research article an efficient approach for energy

Research ArticleAn Efficient Approach for Energy ConsumptionOptimization and Management in Residential BuildingUsing Artificial Bee Colony and Fuzzy Logic

Fazli Wahid and Do Hyeun Kim

Department of Computer Engineering Jeju National University Jeju 690756 Republic of Korea

Correspondence should be addressed to Do Hyeun Kim kimdhjejunuackr

Received 5 January 2016 Revised 1 April 2016 Accepted 12 April 2016

Academic Editor Driss Mehdi

Copyright copy 2016 F Wahid and D H Kim This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The energy management in residential buildings according to occupantrsquos requirement and comfort is of vital importance Thereare many proposals in the literature addressing the issue of userrsquos comfort and energy consumption (management) with keepingdifferent parameters in consideration In this paper we have utilized artificial bee colony (ABC) optimization algorithm formaximizing user comfort and minimizing energy consumption simultaneously We propose a complete user friendly and energyefficient model with different components The user set parameters and the environmental parameters are inputs of the ABCand the optimized parameters are the output of the ABC The error differences between the environmental parameters and theABC optimized parameters are inputs of fuzzy controllers which give the required energy as the outputs The purpose of theoptimization algorithm is tomaximize the comfort index andminimize the error difference between the user set parameters and theenvironmental parameters which ultimately decreases the power consumption The experimental results show that the proposedmodel is efficient in achieving high comfort index along with minimized energy consumption

1 Introduction

For every residential building it is the most importantissue to effectively manage the energy as well as achievehigher occupantrsquos comfort The reason behind the fact isthat the energy consumption increases rapidly with thepassage of time and becomes more and more expensive andthe user cannot compromise on hisher comfort Thereforethe energy consumption minimization and user comfortmaximization need to be balanced to achieve both goalsTherefore a trade-off is required between the user comfortand the energy utilization [1ndash3] In any residential buildingwe need a control system formaintaining user comfort as wellas energy consumption minimization In order to determinethe user comfort we need three basic comfort parametersnamely visual comfort thermal comfort and air quality [4]The thermal comfort is represented by temperature insidethe building In order to preserve the temperature in thecomfortable area of the building the auxiliary cooling or

heating system is required For maintaining the visual com-fort of the user in the residential building the illuminationis considered [5] For managing the user visual comfort theelectrical lighting system is used For the measurement ofair quality in the comfort zone of the residential buildingCO2concentration ismeasuredThe ventilation system keeps

the concentration of CO2as low as possible [6] In order

to maintain the comfort of residential building according touser demand these three parameters are consideredWe havealso considered these three parameters to maintain the usercomfort in residential building

Many energy management systems have been proposedin the literature for energy savings and consumption In pre-vious works many approaches have been introduced whichare based on conventional control systems [7ndash9] Some ofthese controllers are optimal controllers adaptive controllersand PID (Proportional Integral Derivatives) There are manydisadvantages associated with these conventional controllersFor example these controllers were not user friendly and it

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 9104735 13 pageshttpdxdoiorg10115520169104735

2 Mathematical Problems in Engineering

was difficult to monitor and control the parameters In orderto control the environmental parameters in the buildingthe application of optimized fuzzy controllers has been pro-posed in [10] In order to control heating air-conditioningand ventilation many other predictive control approachesapply weather prediction [11 12] The authors in [13] usedmultiagent control system in which information fusion hasbeen usedThe authors have used orderedweighted averagingaggregation for indoor energy and control managementThey have maximized user comfort and minimized energyconsumptionMany different types of factors including socialfactors personal factors and buildings factors have stronginfluence on user comfort In order to understand thecomplex relationship among these different factors a modelhas been proposed by the authors in [14] The authors in [15]have presented amethodology in which they have consideredboth the indoor and outdoor environmental factors anduser comfort and energy utilization management Manytypes of different classification prediction and optimizationalgorithms have been used in the literature for differentpurposes related to energy control andmanagement systemsAs compared to other optimization algorithms artificialbee colony algorithm is a new algorithm which has beenpreviously used in few proposed methods for energy man-agement and control related applications The authors in[16] applied artificial bee colony optimization algorithm foroptimalmanagement ofmicro grid Keeping in considerationdifferent parameters the objective was to give scheduling ofshort-term load forecasting using minimized operation costof micro grid The aim of the paper was to minimize thetotal operating cost of the micro grid using different typesof optimization algorithms and the authors concluded thatartificial bee colony algorithm provided the best results Inorder to bring optimization in process placement schemesof energy efficient data centers the authors in [17] appliedmultiobjective artificial bee colonyThe objective of the paperwas tominimize energy cost for effective and efficient controlandmanagement of data centers as the cost of energy is higherin data centers as compared to office buildingsThe authors in[18] applied artificial bee colony for temperature dependentoptimal power flow The objective was to minimize the fuelcost minimize power loss and improve voltage profile Arti-ficial bee colony was applied by [19] for energy managementsystem in combination with Markov chain

In this paper we propose an optimization methodol-ogy for maximizing user comfort and minimizing powerconsumption using multiobjective artificial bee colony opti-mization algorithm Our proposed system is used for energysaving and achieving user comfort simultaneously The aimis to integrate the fitness function of artificial bee colonywith user comfort index and energy utilization Artificialbee colony algorithm targets the user comfort and energyconsumption for maximizing the first and minimizing thelatter User set parameters including temperature illumina-tion and air quality are used as basic parameters in usercomfort These parameters are selected and then optimizedusing artificial bee colony according to the user comfortindex After ABC does the optimization the error difference

is found between the optimal parameters and the actualenvironmental parameters This error difference is enteredto fuzzy controllers as input and the output of the fuzzycontrollers is the minimum power required for achieving theuser comfort The coordinator agent takes the output of thefuzzy controller (required power) as its inputs Based on theavailable power from the power sources and required powerfrom the fuzzy controllers the coordinator agent adjusts theactual consumed power and gives this power to the actuatorsto change their status accordingly The block diagram ofenergy efficient building is shown in Figure 1

2 Proposed Methodology

In the proposed architecture the temperature illuminationand air quality from environment as well as from the user(user set temperature illumination and air quality) areentered to ABC optimizer The ABC optimizer optimizesthe environmental parameters according to user preferencesto maximize the comfort index The input to the fuzzycontrollers (temperature fuzzy controller illumination fuzzycontroller and air quality fuzzy controller) is the errordifference between the environmental parameters and theoptimized parameters The output of the fuzzy controllers isthe required power for controlling the status of the actuators(coolingheating lighting and ventilation) The coordinatortakes the required power as input and checks the availabilityof power from the power sources and provides the power toall the actuators according to status provided by the fuzzycontrollersThe inputs of the fuzzy controllers are not only theABC optimized values but also the environmental tempera-ture illumination and air quality values The output valuesgenerated by the fuzzy controllers depend upon the error dif-ferences between the environmental temperature illumina-tion and air quality and the ABC optimized values for thesethree parametersThemain aim of theABCoptimization is tominimize these error differences Without applying the ABCoptimization process the error differences are high whichultimately generate higher output values causing higherenergy consumption After applying optimization the errordifferences decrease causing optimized energy consumptionThe proposed architecture is shown in Figure 2

21 Optimization Using Artificial Bee Colony OptimizationArtificial bee colony (ABC) is a nature inspired optimizationalgorithm which is based on the foraging behavior of beesFor the last few decades many algorithms have been devel-oped which have nature inspired behaviors Some of them areevolutionary algorithms [21] ant colony optimization [22]harmony search [23] and particle swarm optimization (PSO)[24]These algorithms can be applied in a variety of problemsand therefore are known as multipurpose algorithms Artifi-cial bee colony is also an optimization algorithm like otheroptimization algorithms initially introduced by Karaboga asa technical report in 2005 for solving numerical optimizationproblems [25] Artificial bee colony is advantageous over

Mathematical Problems in Engineering 3

Energy efficient building model

Energy management

Environmentalsensors

OptimizationPow

er

Use

r

Fuzzy controllers

Building actuators

com

fort

cons

umpt

ion

Figure 1 Energy management building model

other optimization algorithms due to the following reasonsas identified by different authors

(i) ABC is simple robust and flexible as mentioned by[26 27]

(ii) As compared to other optimization techniques ABChas few control parameters [28]

(iii) ABC can be easily used in hybridization with otheroptimization techniques [27]

