a multi-objective evolutionary optimization of fuzzy controller for energy conservation in air...

A multi-objective evolutionary optimization of fuzzycontroller for energy conservation in airconditioning systemsSajid Hussain1 and Hossam A. Gabbar1,2,*,†

1Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe St. North, Oshawa, Ontario,Canada, L1H7K42Faculty of Energy Systems and Nuclear Science, University of Ontario Institute of Technology, 2000 Simcoe St. North, Oshawa,Ontario, Canada, L1H7K4

SUMMARY

This paper presents the use of evolutionary optimization approach to design and tune smart fuzzy controllers for heating,ventilation, and air conditioning systems or HVAC. The objective is to optimize energy consumption while accounting for usercomfort requirements. The problem of energy conservation in air conditioning systems becomes a multi-objective optimizationconstrained problem, which enlarges the solution search space. To solve this problem, a multi-objective evolutionaryoptimization technique based on genetic algorithm (GA) is proposed. A physical experimental setup is constructed for datacollection and formulation of mathematical model. A fuzzy controller is initially designed through expert knowledge, andGA is then used to tune the rules and membership functions of the fuzzy controller in order to optimize multiple objectives.Simulations and real experiments are compared to determine the effectiveness of the proposed strategy. As compared to thecontroller present in the real experimental air conditioner, approximately 15% energy is successfully saved with no increasein average individual dissatisfaction or discomfort index. Also, a decrease in peak individual dissatisfaction or discomfort indexfrom 91% to 62% is observed. Copyright © 2013 John Wiley & Sons, Ltd.

KEY WORDS

energy conservation; fuzzy logic controllers; genetic algorithms; HVAC

Correspondence

*Hossam A. Gabbar, Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe St. North,Oshawa, Ontario, Canada L1H7K4.

†E-mail: [email protected]

Received 17 November 2012; Revised 29 April 2013; Accepted 18 May 2013

1. INTRODUCTION

More than 40%of the energy used inmost cities is used to heator cool buildings [1]. Technologically, it is estimated that withcareful consideration and implementation of building energymanagement systems (BEMS), energy consumption in build-ing sector can be saved up to 20% [2]. BEMS are generallyused to manage building energy in three areas. Effective con-trol strategy for energy-related resources inside a building likeheating, ventilation, and air conditioning (HVAC), lightening,electrical equipment, lifts, and escalators, improvement inefficiency for energy-related resources [3,4], and efficiencyof construction material used in buildings [1,5]. Efficientcontrol of energy-related resources in a building is a complexand challenging task. Therefore, use of appropriate controlstrategies is required. Different control strategies are usedin the past, starting from classical controllers [6] to

Proportional-Integrate-Derivative (PID) controllers [7], andpredictive controllers [8]. Adaptive controllers [9,10] provedto be very successful in building energy conservation.Adaptive controllers self generate and adapt to the changingclimate conditions inside buildings. When combined withfuzzy logic or rule-based reasoning, adaptive fuzzycontrollers achieve superior performance as compared toclassical or conventional PID controllers [11,12]. In designingadaptive controller, various criteria like thermal regulation, en-ergy consumption, and comfort management are considered.In many cases, only thermal regulation and comfortmanagement are given importance [2]. Fuzzy logic controller(FLC) is a very robust tool, which incorporates expertknowledge to implement the control strategies.

A fuzzy controller defines a non-linear mapping fromsystems state space to control space. The output of a fuzzycontroller is a non-linear control fuzzy surface that reflects

INTERNATIONAL JOURNAL OF ENERGY RESEARCHInt. J. Energy Res. 2014; 38:847–859

Published online 7 August 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.3069

Copyright © 2013 John Wiley & Sons, Ltd. 847

an expert’s knowledge. Experts often use rules of thumb todesign FLCs. The resultant FLCs are not always compatiblewith the system’s dynamics, energy performance measures,and user expectations. Hence, the need arises to optimizedifferent objectives at the same time and tune the FLCs. Theaim of tuning is to find a better set of required parameters bychanging the fuzzy rules and membership functions (MFs).

