-tegration of artificial neural network and intelligent optimi-zation techniques on world electricity consumptionestimationrdquo World Academy of Science Engineering andTechnology vol 73 pp 690ndash694 2011

[3] A Azadeh S F Ghaderi and S Sohrabkhani ldquoA simulated-based neural network algorithm for forecasting electrical

Model 1Model 2

Model 3Model 4

2016 2018 2020 2022 2024 2026 2028 20302014Years

0

500

1000

1500

2000

2500

3000

3500

4000

Ener

gy co

nsum

ptio

n (M

boe)

Figure 7 Forecasted values for energy demand in Iran (2014ndash2030) under scenario 3

Mathematical Problems in Engineering 7

energy consumption in Iranrdquo Energy Policy vol 36 no 7pp 2637ndash2644 2008

[4] V Bianco O Manca S Nardini and A A Minea ldquoAnalysisand forecasting of nonresidential electricity consumption inRomaniardquo Applied Energy vol 87 no 11 pp 3584ndash35902010

[5] H Ceylan H Ceylan S Haldenbilen and O BaskanldquoTransport energy modeling with meta-heuristic harmonysearch algorithm an application to Turkeyrdquo Energy Policyvol 36 no 7 pp 2527ndash2535 2008

[6] Z Mohamed and P Bodger ldquoForecasting electricity con-sumption in New Zealand using economic and demographicvariablesrdquo Energy vol 30 no 10 pp 1833ndash1843 2005

[7] M H Amjadi H Nezamabadi-pour and M M FarsangildquoEstimation of electricity demand of Iran using two heuristicalgorithmsrdquo Energy Conversion and Management vol 51no 3 pp 493ndash497 2010

[8] H Sadeghi M Zolfaghari and M Heydarizade ldquoEstimationof electricity demand in residential sector using genetic al-gorithm approachrdquo International Journal of Industrial Engi-neering vol 22 no 1 2011

[9] M A Behrang E Assareh M R Assari andA Ghanbarzadeh ldquoTotal energy demand estimation in Iranusing bees algorithmrdquo Energy Sources Part B EconomicsPlanning and Policy vol 6 no 3 pp 294ndash303 2011

[10] M S Kıran E Ozceylan M Gunduz and T Paksoy ldquoSwarmintelligence approaches to estimate electricity energy demandin Turkeyrdquo Knowledge-Based Systems vol 36 pp 93ndash1032012

[11] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing IEEE Coimbatore India December2009

[12] R Rajabioun ldquoCuckoo optimization algorithmrdquo Applied SoftComputing vol 11 no 8 pp 5508ndash5518 2011

[13] M A Mellal S Adjerida and E J Williams ldquoOptimal se-lection of obsolete tools in manufacturing systems usingcuckoo optimization algorithmrdquo Chemical Engineeringvol 33 no 1 pp 355ndash360 2013

[14] E Shadkam andM Bijari ldquoEvaluation the efficiency of cuckoooptimization algorithmrdquo 2014 httparxivorgabs14052168

[15] M A Mellal S Adjerid E J Williams and D BenazzouzldquoOptimal replacement policy for obsolete components usingcuckoo optimization algorithm based-approach de-pendability contextrdquo Journal of Scientific and Industrial Re-search vol 71 no 11 pp 715ndash721 2012

8 Mathematical Problems in Engineering

Step 4 to use the obtained models for future pro-jections each indicator should be forecasted in thefuture time domain

In this section COA models are coded with MATLAB2013 software Note that all data include 41 annual data(1972ndash2013) +ey are used for finding optimal values ofweighting factors regarding actual data (1972ndash2008) Fol-lowing COA demand estimationmodels have been obtainedfor energy consumption in Iran +e best-obtainedweighting factors by the COA for linear and power modelsare shown in Tables 2 and 3

It can be seen that there is a good agreement between theresults obtained from COA estimation models (COAlinearand COApower) but COA-linear models outperformedCOApower models

Figures 1ndash4 for the modeling and the testing data show theperformance of the linear cuckoo optimization algorithm andthe power cuckoo optimization algorithm for all models +efindings proved that the recommended linear models weremore appropriate tools for effective energy consumptionprediction in Iran For more clarification Table 4 reports actualand estimated values of testing data by utilizing all models

Using the COAlinear models which was determined abovethe energy consumption predictions are forecasted until 2030 forIran For different scenarios differently forecasted data of GDPpopulation employment and export and import volumes areconsidered +e following three scenarios are used for fore-casting each socioeconomic indicator in the years 2014ndash2030

Scenario 1 it is assumed that the average growth ratesof population GDP import export and employment

Model 1Model 2

Model 3Model 4

2016 2018 2020 2022 2024 2026 2028 20302014Years

0

500

1000

1500

2000

2500

3000

Ener

gy co

nsum

ptio

n (M

boe)