(iv) ABC has the capability to cope with objective func-tion having stochastic nature [20]

The major steps of artificial bee colony optimization foroptimization problem are described in the following section[29] The pseudocode for ABC is as follows

Step 1 Initialization of ABC parameters and problemspecific parametersStep 2 Initialization of food sourceRepeat Steps 3 to 6

Step 3 Employed bees are sent to the foodsourceStep 4 Onlooker bees are sent for selection offood sourceStep 5 Scout bees are sent for the search of newfoodStep 6 Best food source is memorized

While (Objective is achieved or termination criterionis met)

Step 1 (parameters initialization) (1) Number of parameters(119863) this shows the number of parameters to be optimized

We have three parameters for optimization namely temper-ature (119879) illumination (119871) and air quality (119860)

(2) Upper bound (UB119894) UB119894represents the upper bounds

of parameter 119894 where 119894 = 1 2 119863 and 119863 represents totalnumber of parameters to be optimized The upper bound oftemperature (119879max) is 78 illumination (119871max) is 880 and airquality (119860max) is 880

(3) Lower bound (LB119894) LB119894represents the lower bounds

of parameter 119894 where 119894 = 1 2 119863 and 119863 represents totalnumber of parameters to be optimized The lower bound oftemperature (119879min) is 68 illumination (119871min) is 720 and airquality (119860min) is 700

(4) Range (119877) range represents the difference between theupper bounds and lower bounds of the parameters given byUB119894minus LB119894 The temperature range (119879

119903) is 10 the illumination

range (119871119903) is 160 and the air quality range (119860

119903) is 180

(5) Colony size (SN) it represents the total number ofsolutions (food sources) in the population This number isequal to total employed bees or onlooker beesThe algorithmhas been tested for different number of colony sizes to findthe best colony size to get best performance results

(6) Foods food represents the total population of the foodsource The total population has been varied for getting thebest optimization results

(7) Maximum cycles (MC)They represent the maximumnumber of generations in algorithm run The algorithm hasbeen tested for different number of cycles

(8) Limit (119871) if a food source is not improved the limitrepresents the number of generations for which the foodsource is abandoned by employed bees The limit has beenset to different values to get best performance results

(9) Objective function this is the function we need tooptimizeThe algorithm has been developed to maximize thevalue of comfort index formulated in (4)

(10) Objective value objective value represents value ofobjective function associated with each food source


Environment

Temperature Illumination Air quality

User

Temperature (s) Illumination (s) Air quality (s)

ABC optimizer

Fuzzy controller(temperature)

Fuzzy controller(illumination)

Fuzzy controller(air quality)

Required power

Coordinator

Power sources

Actuators(coolingheating

lighting ventilation)

Comfort index

Optimizedtemperature

Optimizedillumination

Optimized airquality

Figure 2 Proposed architecture

Step 2 (food source initialization) In order to initialize foodsource we need119863 LB

119894 UB119894 119877 and FN parameters explained

aboveFood source is a matrix of size SN timesD in which each row

represents a food source Each vector is generated by using (1)[20] Consider

119909119895(119894) = LB

119894+ (UB

119894minus LB119894) times 119903 (1)

forall119895 isin (1 2 SN) forall119894 isin (1 2 119863) where 119903 sim (0 1)generates a uniform random number between 0 and 1

Taking into consideration the above values the food sourceis initialized by (2) [20] One has

Food = Random (FN 119863) lowast 119877 + 119871 (2)

Step 3 (assignment of employed bees to food sources) In thisstage (3) is used to assign employed bee to food source and anew solution is generated from the neighbor using [20]

1199091015840(119894) = 119909

119895(119894) + 119903 (119909

119895(119894) minus 119909

119896(119894)) (3)

where for all 119896 isin (1 2 3 SN) 119896 = 119895 and 119903 sim (0 1) Thepseudocode is given in Pseudocode 1


for (119895 = 1 to SN)

for (119894 = 1 to119863)

1199091015840(119894) = 119909

119895(119894) + 119903 (119909

119895(119894) minus 119909

119896(119894))

forall119896isin (1 2 3 SN) 119896 = 119895 and 119903 sim (0 1)

End forCalculation of 119891(119909

119894)

If (119891(1199091015840) gt= 119891(119909119894))

119909119894= 1199091015840

119891(119909119894) = 119891(119909

1015840)

end if

end for

Pseudocode 1 Pseudocode for employed bees [20]

Step 4 (sending onlooker bees) The employed bees andonlooker bees have equal number of food sources Initiallythe selection probability of each food source generated bythe employed bees is calculated by the onlooker bee It thenselects the best food source using Roulette selection methodThe complete process in the onlooker bee phase takes placein Pseudocode 2

In this pseudocode 119904 prob represents the accumulatedprobability of all employed bees

Step 5 (scout bees phase) The scout bees use (2) for thereplacement of abandoned food sources after carrying out arandom search A food source that cannot be improved after apredefined number of cycles is called abandoned food sourceThe scout bee algorithm is given in Pseudocode 3

Step 6 (memorize the best source food) In this phase thesource food and their position are memorized which givesmaximum objective value

Stopping Condition Steps 3 to 6 are repeated until maximumnumber of cycles is specified by MC

22 Comfort Index Comfort index is computed using (4) [3]Consider

CI = 1199011[1 minus (1198901

119879119904

)

2

] + 1199012[1 minus (1198902

119868119904

)

2

]

+ 1199013[1 minus (1198903

119860119904

)

2

]

(4)

where CI is the comfort index of the user 1199011 1199012 and 119901

3

are user set preferences for temperature illumination andair quality respectively and 119901

1+ 1199012+ 1199013= 1 119890

1 1198902and

1198903are error difference between the optimized temperature

and the environmental temperature error difference between

for (119894 = 1 to SN)

119903 sim (0 1)

119904 prob = 0119895 = 0while (119904 prob lt= 119903)

119904 prob = 119904 prob + 119901119895

119895 = 119895 + 1

end whilefor (119896 = 1 to119863)

1199091015840(119895) = 119909

119895(119896) + 119903(119909

119895(119896) minus 119909

119895(119899))

119899 isin (1 2 3 SN)

end forCalculation of 119891(119909

119895)

If

(119891(1199091015840) gt= 119891(119909119895)) put

119909119895= 1199091015840

119895

119891(119909119895) = 119891(119909

1015840

119895)

end if

end for

Pseudocode 2 Pseudocode for onlooker bees [20]

For (119894 = 1 to SN)

If (119878(119894) == Limit)

119909119895is generated using (1)

end if

end for


the optimized illumination and environmental illuminationand the error difference between optimized air quality andenvironmental air quality respectively The maximum valueof CI is 1 119879

119904is the user set temperature 119868

119904is the user set

illumination and119860119904is user set air quality valueThe purpose

of optimization is to maximize the value of CI and minimizethe values of 119890

1 1198902 and 119890

3

23 Fuzzy Controllers The concept of fuzzy has been intro-duced by Zadeh a professor at California University atBerkley [30] In our proposed architecture we have threefuzzy controllers namely temperature fuzzy controller illu-mination fuzzy controller and the air quality fuzzy controllerfor controlling coolingheating lighting and ventilation


Rules

Inferencesystem

Fuzzifier Defuzzifier

Fuzzy input set Fuzzy output set

Inputs Outputs

Fuzzy controller structure

Figure 3 Structure of fuzzy controllers

systems respectively Every fuzzy controller used in theproposed system consists of four main components namelyfuzzifier rules inference engine and defuzzifierThe fuzzifiercalculates its membership function based on its inputs Theoutput membership values are calculated by applying therules stored in rule base and the inference process Thedefuzzifier calculates the actual power required for cool-ingheating (temperature fuzzy controller) lighting (illumi-nation fuzzy controller) and CO

2concentration (air quality

fuzzy controller) All the fuzzy controllers used in theproposed architecture follow the same structure shown inFigure 3

231 Temperature Fuzzy Controller In the proposed archi-tecture the input to the temperature fuzzy controller is theerror difference between the optimized temperature valuesfrom the optimizer and the environmental temperature Theoutput of the temperature fuzzy controller is the requiredpower for coolingheating system The status of the cool-ingheating actuators is changed according to the errordifferences between the actual environmental parameters andthe artificial bee colony optimized parameters in which theoutput of the temperature fuzzy controller is the requiredpower for the actuator statusThe rules for temperature fuzzycontroller are as follows and these are represented in Figures12 13 and 14