Recently, multi-objective evolutionary algorithms(MOEA) are given much attention for multi-objectiveoptimization in energy management systems [13]. An FLCinvolving seven variables is optimized in [14] to decreaseenergy consumption and maintain a temperature set point. In[2,15], a very comprehensive study is carried out, and geneticalgorithm (GA) is used to optimize thermal comfort, indoor airquality, energy consumption, and system’s stability. In [16], acombination of fuzzy logic and GA is used to optimizepredicted mean vote (PMV) index for thermal comfort.Combination of FLCs with evolutionary optimization tech-niques like GA is successfully used in different scenarios ofenvironment control research. In [17], a genetic fuzzy control-ler approach is used to develop an adaptive FLC for a coolingcoil. Another fuzzy controller optimized by GA is used forcontrolling green house micro climate in [18].

The purpose of this research is to develop distributed FLCsfor a large energy optimization and conservation system beingdeveloped in the Energy Safety and Controls Lab (ESCL) atthe University of Ontario Institute of Technology (UOIT) asshown in Figure 1. The scope of this research paper is todevelop and tune an FLC through multi-objective GAoptimization. The rest of the paper is arranged in the followingway. In next sub-sections, the basics of FLC, GA, andGA–FLC combination is discussed. The methodology withexperimental setup and mathematical model formulation isexplained in section 2. Section 3 formulates a multi-objectivecost function to be optimized by GA–FLC combination.Simulation and discussion are performed in section 4 followedby conclusion in section 5.

1.1. Fuzzy logic control

Fuzzy logic was first developed by L.A. Zadeh in 1965 forrepresenting some types of approximate knowledge that can-not be represented by conventional and crisp methods. Fuzzylogic is an extension of crisp bivalent logic in the sense that itprovides a platform for handling approximate knowledge. Theinformation handled in fuzzy systems need not be completeand precise. It may be general, qualitative, and approximate.Fuzzy logic systems largely depend on human knowledge,and they may face problems of incomplete system description.

In defining fuzzy knowledge base, we use IF-THEN rulesof the following form

Rule Rq : If x1 is Aq1 AND . . .AND xn is Aqn

THEN Class Cq with CFq:

Where Rq is the qth fuzzy rule, x is an n-dimensionalpattern vector x= (x1, x2.... xn), Aqi is an antecedent fuzzy set,

Cq is a consequent class, and CFq is a rule weight. Fuzzycontrol uses the principles of fuzzy logic-based decisionmaking to arrive at the control actions. The decision-makingapproach is typically based on the compositional rule ofinference. An expert knowledge base is constructed in theshape of IF-THEN statements as described above. Themonitored process variables are fuzzified, and control deci-sions are made. The control decisions are defuzzified beforethey are used in physical control actions. Figure 1 shows afuzzy control and optimization arrangements of energy-relatedresources in a building. Optimization takes into accountdifferent constraints and information about the health of theenergy resources. The optimization step tunes the fuzzycontroller accordingly and optimum power strategy is defined.Figure 2 describes fuzzy controller structure with fuzzification,defuzzification, and inference blocks.

1.2. GA

GA is a general purpose derivative free global searchalgorithm. GA uses principles of natural evolution orsurvival of the fittest. Holland first described basicprinciples of GA in 1975 [19]. In GA, the idea is tomaintain and evolve a population of knowledge structures.The evolution takes place through a process of competitionand controlled variations called crossover and mutationoperators. Each structure in the population represents acandidate solution to a particular problem at hand andhas an associated fitness value to determine whichstructure can be used to form a new competitivepopulation. In the evolution process, a subset of relativelygood structures is selected for reproduction, and thatreplaces the relatively bad solutions in the new generatedpopulation. Crossover operator makes use of informationcontained into parents and combines them in a newpopulation in order to increase average quality of thepopulation. Mutation operator randomly changes the newindividuals to help avoid local optima.