Figure 5 Forecasted values for energy demand in Iran (2014ndash2030) under scenario 1

Model 1Model 2

Model 3Model 4

2016 2018 2020 2022 2024 2026 2028 20302014Years

0

500

1000

1500

2000

2500

3000

Ener

gy co

nsum

ptio

n (M

boe)

Figure 6 Forecasted values for energy demand in Iran (2014ndash2030) under scenario 2

6 Mathematical Problems in Engineering

are 2 5 3 3 and 6 respectively during2014ndash2030Scenario 2 it is assumed that the average growth ratesof population GDP import export and employmentare 22 67 33 33 and 65 respectivelyduring 2014ndash2030Scenario 3 it is assumed that the average growth ratesof population GDP import export and employmentare 25 8 35 35 and 75 respectively during2014ndash2030

4 Conclusion

+e point of this study is to demonstrate to the authoritiesthe significance of utilizing option estimating strategies

+erefore in this study the COA (cuckoo optimizationalgorithm) has been successfully used to estimate Iranrsquosenergy demand based on the structure of the Iranrsquos socio-economic conditions In the first model energy consump-tion is estimated based on population and GDP In thesecond model population GDP import and export areused to forecast energy consumption In model 3 pop-ulation GDP and employment are used to estimate energyconsumption Finally in the fourth model energy con-sumption is modeled based on population GDP exportimport and employment +e proposed linear models an-ticipated the energy demand superior to anything the powermodels in terms of relative errors and RMSEs In additionapproval of models demonstrates that acquired demandestimation linear models are in great concurrence with thewatched information yet the COAlinear model 4 outflankedother introduced models +us three scenarios are designedto estimate Iranrsquos energy demand during 2014ndash2030 usingCOA-linear models and the results are shown inFigures 5ndash7

In conclusion this paper presented helpful suggestionsand novel insights into experts and policy planners Itrecommended a strong tool for developing energy programsForecasting energy demand can as well be studied by neuralnetworks or other new metaheuristics including harmonysearch and simulated annealing +e results of differentmethods may be compared with the COA method Furtherstudies should concentrate on the comparison of methodsexplained in this study with the rest of the available toolsForecasting energy demand may as well be investigated byusing electromagnetism mechanism algorithm krill herdoptimization algorithm and the rest of intelligent optimi-zation techniques +e results of using different methodscould be put into analogy with the COA method

Data Availability

All data are available in the World Bank depository CentralBank of the Islamic Republic of Iran and Irans Ministry ofEnergy

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] H Pao ldquoComparing linear and nonlinear forecasts for Tai-wanrsquos electricity consumptionrdquo Energy vol 31 no 12pp 2129ndash2141 2006

[2] E Assareh M A Behrang and A Ghanbarzadeh ldquoIn-tegration of artificial neural network and intelligent optimi-zation techniques on world electricity consumptionestimationrdquo World Academy of Science Engineering andTechnology vol 73 pp 690ndash694 2011

[3] A Azadeh S F Ghaderi and S Sohrabkhani ldquoA simulated-based neural network algorithm for forecasting electrical

Model 1Model 2

Model 3Model 4

2016 2018 2020 2022 2024 2026 2028 20302014Years

0

500

1000

1500

2000

2500

3000

3500

4000

Ener

gy co

nsum

ptio

n (M

boe)

Figure 7 Forecasted values for energy demand in Iran (2014ndash2030) under scenario 3

Mathematical Problems in Engineering 7

energy consumption in Iranrdquo Energy Policy vol 36 no 7pp 2637ndash2644 2008

[4] V Bianco O Manca S Nardini and A A Minea ldquoAnalysisand forecasting of nonresidential electricity consumption inRomaniardquo Applied Energy vol 87 no 11 pp 3584ndash35902010

[5] H Ceylan H Ceylan S Haldenbilen and O BaskanldquoTransport energy modeling with meta-heuristic harmonysearch algorithm an application to Turkeyrdquo Energy Policyvol 36 no 7 pp 2527ndash2535 2008

[6] Z Mohamed and P Bodger ldquoForecasting electricity con-sumption in New Zealand using economic and demographicvariablesrdquo Energy vol 30 no 10 pp 1833ndash1843 2005

[7] M H Amjadi H Nezamabadi-pour and M M FarsangildquoEstimation of electricity demand of Iran using two heuristicalgorithmsrdquo Energy Conversion and Management vol 51no 3 pp 493ndash497 2010

[8] H Sadeghi M Zolfaghari and M Heydarizade ldquoEstimationof electricity demand in residential sector using genetic al-gorithm approachrdquo International Journal of Industrial Engi-neering vol 22 no 1 2011