If (1198901= = NH) then RP1 = R1NH

If (1198901= = NM) then RP1 = R1NM

If (1198901= = NL) then RP1 = R1NL

If (1198901= = ZE) then RP1 = R1ZE

If (1198901= = PL) then RP1 = R1PL

If (1198901= = PM) then RP1 = R1PM

If (1198901= = PH) then RP1 = R1PH

In these rules 1198901represents the error difference between

the environmental temperature and the ABC optimizedtemperature and this error difference is the input of tem-perature fuzzy controller Based on this error differencethe temperature fuzzy controller generates the energy as itsoutput represented by RP1 (required power 1) to provide it to

the coolingheating actuators NH representsminimum errordifference between the environmental temperature and ABCoptimized temperature followed byNMNL ZE PL PM andPH So as we go from NH towards PH the error differenceincreases and vice versa Accordingly the required power(RP1) for coolingheating control is minimum (RP1 = R1NH)for error difference NH and maximum for error differencePH that is RP1 = R1PH So NH represents minimum errordifference between the environmental temperature and ABCoptimized temperature and PH represents maximum errordifference between the environmental temperature and ABCoptimized temperature Accordingly R1NH represents mini-mum power required for coolingheating system and R1PHrepresents maximum power required for coolingheatingsystem control

232 Illumination Fuzzy Controller The input to the illu-mination fuzzy controller is the error difference betweenthe optimized illumination from the ABC optimizer and theenvironmental illumination The output of the illuminationfuzzy controller is the required power for lighting systemThe status of the lighting actuators is changed accordingto the error differences between the actual environmentalparameters and the artificial bee colony optimized parame-ters in which the output of the illumination fuzzy controlleris the required power for the actuator status The rules forillumination fuzzy controller are as follows and these arerepresented in Figures 15 16 and 17

If (1198902= = HS) then RP2 = R2HS

If (1198902= = MS) then RP2 = R2MS

If (1198902= = BS) then RP2 = R2BS

If (1198902= = OK) then RP2 = R2OK

If (1198902= = SH) then RP2 = R2SH

If (1198902= = H) then RP2 = R2H


the environmental illumination and the ABC optimizedillumination and this error difference is the input of illu-mination fuzzy controller Based on this error differencethe illumination fuzzy controller generates the energy as itsoutput represented by RP2 (required power 2) to provideit to the lighting system HS represents minimum errordifference between the environmental illumination and ABCoptimized illumination followed by MS BS OK SH andH So as we go from HS towards H the error differenceincreases and vice versa Accordingly the required power(RP2) for lighting control is minimum (RP2 = R2HS) forerror differenceHS andmaximum for error differenceH thatis RP2 = R2H So HS represents minimum error differencebetween the environmental illumination and ABC optimizedillumination and H represents maximum error differencebetween the environmental illumination and ABC optimizedillumination Accordingly R2HS representsminimumpowerrequired for lighting system and R2H represents maximumpower required for lighting system control


233 Air Quality Fuzzy Controller The input of the airquality fuzzy controller is the error difference between theenvironmental air quality and the optimized air qualityfrom the ABC optimizer The output of the air quality isthe required power for ventilation system The status ofthe ventilation actuators is changed according to the errordifferences between the actual environmental parameters andthe artificial bee colony optimized parameters in which theoutput of the ventilation fuzzy controller is the requiredpower for the actuator status The fuzzy rules for air qualityfuzzy controller are as follows and are shown in Figures 18 19and 20

If (1198903= = LOW) then RP3 = R3LOW

If (1198903= = OK) then RP3 = R3OK

If (1198903= = SH) then RP3 = R3SH

If (1198903= = LH) then RP3 = R3LH

If (1198903= = HIGH) then RP3 = R3HIGH

In these rules 1198903represents the error difference between the

environmental air quality and the ABC optimized air qualityand this error difference is the input of air quality fuzzycontroller Based on this error difference the air quality fuzzycontroller generates the energy as its output represented byRP3 (required power 3) to provide it to the ventilation systemcontrol LOW represents minimum error difference betweenthe environmental air quality and ABC optimized air qualityfollowed by OK SH LH and HIGH So as we go from LOWtowards HIGH the error difference increases and vice versaAccordingly the required power (RP3) for ventilation controlis minimum (RP3 = R3LOW) for error difference LOW andmaximum for error differenceHIGH that is RP3 =R3HIGHSo LOW represents minimum error difference between theenvironmental air quality and ABC optimized air qualityand HIGH represents maximum error difference betweenthe environmental air quality and ABC optimized air qualityAccordingly R3LOW represents minimum power requiredfor ventilation system and R3HIGH represents maximumpower required for ventilation system control

24 Coordinator The coordinator takes the total powerrequired for controlling the coolingheating lighting andventilation and provides the power available from the powersources The total required power is computed by the follow-ing formula

TRP = RP1 + RP2 + RP3 (5)

where TRP is the total required power RP1 is requiredpower for coolingheating system RP2 is required power forlighting and RP3 is required power for ventilation

25 Actuators These are the devices inside buildings thatactually use the energy Examples of these actuators are AC(for cooling) heater (for heating) refrigerator (for cooling)and freezer (for cooling) The status of the actuators ischanged according to the error difference between the envi-ronmental parameters and the ABC optimized parameters

0

20

40

60

80

100

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Tem

pera

ture

(F)

Time (s)

Temperature parameter

User set parameterEnvironmental parameterOptimized parameter

Figure 4 User set environmental and optimized temperaturevalues

3 Experimental Results and Discussion

All the experiments were carried out on Intel(R) core(TM)i5-3570 CPU 340GHz with MATLAB R2010a installed onit Figure 4 shows the user set temperature parameters theenvironmental temperature parameters and the temperatureparameters after optimization by ABC Figure 5 shows theuser set illumination parameters the environmental illumi-nation parameters and the illumination parameters afteroptimization by ABC Figure 6 shows the user set air qualityparameters the environmental air quality parameters andthe air quality parameters after optimization by ABC Foreach of the three parameters if the value of the parameter is inthe range of user comfort the ABCdoes notmake any changeto the values of the parameter but when the values of theparameters are outside the comfort zone of the user the ABCoptimizes the values to bring them to the user comfort zoneThe values of the parameters within the comfort zone fortemperature illumination and air quality have been alreadydiscussed

Figure 7 shows the comfort index values for both withoutoptimization and after applyingABCoptimization algorithmIt is evident from the figure that the comfort index values foroptimized parameters are higher than that without optimiza-tionwhich shows that theABCoptimized parameters providehigher comfort index to the occupant The figure also showsthat there are some fluctuations in the comfort index valueof ABC optimization but overall the comfort index value ofABC optimization is higher than that without optimization

The second aim of the ABC algorithm is to minimizepower consumption This is achieved by minimizing theerror differences between the user set parameters and theenvironmental parameters Figures 8ndash11 show the power con-sumption for temperature illumination air quality and totalpower consumption before the optimization and after ABCoptimization All the figures show that the power consump-tion has been minimized using ABC The figures show thatthere are somefluctuations in power consumption usingABCalgorithm but overall the consumption has been decreased

The error difference between the user set temperature andthe ABC optimized temperature is input to the temperature


0

200

400

600

800

10001 10 19 28 37 46 55 64 73 82 91 100

109

118

127

136

145

154

163

172

181

190

199

208

217

226

235

244

Illum

inat

ion

(Lux

)

Time (s)

Illumination parameter


Figure 5 User set environmental and optimized illuminationvalues

0

200

400

600

800

1000

1200

1 11 21 31 41 51 61 71 81 91 101

111

121

131

141

151

161

171

181

191

201

211

221

231

241

Time (s)

Air quality parameter

CO2

conc

entr

atio

n (p

pm)

User set parameterEnvironment parameterOptimized parameter


fuzzy controller and the output of the temperature fuzzycontroller is the minimum required power for temperatureThe coolingheating actuator status is changed according tothis error difference The error difference between the userset illumination and the ABC optimized illumination is inputto the illumination fuzzy controller and the output of the illu-mination fuzzy controller is theminimum required power forillumination The lighting actuator status is changed accord-ing to this error difference The error difference between theuser set air quality and the ABC optimized air quality is inputto the air quality fuzzy controller and the output of the airquality fuzzy controller is the minimum required power forventilationThe air quality actuator status is changed accord-ing to this error difference