Figure 3 shows a flow chart of basic genetic operation.Here, an initial random population of candidate solutions isgenerated in form of chromosomes. Each chromosome isranked according to its fitness value. The fitness value is calcu-lated based on pre-defined objective functions to be optimized.Two individuals based on their fitness values are selected andevolved by performing crossover and mutation operators. Theprocess continues until required criteria are met. GAs can bedesigned to evolve multiple objectives at the same time.Hence, they form basis of multi-objective evolutionarycomputing. The use of GAs in energy-related conservationapplications is very useful because of complex nature of theproblem and large solution search space with multipleobjectives.

1.3. GA–FLC

GAs can be combined with FLC in different ways asfollows. GAs can be used to evolve the fuzzy controllerknowledge base or in other words fuzzy rule matrices

Evolutionary optimization of fuzzy controller for energy conservationS. Hussain and H. A. Gabbar

848 Int. J. Energy Res. 2014; 38:847–859 © 2013 John Wiley & Sons, Ltd.DOI: 10.1002/er

(FRMs) as explained in [17]. The FRM is a matrix ofnumbers that represents the rules that govern thecontroller’s operation and is explained in more detail laterin this paper. The GA method, also explained in moredetail later, generates many possible FRMs. The fitnessvalue is calculated based on multiple objectives for eachFRM. The FRMs that have better FLC performance arefurther modified using GAs to evolve improved FRMs.Thus, with the repeated application of GAs, near-optimalFLCs for the application can be achieved.

Fuzzy MF shapes and positions are also tuned throughGAs as shown in [2,13,15]. In tuning fuzzy MFs, differentshapes (trapezoid, triangular, Gaussian etc.), and positionsare randomly selected and evaluated with their fitnessvalues. The MFs that have better FLC performance are

further modified using GAs to evolve improved MFs. Inboth the cases above, GAs main purpose is to design abetter improved fuzzy controller with highest fitness valuepossible. Figure 4 shows the concept of using GAs withFLCs.

2. METHODOLOGY

An experimental setup with a small room, air condition,temperature sensors, and data acquisition hardware withcomputer is constructed in the ESCL at UOIT. Theproposed process of energy conservation system isdepicted in Figure 5.

2.1. Room response modelling

We consider the constructed room as a single energystorage element and use a relatively simple first-ordersystem to model the room temperature response with thefollowing differential equation.

_T þ 1RC

T ¼ Pbulb

Cþ Ti

RC⇒ _T þ k1T ¼ k2⇒ _xþ ax

¼ f xð Þ: (1)

Where _T is the rate of change of temperature within thehouse, C is the heat capacity of the material within theroom, R is the thermal resistance of the room, and Pbulb

Figure 2. Fuzzy logic control architecture.

Figure 1. Energy optimization and conservation system.

Evolutionary optimization of fuzzy controller for energy conservation S. Hussain and H. A. Gabbar

849Int. J. Energy Res. 2014; 38:847–859 © 2013 John Wiley & Sons, Ltd.DOI: 10.1002/er

Figure 3. Genetic algorithm flow chart.

Figure 4. GA tuning of fuzzy logic controller.

Figure 5. The proposed process of energy conservation.



is power flow inside the room. The solution to this ordinarydifferential equation is given by

T tð Þ ¼ Ti þ PiR 1� e�t=RC� �

¼ Ti þ ΔT 1� e�t=t� �

: (2)

We use data, recorded from the experimental setup, andsolve non-linear curve-fitting problem in least-squaressense as

minx

F x; xdatað Þ � ydatak k22¼ min

x

Xi

F x; xdataið Þ � ydataið Þ2: (3)