[9] M A Behrang E Assareh M R Assari andA Ghanbarzadeh ldquoTotal energy demand estimation in Iranusing bees algorithmrdquo Energy Sources Part B EconomicsPlanning and Policy vol 6 no 3 pp 294ndash303 2011

[10] M S Kıran E Ozceylan M Gunduz and T Paksoy ldquoSwarmintelligence approaches to estimate electricity energy demandin Turkeyrdquo Knowledge-Based Systems vol 36 pp 93ndash1032012

[11] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing IEEE Coimbatore India December2009

[12] R Rajabioun ldquoCuckoo optimization algorithmrdquo Applied SoftComputing vol 11 no 8 pp 5508ndash5518 2011

[13] M A Mellal S Adjerida and E J Williams ldquoOptimal se-lection of obsolete tools in manufacturing systems usingcuckoo optimization algorithmrdquo Chemical Engineeringvol 33 no 1 pp 355ndash360 2013

[14] E Shadkam andM Bijari ldquoEvaluation the efficiency of cuckoooptimization algorithmrdquo 2014 httparxivorgabs14052168

[15] M A Mellal S Adjerid E J Williams and D BenazzouzldquoOptimal replacement policy for obsolete components usingcuckoo optimization algorithm based-approach de-pendability contextrdquo Journal of Scientific and Industrial Re-search vol 71 no 11 pp 715ndash721 2012

8 Mathematical Problems in Engineering

are 2 5 3 3 and 6 respectively during2014ndash2030Scenario 2 it is assumed that the average growth ratesof population GDP import export and employmentare 22 67 33 33 and 65 respectivelyduring 2014ndash2030Scenario 3 it is assumed that the average growth ratesof population GDP import export and employmentare 25 8 35 35 and 75 respectively during2014ndash2030

4 Conclusion

+e point of this study is to demonstrate to the authoritiesthe significance of utilizing option estimating strategies

+erefore in this study the COA (cuckoo optimizationalgorithm) has been successfully used to estimate Iranrsquosenergy demand based on the structure of the Iranrsquos socio-economic conditions In the first model energy consump-tion is estimated based on population and GDP In thesecond model population GDP import and export areused to forecast energy consumption In model 3 pop-ulation GDP and employment are used to estimate energyconsumption Finally in the fourth model energy con-sumption is modeled based on population GDP exportimport and employment +e proposed linear models an-ticipated the energy demand superior to anything the powermodels in terms of relative errors and RMSEs In additionapproval of models demonstrates that acquired demandestimation linear models are in great concurrence with thewatched information yet the COAlinear model 4 outflankedother introduced models +us three scenarios are designedto estimate Iranrsquos energy demand during 2014ndash2030 usingCOA-linear models and the results are shown inFigures 5ndash7

In conclusion this paper presented helpful suggestionsand novel insights into experts and policy planners Itrecommended a strong tool for developing energy programsForecasting energy demand can as well be studied by neuralnetworks or other new metaheuristics including harmonysearch and simulated annealing +e results of differentmethods may be compared with the COA method Furtherstudies should concentrate on the comparison of methodsexplained in this study with the rest of the available toolsForecasting energy demand may as well be investigated byusing electromagnetism mechanism algorithm krill herdoptimization algorithm and the rest of intelligent optimi-zation techniques +e results of using different methodscould be put into analogy with the COA method

Data Availability

All data are available in the World Bank depository CentralBank of the Islamic Republic of Iran and Irans Ministry ofEnergy

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] H Pao ldquoComparing linear and nonlinear forecasts for Tai-wanrsquos electricity consumptionrdquo Energy vol 31 no 12pp 2129ndash2141 2006

[2] E Assareh M A Behrang and A Ghanbarzadeh ldquoIn-tegration of artificial neural network and intelligent optimi-zation techniques on world electricity consumptionestimationrdquo World Academy of Science Engineering andTechnology vol 73 pp 690ndash694 2011

[3] A Azadeh S F Ghaderi and S Sohrabkhani ldquoA simulated-based neural network algorithm for forecasting electrical

Model 1Model 2

Model 3Model 4

2016 2018 2020 2022 2024 2026 2028 20302014Years

0

500

1000

1500

2000

2500

3000

3500

4000

Ener

gy co

nsum

ptio

n (M

boe)

Figure 7 Forecasted values for energy demand in Iran (2014ndash2030) under scenario 3

Mathematical Problems in Engineering 7

energy consumption in Iranrdquo Energy Policy vol 36 no 7pp 2637ndash2644 2008

[4] V Bianco O Manca S Nardini and A A Minea ldquoAnalysisand forecasting of nonresidential electricity consumption inRomaniardquo Applied Energy vol 87 no 11 pp 3584ndash35902010

[5] H Ceylan H Ceylan S Haldenbilen and O BaskanldquoTransport energy modeling with meta-heuristic harmonysearch algorithm an application to Turkeyrdquo Energy Policyvol 36 no 7 pp 2527ndash2535 2008