4 Comparative Analysis of OptimizationResults of Artificial Bee Colony with GeneticAlgorithm and Particle Swarm Optimization

The authors in [1] applied genetic algorithm and particleswarm optimization to minimize the power consumptionand maximize user comfort index using the same data set

09

092

094

096

098

1

102

1 16 31 46 61 76 91 106

121

136

151

166

181

196

211

226

241

Com

fort

inde

x va

lue

Time (s)

Comfort index comparison

With ABC optimizationWithout optimization

Figure 7 User comfort index values with and without ABC optimi-zation

0

5

10

15

20

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)

Power consumption for temperature


Pow

er co

nsum

ptio

n(k

Wh)

Figure 8 Power consumption for temperature usingABC andwith-out using ABC

applied in this proposed work The authors have given thegraphical representation for minimizing power consumptionand maximizing user comfort The power is consumed fortemperature control and illumination control and the authorshave computed air control In this section we comparethe computed power consumed for temperature controlillumination control and air quality control by artificial beecolony with genetic algorithm and particle swarm optimiza-tion as described by the authors The power consumed fortemperature control by artificial bee colony is more than thepower consumed by genetic algorithm and particle swarmoptimization whereas the power consumed for both theillumination control and the air quality control by artificialbee colony is less than the power consumed by both thegenetic algorithm and particle swarm optimizationThe totalpower consumed by artificial bee colony (ABC) is less thanthe power consumed by genetic algorithm (GA) and particleswarm optimization (PSO) as shown in Table 1

It is evident from the facts and figures given by theauthors in [1] and our proposed model that ABC consumesless power as compared to GA and PSO The reason forthis less power consumption is that the ABC generates moreoptimal parameters than both the GA and PSOThe artificialbee colony is also advantageous over genetic algorithm andparticle swarm optimization in optimizing the parameters


Table 1 Power consumption comparison of ABC with GA and PSO

Algorithm Temperature powerconsumption

Illumination powerconsumption

Air quality powerconsumption

Total powerconsumption

GA 43919 147516 65178 256614PSO 52173 153101 69454 274729ABC [proposed approach] 102374 94138 54786 251298

0

5

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15

20

1 12 23 34 45 56 67 78 89 100

111

122

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210

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243

Time (s)

Power consumption for illumination


Pow

er co

nsum

ptio

n(k

Wh)

Figure 9 Power consumption for illumination using ABC andwithout using ABC

02468

1012

1 12 23 34 45 56 67 78 89 100

111

122

133

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155

166

177

188

199

210

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243

Time (s)

Power consumption for air quality


Pow

er co

nsum

ptio

n(k

Wh)

Figure 10 Power consumption for air quality using ABC andwithout using ABC

in a smooth manner whereas there are more fluctuations inthe parameters optimized by genetic algorithm and particleswarm optimization as described by the authors in [1] Thesecond aim of the ABC optimization algorithm in this workis to maximize the user comfort index The minimum valueof comfort index achieved by ABC is more than the mini-mum value of comfort index achieved by both the geneticalgorithm and particle swarm optimization which shows thatthe artificial bee colony is more efficient in maximizing usercomfort index than the genetic algorithm and particle swarmoptimization

5 Conclusions

In this paper the issue of maximizing user comfort andminimizing power consumption in residential buildingsusing artificial bee colony optimization algorithm and fuzzycontroller has been addressed The whole architecture of the

0

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1 12 23 34 45 56 67 78 89 100

111

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155

166

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243

Time (s)

Total power consumption

Pow

er co

nsum

ptio

n(k

Wh)


Figure 11 The total power consumption using ABC and withoutusing ABC

1

08

06

04

02

0

Deg

ree o

f mem

bers

hip

minus25 minus20 minus15 minus10 minus5 0 5 10 15 20 25

NH NM NL ZE PM PL PH

e1

Figure 12 Input membership function for temperature

proposed system consists of different components includingenvironmental parameters (temperature illumination andair quality) ABC optimizer comfort index fuzzy controllercoordinator and different types of actuatorsThe inputs to theABC optimizer are environmental parameters (temperatureillumination and air quality) and user set parameters (tem-perature illumination and air quality) The outputs of theABC optimizer are the optimized temperature illuminationand air quality parametersThe inputs to the fuzzy controllersare the environmental parameters and the ABC optimizedparameters and the outputs of the fuzzy controllers are theminimum power required to set the environment accordingto user preferences The coordinator calculates the totalpower required sent by the fuzzy controller and checks theavailability of required powerThe statuses of the actuators arechanged according to this power sent by the fuzzy controllersThe user comfort index has been increased and the powerconsumption has been decreased


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip

minus20 minus15 minus10 minus5 0 5 10 15 20

R1NH R1NM

RP1

R1NL R1ZE R1PMR1PL R1PH

Figure 13 Output membership function for temperature (required power for temperature)

Temperature = 17

1

2

3

4

5

6

7

minus28 28

Consumption = 121

minus20 20

Figure 14 Example of fuzzy rule applied to temperature

1

08

06

04

02

0

Deg

ree o

f mem

bers

hip

minus150 minus100 minus50 0 50 100 150 200 250

HS MS BS OK SH H

e2

Figure 15 Input membership function for illumination

1

08

06

04

02

0

Deg

ree o

f mem

bers

hip

minus15 minus10 minus5 0 5 10 15 20

RP2

R2HS R2MS R2BS R2OK R2SH R2H

Figure 16 Output membership function for illumination (required power for lighting)


Illumination = 200

1

2

3

4

5

6

minus175 275

Consumption = 15

minus15 20

Figure 17 Example of fuzzy rule applied to illumination

1

08

06

04

02

0

Deg

ree o

f mem

bers

hip

minus300 minus200 minus100 0 100 200 300

LOW OK SH LH HIGH

e3

Figure 18 Input membership function for air quality

1

08

06

04

02

0

Deg

ree o

f mem

bers

hip

0 2 4 6 8 10 12

RP3

R3LOW R3OK R3SH R3LH R3HIGH

Figure 19 Output membership function for air quality (required power for ventilation)

Error = 200

1

2

3

4

5

minus300 300

Consumption = 973

0 13

Figure 20 Example of fuzzy rule applied to air quality


Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was partly supported by Institute for Informationamp Communications Technology Promotion (IITP) grantfunded by the Korea government (MSIP) (no 10043907Development of High Performance IoT Device and OpenPlatform with Intelligent Software) And this research wassupported by the MSIP (Ministry of Science ICT and FuturePlanning) Korea under the ITRC (Information TechnologyResearch Center) support program (IITP-2015-H8501-15-1017) supervised by the IITP (Institute for Information ampCommunications Technology Promotion)

References

[1] S Ali and D-H Kim ldquoOptimized power control methodologyusing genetic algorithmrdquo Wireless Personal Communicationsvol 83 no 1 pp 493ndash505 2015

[2] S Ali and D-H Kim ldquoEffective and comfortable power controlmodel using Kalman filter for building energy managementrdquoWireless Personal Communications vol 73 no 4 pp 1439ndash14532013

[3] Z Wang R Yang and L Wang ldquoMulti-agent control systemwith intelligent optimization for smart and energy-efficientbuildingsrdquo in Proceedings of the 36th Annual Conference of theIEEE Industrial Electronics Society (IECON rsquo10) pp 1144ndash1149November 2010

[4] A I Dounis and C Caraiscos ldquoAdvanced control systemsengineering for energy and comfort management in a buildingenvironment A reviewrdquo Renewable and Sustainable EnergyReviews vol 13 no 6-7 pp 1246ndash1261 2009

[5] Z Wang R Yang and L Wang ldquoMulti-agent intelligentcontroller design for smart and sustainable buildingsrdquo in Pro-ceedings of the 4th Annual IEEE Systems Conference pp 277ndash282 IEEE San Diego Calif USA April 2010

[6] S J Emmerich and A K Persily State-of-the-Art Review of CO2

Demand Controlled Ventilation Technology and ApplicationCollingdale Pa USA Diane 2001

[7] G J Levermore Building Energy Management Systems AnApplication to Heating and Control E amp FN Spon 1992

[8] C Benard B Guerrier and M-M Rosset-Loueerat ldquoOptimalbuilding energymanagement part IImdashcontrolrdquo Journal of SolarEnergy Engineering vol 114 no 1 pp 13ndash22 1992