The air condition cooling models are also formulatedthrough data fitting for three fan speed settings of the aircondition. Here, we use Gaussian functions to model thecooling response of the air condition as

g xð Þ ¼ ae� x�bð Þ2=c2 : (4)

Where a, b, and c are the model coefficients to be tuned.Figure 6 plots and compares the experimental andmathematical model response of the air condition coolingand room energy dissipation. In Figure 6(a), air conditioncooling response models are plotted for fan speeds of slow,medium, and fast. When the fan speed is increased, the aircondition cools the room relatively faster and after 256 s of

cooling as shown in Figure 6(a), the temperature differenceamong three fan settings is 1 �F. Figure 6(b) plotsexperimental and simulated room response data when aircondition is run for approximately 34.4min at set pointof 67 �F. Figure 6(b) also plots basic mathematical modelobtained through curve fitting and tuned model obtainedthrough one-dimensional accelerated search as explainedin model tuning section next.

The error between real-time data and model is shown inFigure 6(c). The error has zero mean with standarddeviation of 0.5. The error plot shows how best the modelis fitted with the real experimental data.

2.1.1. Model tuningModel tuning is performed through an accelerated

one-dimensional search. The method we use here isgolden section search, which deals with a unimodalobjective by rapidly narrowing an interval guaranteed tocontain optimum [20]. Figure 7(a) illustrates the idea ofgolden section search, where four carefully spaced pointsare iteratively considered. Leftmost x(lo) is always a lowerbound on the optimal x*, and x(hi) is an upper bound. Thefunction optimum lies between the interval [x(lo),x(hi)].Points x(1) and x(2) are the intermediate points. Eachiteration determines whether the objective is better atx(1) or x(2), if x(1) proves better, the move direction for thenext iteration is left and x(2) becomes x(hi) and if x(2) provesbetter, the more direction for the next iteration is right andx(1) becomes x(lo). The choice of interior points defines theefficiency of the search, whether it is [x(1),x(hi)] or [x(lo),x(2)]

A/C switched OFF at sample 258or 34.4 minutes

(a) (b)

(c)

Figure 6. Data modelling (a) A/C cooling response (different fan speeds) (b) A/C ON–OFF response at set point 67 �F (record time=2 h)(c) Error between real-time data and model.



interval, golden section search proceeds by keeping boththese intervals equal in length. The two middle points ofthe golden section search are spaced according to

x 1ð Þ ¼ x hið Þ � a x hið Þ � x loð Þ� �x 2ð Þ ¼ x loð Þ þ a x hið Þ � x loð Þ� �

:(5)

Where a= 0.618 is the golden ratio and a ¼�1þ ffiffiffi

5p� �

=2 . Although, the golden section searchalgorithm is reliable, it is slow and the narrowing ofthe optimum containing interval requires considerablecomputation before an optimum is defined with considerableefficiency. We combine quadratic fit search with goldensection search for rapid convergence taking full advantage ofthree point pattern fit. We can fit a quadratic function throughthree points and have a unique minimum ormaximum, which-ever, we are seeking for the given objective function f(x). Theunique optimum of quadratic function agreeing with f(x) atthree point pattern (x(lo),x(mid),x(hi)) occurs at

Where f (lo)≜ f(x(lo)), f (mid)≜ f(x(mid)), f (hi)≜ f(x(hi)),s(lo)≜ (x(lo))2, s(mid)≜ (x(mid))2, and s(hi)≜ (x(hi))2. Thealgorithm starts with golden section search andcalculates four points (x(lo),x(1),x(2),x(hi)). It thendetermines the search direction (right or left) and fitsa quadratic function with either (x(lo),x(1),x(2)) or (x(1),x(2),x(hi)). It calculates the quadratic fit x(qu) fromequation (6) and again applies criteria similar to goldensection search to discard one point and so on. Figure 7(b) illustrates the idea of combining golden sectionsearch with parabolic interpolation. The combinationof parabolic interpolation and golden section searchcan speed up the optimal search process by 35–40%as compared to golden section search only [21].Figure 6(b) plots the room temperature responseobtained through tuned model.