[6] Z Mohamed and P Bodger ldquoForecasting electricity con-sumption in New Zealand using economic and demographicvariablesrdquo Energy vol 30 no 10 pp 1833ndash1843 2005

[7] M H Amjadi H Nezamabadi-pour and M M FarsangildquoEstimation of electricity demand of Iran using two heuristicalgorithmsrdquo Energy Conversion and Management vol 51no 3 pp 493ndash497 2010

[8] H Sadeghi M Zolfaghari and M Heydarizade ldquoEstimationof electricity demand in residential sector using genetic al-gorithm approachrdquo International Journal of Industrial Engi-neering vol 22 no 1 2011

[9] M A Behrang E Assareh M R Assari andA Ghanbarzadeh ldquoTotal energy demand estimation in Iranusing bees algorithmrdquo Energy Sources Part B EconomicsPlanning and Policy vol 6 no 3 pp 294ndash303 2011

[10] M S Kıran E Ozceylan M Gunduz and T Paksoy ldquoSwarmintelligence approaches to estimate electricity energy demandin Turkeyrdquo Knowledge-Based Systems vol 36 pp 93ndash1032012

[11] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing IEEE Coimbatore India December2009

[12] R Rajabioun ldquoCuckoo optimization algorithmrdquo Applied SoftComputing vol 11 no 8 pp 5508ndash5518 2011

[13] M A Mellal S Adjerida and E J Williams ldquoOptimal se-lection of obsolete tools in manufacturing systems usingcuckoo optimization algorithmrdquo Chemical Engineeringvol 33 no 1 pp 355ndash360 2013

[14] E Shadkam andM Bijari ldquoEvaluation the efficiency of cuckoooptimization algorithmrdquo 2014 httparxivorgabs14052168

[15] M A Mellal S Adjerid E J Williams and D BenazzouzldquoOptimal replacement policy for obsolete components usingcuckoo optimization algorithm based-approach de-pendability contextrdquo Journal of Scientific and Industrial Re-search vol 71 no 11 pp 715ndash721 2012

8 Mathematical Problems in Engineering

energy consumption in Iranrdquo Energy Policy vol 36 no 7pp 2637ndash2644 2008

[4] V Bianco O Manca S Nardini and A A Minea ldquoAnalysisand forecasting of nonresidential electricity consumption inRomaniardquo Applied Energy vol 87 no 11 pp 3584ndash35902010

[5] H Ceylan H Ceylan S Haldenbilen and O BaskanldquoTransport energy modeling with meta-heuristic harmonysearch algorithm an application to Turkeyrdquo Energy Policyvol 36 no 7 pp 2527ndash2535 2008

[6] Z Mohamed and P Bodger ldquoForecasting electricity con-sumption in New Zealand using economic and demographicvariablesrdquo Energy vol 30 no 10 pp 1833ndash1843 2005

[7] M H Amjadi H Nezamabadi-pour and M M FarsangildquoEstimation of electricity demand of Iran using two heuristicalgorithmsrdquo Energy Conversion and Management vol 51no 3 pp 493ndash497 2010

[8] H Sadeghi M Zolfaghari and M Heydarizade ldquoEstimationof electricity demand in residential sector using genetic al-gorithm approachrdquo International Journal of Industrial Engi-neering vol 22 no 1 2011

[9] M A Behrang E Assareh M R Assari andA Ghanbarzadeh ldquoTotal energy demand estimation in Iranusing bees algorithmrdquo Energy Sources Part B EconomicsPlanning and Policy vol 6 no 3 pp 294ndash303 2011

[10] M S Kıran E Ozceylan M Gunduz and T Paksoy ldquoSwarmintelligence approaches to estimate electricity energy demandin Turkeyrdquo Knowledge-Based Systems vol 36 pp 93ndash1032012

[11] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing IEEE Coimbatore India December2009

[12] R Rajabioun ldquoCuckoo optimization algorithmrdquo Applied SoftComputing vol 11 no 8 pp 5508ndash5518 2011

[13] M A Mellal S Adjerida and E J Williams ldquoOptimal se-lection of obsolete tools in manufacturing systems usingcuckoo optimization algorithmrdquo Chemical Engineeringvol 33 no 1 pp 355ndash360 2013

[14] E Shadkam andM Bijari ldquoEvaluation the efficiency of cuckoooptimization algorithmrdquo 2014 httparxivorgabs14052168

[15] M A Mellal S Adjerid E J Williams and D BenazzouzldquoOptimal replacement policy for obsolete components usingcuckoo optimization algorithm based-approach de-pendability contextrdquo Journal of Scientific and Industrial Re-search vol 71 no 11 pp 715ndash721 2012

8 Mathematical Problems in Engineering

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