[9] P S Curtiss J Kreider and G Shavit Neural Networks Appliedto BuildingsmdashA Tutorial and Case Studies in Prediction andAdaptive Control American Society of Heating Refrigeratingand Air-Conditioning Engineers Atlanta Ga USA 1996

[10] D Kolokotsa G S Stavrakakis K Kalaitzakis and D AgorisldquoGenetic algorithms optimized fuzzy controller for the indoorenvironmental management in buildings implemented usingPLC and local operating networksrdquo Engineering Applications ofArtificial Intelligence vol 15 no 5 pp 417ndash428 2002

[11] A Kusiak M Li and Z Zhang ldquoA data-driven approach forsteam load prediction in buildingsrdquo Applied Energy vol 87 no3 pp 925ndash933 2010

[12] J Siroky F Oldewurtel J Cigler and S Prıvara ldquoExperimentalanalysis of model predictive control for an energy efficient

building heating systemrdquo Applied Energy vol 88 no 9 pp3079ndash3087 2011

[13] Z Wang L Wang A I Dounis and R Yang ldquoMulti-agentcontrol system with information fusion based comfort modelfor smart buildingsrdquo Applied Energy vol 99 pp 247ndash254 2012

[14] P M Bluyssen M Aries and P van Dommelen ldquoComfortof workers in office buildings The European HOPE projectrdquoBuilding and Environment vol 46 no 1 pp 280ndash288 2011

[15] C Marino A Nucara and M Pietrafesa ldquoProposal of comfortclassification indexes suitable for both single environments andwhole buildingsrdquo Building and Environment vol 57 pp 58ndash672012

[16] M D Govardhan and R Roy ldquoArtificial Bee Colony basedoptimal management of microgridrdquo in Proceedings of the 11thInternational Conference on Environment and Electrical Engi-neering (EEEIC rsquo12) pp 334ndash339 Venice Italy May 2012

[17] P Tiwari K Jintamuttha K Manakul and T AchalakulldquoProcess placement scheme optimization for energy-efficientdata centerrdquo in Proceedings of the 9th International Conferenceon Electrical EngineeringElectronics Computer Telecommuni-cations and Information Technology (ECTI-CON rsquo12) pp 1ndash4May 2012

[18] P D Bamane A N Kshirsagar S Raj and H T JadhavldquoTemperature dependent Optimal Power Flow using gbest-guided artificial bee colony algorithmrdquo in Proceedings of the 3rdIEEE International Conference onComputation of Power EnergyInformation and Communication (ICCPEIC rsquo14) pp 321ndash327Chennai India April 2014

[19] M Marzband F Azarinejadian M Savaghebi and J MGuerrero ldquoAn optimal energy management system for islandedmicrogrids based onmultiperiod artificial bee colony combinedwithMarkovChainrdquo IEEE Systems Journal no 99 pp 1ndash11 2015

[20] D Karaboga and B Basturk ldquoA powerful and efficient algo-rithm for numerical function optimization artificial bee colony(ABC) algorithmrdquo Journal of Global Optimization vol 39 no 3pp 459ndash471 2007

[21] P J Angeline G M Saunders and J B Pollack ldquoAn evolution-ary algorithm that constructs recurrent neural networksrdquo IEEETransactions on Neural Networks vol 5 no 1 pp 54ndash65 1994

[22] MDorigoM Birattari andT Stutzle ldquoAnt colony optimizationartificial ants as a computational intelligence techniquerdquo IEEEComputational Intelligence Magazine vol 1 no 4 pp 28ndash392006

[23] Z W Geem J H Kim and G V Loganathan ldquoA new heuristicoptimization algorithm harmony searchrdquo Simulation vol 76no 2 pp 60ndash68 2001

[24] J Kennedy ldquoParticle swarm optimizationrdquo in Encyclopedia ofMachine Learning pp 760ndash766 Springer New York NY USA2011

[25] D Karaboga ldquoAn idea based on honey bee swarm for numericaloptimizationrdquo Tech Rep tr06 Erciyes University EngineeringFaculty Computer Engineering Department 2005

[26] R S Rao S Narasimham and M Ramalingaraju ldquoOptimiza-tion of distribution network configuration for loss reductionusing artificial bee colony algorithmrdquo International Journal ofElectrical Power and Energy Systems Engineering vol 1 pp 116ndash122 2008

[27] A Singh ldquoAn artificial bee colony algorithm for the leaf-constrained minimum spanning tree problemrdquo Applied SoftComputing vol 9 no 2 pp 625ndash631 2009


[28] D Karaboga and B Akay ldquoA comparative study of artificial Beecolony algorithmrdquo Applied Mathematics and Computation vol214 no 1 pp 108ndash132 2009

[29] A L A Bolaji A T Khader M A Al-Betar and M AAwadallah ldquoArtificial bee colony algorithm its variants andapplications a surveyrdquo Journal of Theoretical amp Applied Infor-mation Technology vol 47 no 2 pp 434ndash459 2013

[30] L A Zadeh ldquoFuzzy algorithmsrdquo Information and Control vol12 no 2 pp 94ndash102 1968

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


was difficult to monitor and control the parameters In orderto control the environmental parameters in the buildingthe application of optimized fuzzy controllers has been pro-posed in [10] In order to control heating air-conditioningand ventilation many other predictive control approachesapply weather prediction [11 12] The authors in [13] usedmultiagent control system in which information fusion hasbeen usedThe authors have used orderedweighted averagingaggregation for indoor energy and control managementThey have maximized user comfort and minimized energyconsumptionMany different types of factors including socialfactors personal factors and buildings factors have stronginfluence on user comfort In order to understand thecomplex relationship among these different factors a modelhas been proposed by the authors in [14] The authors in [15]have presented amethodology in which they have consideredboth the indoor and outdoor environmental factors anduser comfort and energy utilization management Manytypes of different classification prediction and optimizationalgorithms have been used in the literature for differentpurposes related to energy control andmanagement systemsAs compared to other optimization algorithms artificialbee colony algorithm is a new algorithm which has beenpreviously used in few proposed methods for energy man-agement and control related applications The authors in[16] applied artificial bee colony optimization algorithm foroptimalmanagement ofmicro grid Keeping in considerationdifferent parameters the objective was to give scheduling ofshort-term load forecasting using minimized operation costof micro grid The aim of the paper was to minimize thetotal operating cost of the micro grid using different typesof optimization algorithms and the authors concluded thatartificial bee colony algorithm provided the best results Inorder to bring optimization in process placement schemesof energy efficient data centers the authors in [17] appliedmultiobjective artificial bee colonyThe objective of the paperwas tominimize energy cost for effective and efficient controlandmanagement of data centers as the cost of energy is higherin data centers as compared to office buildingsThe authors in[18] applied artificial bee colony for temperature dependentoptimal power flow The objective was to minimize the fuelcost minimize power loss and improve voltage profile Arti-ficial bee colony was applied by [19] for energy managementsystem in combination with Markov chain

In this paper we propose an optimization methodol-ogy for maximizing user comfort and minimizing powerconsumption using multiobjective artificial bee colony opti-mization algorithm Our proposed system is used for energysaving and achieving user comfort simultaneously The aimis to integrate the fitness function of artificial bee colonywith user comfort index and energy utilization Artificialbee colony algorithm targets the user comfort and energyconsumption for maximizing the first and minimizing thelatter User set parameters including temperature illumina-tion and air quality are used as basic parameters in usercomfort These parameters are selected and then optimizedusing artificial bee colony according to the user comfortindex After ABC does the optimization the error difference

is found between the optimal parameters and the actualenvironmental parameters This error difference is enteredto fuzzy controllers as input and the output of the fuzzycontrollers is the minimum power required for achieving theuser comfort The coordinator agent takes the output of thefuzzy controller (required power) as its inputs Based on theavailable power from the power sources and required powerfrom the fuzzy controllers the coordinator agent adjusts theactual consumed power and gives this power to the actuatorsto change their status accordingly The block diagram ofenergy efficient building is shown in Figure 1