2.2. FLC design

An initial FLC is designed using a grid-type fuzzypartitioning of the input space. In grid-type fuzzyportioning approach, the domain interval of each inputis divided into antecedent fuzzy sets with linguisticlabels as shown in Figure 8. The advantage of thisapproach is that fuzzy rule-based systems with highinterpretability can be generated from this type of fuzzypartitions. As discussed in [22], homogeneous fuzzypartitions are more interpretable than adjusted ones.Thus, we use homogeneous fuzzy partitions as shownin Figure 8. Usually, we do not know an appropriatefuzzy partition for each input. In general, each inputmay have a different fuzzy partition for each input asdepicted in Figure 8. In Figure 8, we use ‘Error’ and‘Change in Error’ as two inputs for our FLC. Thefuzzy grid should be divided in such a way that itshould have high resolution in normal operating rangeof the system and low resolution otherwise. The end

points of the MFs for ‘Error’ and ‘Change in Error’are kept open or comparatively large in order to caterfor unseen changes in the system dynamics.

There are two outputs of our fuzzy controller,‘Control Action’ and ‘Fan Speed’. Based on informa-tion presented in Figure 8, FRM is formulated asshown in Figure 9. In Figure 9, control action isdivided into five MFs, ‘NL, NM, ZE, PS, PM’ andfan speed is divided into three MFs, ‘S, M, F’ for slow,medium, and fast, respectively. The initial rule selectionis of the form

IF ‘Error’ is NL AND ‘Change in Error’ is NL, THEN‘Control Action’ is NL ALSO ‘Fan Speed’ is F

IF ‘Error’ is PM AND ‘Change in Error’ is PL, THEN‘Control Action’ is PM ALSO ‘Fan Speed’ is M

x quð Þ ¼ 12

f loð Þ s midð Þ � s hið Þ� �þ f midð Þ s hið Þ � s loð Þ� �þ f hið Þ s loð Þ � s midð Þ� �f loð Þ x midð Þ � x hið Þ½ � þ f midð Þ x hið Þ � x loð Þ½ � þ f hið Þ x loð Þ � x midð Þ½ � : (6)

(a) (b)

Figure 7. (a) Golden section search (b) combined with parabolic interpolation.



2.3. GA design

The tuning of FLCs for air conditioning systemspresents two main restrictions.

• The evaluation is based on multiple objectives likeenergy consumption, occupant’s thermal comfort, andmean square error (MSE). This fact adds complexity tothe search space because we must obtain the besttrade-off among different criteria.

• The controller accuracy is assessed by means of simula-tions which usually take a long time. This causes the runtime of the algorithms to be extremely long.

The first restriction will be solved by using multi-criteria genetic optimization techniques that will allowus to work with fitness functions comprised bycompetitive objectives. In these cases, we could obtainnot only an optimal solution, but a possible solutionset. In order to solve the second restriction, we use realcoded or integer coded GA to reduce the computationalcomplexity of encoding/decoding from/to binarystrings. This will considerably reduce the run time forthe GA search. We also use a steady-state GA, whichinvolves selecting two of the best individuals in thepopulation and combining them to obtain two offspring.This approach improves the convergence and simultaneouslydecreases the number of evaluations. The following geneticoperators are used.

2.3.1. EncodingThe GA used in this study is real coded GA

(RCGA) to decrease the computational complexity andhence, increase the speed. In RCGA, the outputs ofthe fuzzy controller, ‘Control Action’ and ‘Fan Speed’are represented by an integer in the chromosome whileevolving FRM, e.g.Control Action NL= 0, NM=1, ZE= 2, PS = 3 and

PM=4Fan Speed S= 0, M= 1 and F = 2

While evolving MFs, the chromosome contains theoriginal floating point values, e.g.Control Action [�1.5 �1 �0.5 �1 �0.5 0 �0.5 0 0.5

0 0.5 1 0.5 1 1.5]Fan Speed [1 1.5 2 2 2.5 3 3 3.5 4]

2.3.2. SelectionWe use a very simple selection approach called rou-

lette-wheel selection, also named as stochastic samplingwith replacement. The individuals are mapped tocontiguous segments of a line, such that eachindividual’s segment is equal in size to its fitness. Arandom number is generated, and the individual whosesegment spans the random number is selected. Theprocess is repeated until the desired number ofindividuals is obtained (called mating population).

Figure 8. Grid partitioning in fuzzy rule selection.



2.3.3. Arithmetic crossoverReproduction involves creation of new offspring

from the mating of two selected parents or matingpairs. It is thought that the crossover operator is mainlyresponsible for the global search property of the GA.We use an arithmetic crossover operator that defines alinear combination of two chromosomes [23]. Twochromosomes, selected randomly for crossover, CGen

i

and CGenj , may produce two offspring, CGenþ1

i and

CGenþ1j , which is a linear combination of their parents as

CGenþ1i ¼ b:CGen

i þ 1� bð Þ:CGenj

CGenþ1j ¼ b:CGen

j þ 1� bð Þ:CGeni :

(7)

Where CGen and CGen+1 are the individuals from oldand new generations, respectively, and b is a weightingfactor, which governs dominant individual in reproduc-tion process. The value of b ranges from 0 to 1.

2.3.4. Arithmetic mutationThe mutation operator is used to inject new genetic

material into the population, and it is applied to each

new structure individually. A given mutation involvesrandomly altering each gene with a small probability.We generate a random real value which makes a ran-dom change in the kth element selected randomly ofthe chromosome. In arithmetic mutation, we again in-volve two chromosomes but mutate only one accordingto some mutation probability. The two chromosomesCGeni and CGen

j selected for crossover in the previous

section can undergo mutation, and any one of themhas equal probability of selection for mutation. As anexample, if two offspring, CGenþ1

i and CGenþ1j are pro-

duced in crossover operation and kth element ofCGenþ1i is selected for mutation. The mutation will occur

as follows

CGenþ1i ¼ Ci1;Ci2; . . .Ci k�1ð Þ;b:CGenþ1

jk

þ 1� bð Þ:CGenþ1ik ; . . .Ci n�1ð Þ;Cini:

*(8)

2.3.5. ElitismElitism is the process of selecting the better

individuals, or more to the point, selecting individual

Figure 9. Fuzzy system initial expert design.



with a bias towards the better ones. Elitism is importantsince it allows the solutions to get better over time.

2.4. Objective function formulation

The objective function or fitness function used for this study is

minf Obj ¼ ECool þ EFanð Þ:TON þ EFan:TOFF

þ1þ tanh 2 votej j � 3ð Þ2

þ 1n

Xn

To � Tð Þ2 þ . . .

m max2 0;T � To þ ΔTð Þf g þ max2 0; To � ΔTð Þ � Tf g� �:

(9)

Where ECool is energy consumption for the aircondition when cooling is ON, EFan is energyconsumption for the fan in different speeds, TON isON time and TOFF is the OFF time for cooling com-

pressor, 1þ tanh 2 votej j�3ð Þ2 is a degree of individual dissatis-

faction (DID) index as explained in [24]. The proposedindex in [24] matches with well-established predictedpercentage dissatisfied–PMV (PPD–PMV) curve asdescribed in American Society of Heating, Refrigerat-ing, and Air-Conditioning Engineers ANSI/ASHRAE

Standard 55-2004. In equation (9), the vote is

vote ¼þ3 T > To þ 2ΔT

�3 T < To � 2ΔT

1:5T � To

ΔTOtherwise

2664 (10)