2 Proposed Methodology

In the proposed architecture the temperature illuminationand air quality from environment as well as from the user(user set temperature illumination and air quality) areentered to ABC optimizer The ABC optimizer optimizesthe environmental parameters according to user preferencesto maximize the comfort index The input to the fuzzycontrollers (temperature fuzzy controller illumination fuzzycontroller and air quality fuzzy controller) is the errordifference between the environmental parameters and theoptimized parameters The output of the fuzzy controllers isthe required power for controlling the status of the actuators(coolingheating lighting and ventilation) The coordinatortakes the required power as input and checks the availabilityof power from the power sources and provides the power toall the actuators according to status provided by the fuzzycontrollersThe inputs of the fuzzy controllers are not only theABC optimized values but also the environmental tempera-ture illumination and air quality values The output valuesgenerated by the fuzzy controllers depend upon the error dif-ferences between the environmental temperature illumina-tion and air quality and the ABC optimized values for thesethree parametersThemain aim of theABCoptimization is tominimize these error differences Without applying the ABCoptimization process the error differences are high whichultimately generate higher output values causing higherenergy consumption After applying optimization the errordifferences decrease causing optimized energy consumptionThe proposed architecture is shown in Figure 2

21 Optimization Using Artificial Bee Colony OptimizationArtificial bee colony (ABC) is a nature inspired optimizationalgorithm which is based on the foraging behavior of beesFor the last few decades many algorithms have been devel-oped which have nature inspired behaviors Some of them areevolutionary algorithms [21] ant colony optimization [22]harmony search [23] and particle swarm optimization (PSO)[24]These algorithms can be applied in a variety of problemsand therefore are known as multipurpose algorithms Artifi-cial bee colony is also an optimization algorithm like otheroptimization algorithms initially introduced by Karaboga asa technical report in 2005 for solving numerical optimizationproblems [25] Artificial bee colony is advantageous over



Energy management


OptimizationPow

er

Use

r

Fuzzy controllers

Building actuators

com

fort

cons

umpt

ion




















119903) is 180








Environment


User


ABC optimizer




Required power

Coordinator

Power sources



Comfort index









119909119895(119894) = LB

119894+ (UB

119894minus LB119894) times 119903 (1)





1199091015840(119894) = 119909

119895(119894) + 119903 (119909

119895(119894) minus 119909

119896(119894)) (3)



for (119895 = 1 to SN)

for (119894 = 1 to119863)

1199091015840(119894) = 119909

119895(119894) + 119903 (119909

119895(119894) minus 119909

119896(119894))



119894)

If (119891(1199091015840) gt= 119891(119909119894))

119909119894= 1199091015840

119891(119909119894) = 119891(119909

1015840)

end if

end for








CI = 1199011[1 minus (1198901

119879119904

)

2

] + 1199012[1 minus (1198902

119868119904

)

2

]

+ 1199013[1 minus (1198903

119860119904

)

2

]

(4)


3


1+ 1199012+ 1199013= 1 119890

1 1198902and



for (119894 = 1 to SN)

119903 sim (0 1)


119904 prob = 119904 prob + 119901119895

119895 = 119895 + 1

end whilefor (119896 = 1 to119863)

1199091015840(119895) = 119909

119895(119896) + 119903(119909

119895(119896) minus 119909

119895(119899))

119899 isin (1 2 3 SN)


119895)

If

(119891(1199091015840) gt= 119891(119909119895)) put

119909119895= 1199091015840

119895

119891(119909119895) = 119891(119909

1015840

119895)

end if

end for


For (119894 = 1 to SN)

If (119878(119894) == Limit)


end if

end for







1 1198902 and 119890

3



Rules

Inferencesystem



Inputs Outputs







If (1198901= = NH) then RP1 = R1NH

If (1198901= = NM) then RP1 = R1NM

If (1198901= = NL) then RP1 = R1NL

If (1198901= = ZE) then RP1 = R1ZE

If (1198901= = PL) then RP1 = R1PL

If (1198901= = PM) then RP1 = R1PM

If (1198901= = PH) then RP1 = R1PH





If (1198902= = HS) then RP2 = R2HS

If (1198902= = MS) then RP2 = R2MS

If (1198902= = BS) then RP2 = R2BS

If (1198902= = OK) then RP2 = R2OK

If (1198902= = SH) then RP2 = R2SH

If (1198902= = H) then RP2 = R2H






If (1198903= = OK) then RP3 = R3OK

If (1198903= = SH) then RP3 = R3SH

If (1198903= = LH) then RP3 = R3LH





TRP = RP1 + RP2 + RP3 (5)



0

20

40

60

80

100

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Tem

pera

ture

(F)

Time (s)










0

200

400

600

800

10001 10 19 28 37 46 55 64 73 82 91 100

109

118

127

136

145

154

163

172

181

190

199

208

217

226

235

244

Illum

inat

ion

(Lux

)

Time (s)




0

200

400

600

800

1000

1200

1 11 21 31 41 51 61 71 81 91 101

111

121

131

141

151

161

171

181

191

201

211

221

231

241

Time (s)


CO2

conc

entr

atio

n (p

pm)






09

092

094

096

098

1

102

1 16 31 46 61 76 91 106

121

136

151

166

181

196

211

226

241

Com

fort

inde

x va

lue

Time (s)




0

5

10

15

20

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)











0

5

10

15

20

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)


02468

1012

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)



5 Conclusions


0

10

20

30

40

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)


Pow

er co

nsum

ptio

n(k

Wh)



1

08

06

04

02

0

Deg

ree o

f mem

bers

hip



e1




1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


R1NH R1NM

RP1



Temperature = 17

1

2

3

4

5

6

7

minus28 28

Consumption = 121

minus20 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


HS MS BS OK SH H

e2


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


RP2




Illumination = 200

1

2

3

4

5

6

minus175 275

Consumption = 15

minus15 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


LOW OK SH LH HIGH

e3


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip

0 2 4 6 8 10 12

RP3



Error = 200

1

2

3

4

5

minus300 300

Consumption = 973

0 13



Competing Interests


Acknowledgments


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Energy management


OptimizationPow

er

Use

r

Fuzzy controllers

Building actuators

com

fort

cons

umpt

ion




















119903) is 180








Environment


User


ABC optimizer




Required power

Coordinator

Power sources



Comfort index









119909119895(119894) = LB

119894+ (UB

119894minus LB119894) times 119903 (1)





1199091015840(119894) = 119909

119895(119894) + 119903 (119909

119895(119894) minus 119909

119896(119894)) (3)



for (119895 = 1 to SN)

for (119894 = 1 to119863)

1199091015840(119894) = 119909

119895(119894) + 119903 (119909

119895(119894) minus 119909

119896(119894))



119894)

If (119891(1199091015840) gt= 119891(119909119894))

119909119894= 1199091015840

119891(119909119894) = 119891(119909

1015840)

end if

end for








CI = 1199011[1 minus (1198901

119879119904

)

2

] + 1199012[1 minus (1198902

119868119904

)

2

]

+ 1199013[1 minus (1198903

119860119904

)

2

]

(4)


3


1+ 1199012+ 1199013= 1 119890

1 1198902and



for (119894 = 1 to SN)

119903 sim (0 1)


119904 prob = 119904 prob + 119901119895

119895 = 119895 + 1

end whilefor (119896 = 1 to119863)

1199091015840(119895) = 119909

119895(119896) + 119903(119909

119895(119896) minus 119909

119895(119899))

119899 isin (1 2 3 SN)


119895)

If

(119891(1199091015840) gt= 119891(119909119895)) put

119909119895= 1199091015840

119895

119891(119909119895) = 119891(119909

1015840

119895)

end if

end for


For (119894 = 1 to SN)

If (119878(119894) == Limit)


end if

end for







1 1198902 and 119890

3



Rules

Inferencesystem



Inputs Outputs







If (1198901= = NH) then RP1 = R1NH

If (1198901= = NM) then RP1 = R1NM

If (1198901= = NL) then RP1 = R1NL

If (1198901= = ZE) then RP1 = R1ZE

If (1198901= = PL) then RP1 = R1PL

If (1198901= = PM) then RP1 = R1PM

If (1198901= = PH) then RP1 = R1PH





If (1198902= = HS) then RP2 = R2HS

If (1198902= = MS) then RP2 = R2MS

If (1198902= = BS) then RP2 = R2BS

If (1198902= = OK) then RP2 = R2OK

If (1198902= = SH) then RP2 = R2SH

If (1198902= = H) then RP2 = R2H






If (1198903= = OK) then RP3 = R3OK

If (1198903= = SH) then RP3 = R3SH

If (1198903= = LH) then RP3 = R3LH





TRP = RP1 + RP2 + RP3 (5)