Where To is a set point or desired temperature, T iscurrent temperature in the room, and ΔT is individual’stemperature tolerance. The DID curve is shown inFigure 10 [24], where ΔT =� 1.5, and vote is taken asa qualitative fuzzy parameters as �3 (cold), �2 (cool),�1 (slightly cool), 0 (neutral), +1 (slightly warm),+2 (warm), and +3 (hot). According to the set pointtemperature To and individual’s tolerance ΔT, the votevalue is calculated, and the corresponding DID indexis updated. The objective function in equation (9) hassome constraints included. The term m[max 2{0, T�(To +ΔT)} +max 2{0, (To�ΔT)� T}] is a penaltymethod to convert constrained non-linear objectivefunction to unconstrained one. Here, we do not wantto deviate from the limits To�ΔT< T<To +ΔT.Penalty methods drop constraints of non-linearobjective functions and substitute new terms in theobjective functions penalising infeasibility in the form

Figure 10. Degree of individual dissatisfaction curve [24].

Figure 11. Experimental ON–OFF controller vs initial fuzzy logic controller.



maxorminf xð Þ ¼ F xð Þ � mXi

pi xð Þ: (11)

Here, ‘+’ for minimize problems and ‘–’ formaximize problems, m is a positive penalty multiplier,and pi are functions satisfying

pi xð Þ ¼ 0 if x satisfies constraint i

> 0 otherwise

(12)

As an example, if the constraints To�ΔT< T<To+ΔTget satisfied, the m part in equation (9) becomes zero,and if the constraints are not satisfied, a squared penalty

Table I. GA tuning of fuzzy relation matrix (FRM) and membership functions.

ControllerCooling(min) MSE

MDID%

PDID%

MDIDincrease

%

Energysaving%

Fan speed (min) ON Time (34.4min)

S M F

ON–OFF 17.0 2.963 17.6% 91.6% - - - - 34.4Initial FLC 15.6 3.357 20.4% 56.6% 2.8% 8.2% 23.8 1.06 9.46GA_FLC1 14.4 3.165 18.6% 67.2% 1.0% 15.2% 14.5 12.8 6.93GA_FLC2 14.2 3.320 20.5% 76.3% 2.9% 16.4% 20.6 6.93 6.66GA_FLC3 13.2 4.350 34.7% 94.1% 17.1% 22.3% 14.9 8.13 12.8GA_FLC4 12.8 4.490 36.5% 92.7% 18.9% 24.7% 21.0 4.53 9.20GA_FLC5 14.5 3.074 17.5% 61.8% �0.1% 14.7% 27.4 0.80 6.13GA_FLC6 14.6 3.001 16.5% 55.2% �1.1% 14.1% 25.4 2.00 6.80

Population Size = 100, Generations= 2000, Crossover Probability = 0.85, Mutation Rate= 0.01, Mutation Mode=One-point fixed, Re-production Plan= Steady-State Replace Worst, Elitism=ON

Figure 12. GA evolved fuzzy logic controller.



is included in the objective function. This step also makesunfit chromosomes in the population worse so that theycan be replaced or die soon and the population convergesoon.

3. SIMULATIONS ANDDISCUSSIONS

Simulations are performed in LabVIEWW G programmingenvironment. Data collected from the experimental setupas shown in Figure 6(b) is used for fitness calculation.The air condition is in operation for 34.4min. Figure 11zooms out the data in Figure 6(b) only for 34.4min ofoperation and compares it with simulated mathematicalmodel controlled by initially designed FLC in section 2.2.The cooling ON time for classical ON–OFF controlleris 17min in 34.4min, MSE is 2.96, mean DID (MDID)is 17.6%, and peak DID (PDID) is 91.6% as shown inTable I.

On the other hand, cooling ON time for initiallydesigned FLC is 15.6min in 34.4min, MSE is 3.35, MDIDis 20.4%, and PDID is 56.6% as shown in Table I. Thus,FLC controller gives an energy conservation of around8% on the expense of 2.8% increase in MDID and alsodecreases PDID by 35%.