0

20

40

60

80

100

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Tem

pera

ture

(F)

Time (s)










0

200

400

600

800

10001 10 19 28 37 46 55 64 73 82 91 100

109

118

127

136

145

154

163

172

181

190

199

208

217

226

235

244

Illum

inat

ion

(Lux

)

Time (s)




0

200

400

600

800

1000

1200

1 11 21 31 41 51 61 71 81 91 101

111

121

131

141

151

161

171

181

191

201

211

221

231

241

Time (s)


CO2

conc

entr

atio

n (p

pm)






09

092

094

096

098

1

102

1 16 31 46 61 76 91 106

121

136

151

166

181

196

211

226

241

Com

fort

inde

x va

lue

Time (s)




0

5

10

15

20

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)











0

5

10

15

20

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)


02468

1012

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)



5 Conclusions


0

10

20

30

40

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)


Pow

er co

nsum

ptio

n(k

Wh)



1

08

06

04

02

0

Deg

ree o

f mem

bers

hip



e1




1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


R1NH R1NM

RP1



Temperature = 17

1

2

3

4

5

6

7

minus28 28

Consumption = 121

minus20 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


HS MS BS OK SH H

e2


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


RP2




Illumination = 200

1

2

3

4

5

6

minus175 275

Consumption = 15

minus15 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


LOW OK SH LH HIGH

e3


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip

0 2 4 6 8 10 12

RP3



Error = 200

1

2

3

4

5

minus300 300

Consumption = 973

0 13



Competing Interests


Acknowledgments


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Environment


User


ABC optimizer




Required power

Coordinator

Power sources



Comfort index









119909119895(119894) = LB

119894+ (UB

119894minus LB119894) times 119903 (1)





1199091015840(119894) = 119909

119895(119894) + 119903 (119909

119895(119894) minus 119909

119896(119894)) (3)



for (119895 = 1 to SN)

for (119894 = 1 to119863)

1199091015840(119894) = 119909

119895(119894) + 119903 (119909

119895(119894) minus 119909

119896(119894))



119894)

If (119891(1199091015840) gt= 119891(119909119894))

119909119894= 1199091015840

119891(119909119894) = 119891(119909

1015840)

end if

end for








CI = 1199011[1 minus (1198901

119879119904

)

2

] + 1199012[1 minus (1198902

119868119904

)

2

]

+ 1199013[1 minus (1198903

119860119904

)

2

]

(4)


3


1+ 1199012+ 1199013= 1 119890

1 1198902and



for (119894 = 1 to SN)

119903 sim (0 1)


119904 prob = 119904 prob + 119901119895

119895 = 119895 + 1

end whilefor (119896 = 1 to119863)

1199091015840(119895) = 119909

119895(119896) + 119903(119909

119895(119896) minus 119909

119895(119899))

119899 isin (1 2 3 SN)


119895)

If

(119891(1199091015840) gt= 119891(119909119895)) put

119909119895= 1199091015840

119895

119891(119909119895) = 119891(119909

1015840

119895)

end if

end for


For (119894 = 1 to SN)

If (119878(119894) == Limit)


end if

end for







1 1198902 and 119890

3



Rules

Inferencesystem



Inputs Outputs







If (1198901= = NH) then RP1 = R1NH

If (1198901= = NM) then RP1 = R1NM

If (1198901= = NL) then RP1 = R1NL

If (1198901= = ZE) then RP1 = R1ZE

If (1198901= = PL) then RP1 = R1PL

If (1198901= = PM) then RP1 = R1PM

If (1198901= = PH) then RP1 = R1PH





If (1198902= = HS) then RP2 = R2HS

If (1198902= = MS) then RP2 = R2MS

If (1198902= = BS) then RP2 = R2BS

If (1198902= = OK) then RP2 = R2OK

If (1198902= = SH) then RP2 = R2SH

If (1198902= = H) then RP2 = R2H






If (1198903= = OK) then RP3 = R3OK

If (1198903= = SH) then RP3 = R3SH

If (1198903= = LH) then RP3 = R3LH





TRP = RP1 + RP2 + RP3 (5)



0

20

40

60

80

100

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Tem

pera

ture

(F)

Time (s)










0

200

400

600

800

10001 10 19 28 37 46 55 64 73 82 91 100

109

118

127

136

145

154

163

172

181

190

199

208

217

226

235

244

Illum

inat

ion

(Lux

)

Time (s)




0

200

400

600

800

1000

1200

1 11 21 31 41 51 61 71 81 91 101

111

121

131

141

151

161

171

181

191

201

211

221

231

241

Time (s)


CO2

conc

entr

atio

n (p

pm)






09

092

094

096

098

1

102

1 16 31 46 61 76 91 106

121

136

151

166

181

196

211

226

241

Com

fort

inde

x va

lue

Time (s)




0

5

10

15

20

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)











0

5

10

15

20

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)


02468

1012

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)



5 Conclusions


0

10

20

30

40

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)


Pow

er co

nsum

ptio

n(k

Wh)



1

08

06

04

02

0

Deg

ree o

f mem

bers

hip



e1




1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


R1NH R1NM

RP1



Temperature = 17

1

2

3

4

5

6

7

minus28 28

Consumption = 121

minus20 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


HS MS BS OK SH H

e2


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


RP2




Illumination = 200

1

2

3

4

5

6

minus175 275

Consumption = 15

minus15 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


LOW OK SH LH HIGH

e3


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip

0 2 4 6 8 10 12

RP3



Error = 200

1

2

3

4

5

minus300 300

Consumption = 973

0 13



Competing Interests


Acknowledgments


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










for (119895 = 1 to SN)

for (119894 = 1 to119863)

1199091015840(119894) = 119909

119895(119894) + 119903 (119909

119895(119894) minus 119909

119896(119894))



119894)

If (119891(1199091015840) gt= 119891(119909119894))

119909119894= 1199091015840

119891(119909119894) = 119891(119909

1015840)

end if

end for








CI = 1199011[1 minus (1198901

119879119904

)

2

] + 1199012[1 minus (1198902

119868119904

)

2

]

+ 1199013[1 minus (1198903

119860119904

)

2

]

(4)


3


1+ 1199012+ 1199013= 1 119890

1 1198902and



for (119894 = 1 to SN)

119903 sim (0 1)


119904 prob = 119904 prob + 119901119895

119895 = 119895 + 1

end whilefor (119896 = 1 to119863)

1199091015840(119895) = 119909

119895(119896) + 119903(119909

119895(119896) minus 119909

119895(119899))

119899 isin (1 2 3 SN)


119895)

If

(119891(1199091015840) gt= 119891(119909119895)) put

119909119895= 1199091015840

119895

119891(119909119895) = 119891(119909

1015840

119895)

end if

end for


For (119894 = 1 to SN)

If (119878(119894) == Limit)


end if

end for







1 1198902 and 119890

3



Rules

Inferencesystem



Inputs Outputs







If (1198901= = NH) then RP1 = R1NH

If (1198901= = NM) then RP1 = R1NM

If (1198901= = NL) then RP1 = R1NL

If (1198901= = ZE) then RP1 = R1ZE

If (1198901= = PL) then RP1 = R1PL

If (1198901= = PM) then RP1 = R1PM

If (1198901= = PH) then RP1 = R1PH





If (1198902= = HS) then RP2 = R2HS

If (1198902= = MS) then RP2 = R2MS

If (1198902= = BS) then RP2 = R2BS

If (1198902= = OK) then RP2 = R2OK

If (1198902= = SH) then RP2 = R2SH

If (1198902= = H) then RP2 = R2H






If (1198903= = OK) then RP3 = R3OK

If (1198903= = SH) then RP3 = R3SH

If (1198903= = LH) then RP3 = R3LH





TRP = RP1 + RP2 + RP3 (5)



0

20

40

60

80

100

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Tem

pera

ture

(F)

Time (s)










0

200

400

600

800

10001 10 19 28 37 46 55 64 73 82 91 100

109

118

127

136

145

154

163

172

181

190

199

208

217

226

235

244

Illum

inat

ion

(Lux

)

Time (s)




0

200

400

600

800

1000

1200

1 11 21 31 41 51 61 71 81 91 101

111

121

131

141

151

161

171

181

191

201

211

221

231

241

Time (s)


CO2

conc

entr

atio

n (p

pm)






09

092

094

096

098

1

102

1 16 31 46 61 76 91 106

121

136

151

166

181

196

211

226

241

Com

fort

inde

x va

lue

Time (s)




0

5

10

15

20

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)











0

5

10

15

20

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)


02468

1012

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)



5 Conclusions


0

10

20

30

40

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)


Pow

er co

nsum

ptio

n(k

Wh)



1

08

06

04

02

0

Deg

ree o

f mem

bers

hip



e1




1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


R1NH R1NM

RP1



Temperature = 17

1

2

3

4

5

6

7

minus28 28

Consumption = 121

minus20 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


HS MS BS OK SH H

e2


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


RP2




Illumination = 200

1

2

3

4

5

6

minus175 275

Consumption = 15

minus15 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


LOW OK SH LH HIGH

e3


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip

0 2 4 6 8 10 12

RP3



Error = 200

1

2

3

4

5

minus300 300

Consumption = 973

0 13



Competing Interests


Acknowledgments


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Rules

Inferencesystem



Inputs Outputs







If (1198901= = NH) then RP1 = R1NH

If (1198901= = NM) then RP1 = R1NM

If (1198901= = NL) then RP1 = R1NL

If (1198901= = ZE) then RP1 = R1ZE

If (1198901= = PL) then RP1 = R1PL

If (1198901= = PM) then RP1 = R1PM

If (1198901= = PH) then RP1 = R1PH





If (1198902= = HS) then RP2 = R2HS

If (1198902= = MS) then RP2 = R2MS

If (1198902= = BS) then RP2 = R2BS

If (1198902= = OK) then RP2 = R2OK

If (1198902= = SH) then RP2 = R2SH

If (1198902= = H) then RP2 = R2H






If (1198903= = OK) then RP3 = R3OK

If (1198903= = SH) then RP3 = R3SH

If (1198903= = LH) then RP3 = R3LH





TRP = RP1 + RP2 + RP3 (5)



0

20

40

60

80

100

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Tem

pera

ture

(F)

Time (s)










0

200

400

600

800

10001 10 19 28 37 46 55 64 73 82 91 100

109

118

127

136

145

154

163

172

181

190

199

208

217

226

235

244

Illum

inat

ion

(Lux

)

Time (s)




0

200

400

600

800

1000

1200

1 11 21 31 41 51 61 71 81 91 101

111

121

131

141

151

161

171

181

191

201

211

221

231

241

Time (s)


CO2

conc

entr

atio

n (p

pm)






09

092

094

096

098

1

102

1 16 31 46 61 76 91 106

121

136

151

166

181

196

211

226

241

Com

fort

inde

x va

lue

Time (s)




0

5

10

15

20

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)











0

5

10

15

20

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)


02468

1012

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)



5 Conclusions


0

10

20

30

40

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)


Pow

er co

nsum

ptio

n(k

Wh)



1

08

06

04

02

0

Deg

ree o

f mem

bers

hip



e1




1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


R1NH R1NM

RP1



Temperature = 17

1

2

3

4

5

6

7

minus28 28

Consumption = 121

minus20 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


HS MS BS OK SH H

e2


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


RP2




Illumination = 200

1

2

3

4

5

6

minus175 275

Consumption = 15

minus15 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


LOW OK SH LH HIGH

e3


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip

0 2 4 6 8 10 12

RP3



Error = 200

1

2

3

4

5

minus300 300

Consumption = 973

0 13



Competing Interests


Acknowledgments


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












If (1198903= = OK) then RP3 = R3OK

If (1198903= = SH) then RP3 = R3SH

If (1198903= = LH) then RP3 = R3LH





TRP = RP1 + RP2 + RP3 (5)



0

20

40

60

80

100

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Tem

pera

ture

(F)

Time (s)










0

200

400

600

800

10001 10 19 28 37 46 55 64 73 82 91 100

109

118

127

136

145

154

163

172

181

190

199

208

217

226

235

244

Illum

inat

ion

(Lux

)

Time (s)




0

200

400

600

800

1000

1200

1 11 21 31 41 51 61 71 81 91 101

111

121

131

141

151

161

171

181

191

201

211

221

231

241

Time (s)


CO2

conc

entr

atio

n (p

pm)






09

092

094

096

098

1

102

1 16 31 46 61 76 91 106

121

136

151

166

181

196

211

226

241

Com

fort

inde

x va

lue

Time (s)




0

5

10

15

20

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)











0

5

10

15

20

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)


02468

1012

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)



5 Conclusions


0

10

20

30

40

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)


Pow

er co

nsum

ptio

n(k

Wh)



1

08

06

04

02

0

Deg

ree o

f mem

bers

hip



e1




1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


R1NH R1NM

RP1



Temperature = 17

1

2

3

4

5

6

7

minus28 28

Consumption = 121

minus20 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


HS MS BS OK SH H

e2


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


RP2




Illumination = 200

1

2

3

4

5

6

minus175 275

Consumption = 15

minus15 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


LOW OK SH LH HIGH

e3


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip

0 2 4 6 8 10 12

RP3



Error = 200

1

2

3

4

5

minus300 300

Consumption = 973

0 13



Competing Interests


Acknowledgments


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

200

400

600

800

10001 10 19 28 37 46 55 64 73 82 91 100

109

118

127

136

145

154

163

172

181

190

199

208

217

226

235

244

Illum

inat

ion

(Lux

)

Time (s)




0

200

400

600

800

1000

1200

1 11 21 31 41 51 61 71 81 91 101

111

121

131

141

151

161

171

181

191

201

211

221

231

241

Time (s)


CO2

conc

entr

atio

n (p

pm)






09

092

094

096

098

1

102

1 16 31 46 61 76 91 106

121

136

151

166

181

196

211

226

241

Com

fort

inde

x va

lue

Time (s)




0

5

10

15

20

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)











0

5

10

15

20

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)


02468

1012

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)



5 Conclusions


0

10

20

30

40

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)


Pow

er co

nsum

ptio

n(k

Wh)



1

08

06

04

02

0

Deg

ree o

f mem

bers

hip



e1




1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


R1NH R1NM

RP1



Temperature = 17

1

2

3

4

5

6

7

minus28 28

Consumption = 121

minus20 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


HS MS BS OK SH H

e2


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


RP2




Illumination = 200

1

2

3

4

5

6

minus175 275

Consumption = 15

minus15 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


LOW OK SH LH HIGH

e3


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip

0 2 4 6 8 10 12

RP3



Error = 200

1

2

3

4

5

minus300 300

Consumption = 973

0 13



Competing Interests


Acknowledgments


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















0

5

10

15

20

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)


02468

1012

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)



Pow

er co

nsum

ptio

n(k

Wh)



5 Conclusions


0

10

20

30

40

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

243

Time (s)


Pow

er co

nsum

ptio

n(k

Wh)



1

08

06

04

02

0

Deg

ree o

f mem

bers

hip



e1




1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


R1NH R1NM

RP1



Temperature = 17

1

2

3

4

5

6

7

minus28 28

Consumption = 121

minus20 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


HS MS BS OK SH H

e2


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


RP2




Illumination = 200

1

2

3

4

5

6

minus175 275

Consumption = 15

minus15 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


LOW OK SH LH HIGH

e3


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip

0 2 4 6 8 10 12

RP3



Error = 200

1

2

3

4

5

minus300 300

Consumption = 973

0 13



Competing Interests


Acknowledgments


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


R1NH R1NM

RP1



Temperature = 17

1

2

3

4

5

6

7

minus28 28

Consumption = 121

minus20 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


HS MS BS OK SH H

e2


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


RP2




Illumination = 200

1

2

3

4

5

6

minus175 275

Consumption = 15

minus15 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


LOW OK SH LH HIGH

e3


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip

0 2 4 6 8 10 12

RP3



Error = 200

1

2

3

4

5

minus300 300

Consumption = 973

0 13



Competing Interests


Acknowledgments


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Illumination = 200

1

2

3

4

5

6

minus175 275

Consumption = 15

minus15 20


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip


LOW OK SH LH HIGH

e3


1

08

06

04

02

0

Deg

ree o

f mem

bers

hip

0 2 4 6 8 10 12

RP3



Error = 200

1

2

3

4

5

minus300 300

Consumption = 973

0 13



Competing Interests


Acknowledgments


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Competing Interests


Acknowledgments


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article an efficient approach for energy

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