The FLC is now tuned through GA to evolve new FLC inorder to achieve more energy conservation. Both the fuzzyrelation matrix and MFs are evolved through separate GAs.Table I lists different FLCs obtained though different runs ofGAs. As compared to the ON–OFF controller present in thereal experimental air conditioner, approximately 15% energyis successfully saved with no increase in average individualdissatisfaction or discomfort index as in GA_FLC5 case inTable I. Also, a decrease in peak individual dissatisfaction ordiscomfort index from 91% to 62% is achieved in GA_FLC5case. Figure 12 shows an evolved FLC GA_FLC5 fromTable I. The fuzzy relationship matrix (FRM), fuzzy surface,and fuzzyMFs are evolved as compared to that of in Figure 9.Figure 13 compares the experimental ON–OFF controller withinitial FLC and GA evolved FLC. The real experiment was

runwith fan speed of ‘Fast’ for the entire 34.4min. Fan speedsin GA evolved FLCs are changing, and Table I also lists thefan speeds and corresponding run time in minutes for initialFLC and all GA evolved FLCs.

Although, there are other evolutionary techniques likegenetic programming (GP), we use GA because of their natureof dealing with fixed length chromosomes. On the other hand,GP uses variable length trees and is normally used to evolvemathematical model, programs, and equations. We further useRCGA as the efficiency of RCGA is better than classical GA,and it takes less storage space. Since, RCGA do not involveencoding and decoding of binary variables in each iteration, itis inherently faster. RCGA can still pose serious limitationswhile working with complex objective functions. This can beovercome by combining other local optimizers with RCGA.Hence, reducing the solutions search space for the RCGA.

4. CONCLUSION AND FUTUREWORK

In this paper, a multi-objective evolutionary optimizationtechnique based on GAs is used for energy conservation. GAis a general purpose derivative free global search algorithm.GA uses principles of natural evolution or survival of the fittest.Two main restrictions in approaching energy conservationproblems are optimization of multiple objectives and algorithmrun complexity. GA can solve both the problems efficientlyif its parameters are carefully chosen. We used an RCGA tospeed up the operation and avoid unnecessary delays inencoding/decoding to/from binary strings.

In this paper, we tune an FLC through GA and minimizecertain energy-related and comfort-related objectives. Ascompared to the ON–OFF control action of experimental airconditioner, approximately 15% energy is successfully savedwith no increase in average individual dissatisfaction ordiscomfort index. Also, a decrease in peak individualdissatisfaction or discomfort index from 91% to 62% isobserved. The experimental setup constructed in ESCL atUOIT, uses polythene as its walls and polythene has aU-valuemore than 1. The lower theU-value of the wall, the less energy

Figure 13. Experimental ON–OFF controller vs initial FLC vs GA evolved FLC.



is lost, and the better is its insulating characteristics. A wallwith a U-value of 0.3W/m2.K is twice as well insulated as awall with a U-value of 0.6W/m2.K. Thus, polythene materialhas comparatively high U value and energy conservationtechniques may suffer or may conserve limited amount ofenergy while maintaining individual dissatisfaction index withacceptable limits. The future work is to conduct the sameexperiment in a better insulated room with lower U values.

NOMENCLATURE

HVAC ¼ Heating, ventilation, and air conditioningPID ¼ Proportional-Integrate-DerivativeBEMS ¼ Building energy management systemsMOEA ¼ Multi-objective evolutionary algorithmsFLC ¼ Fuzzy logic controllerFRM ¼ Fuzzy rule matricesMF ¼ Membership functionsPMV ¼ Predicted mean voteESCL ¼ Energy Safety and Controls LabUOIT ¼ University of Ontario Institute of

TechnologyGA ¼ Genetic algorithmRCGA ¼ Real coded genetic algorithmDID ¼ Degree of individual dissatisfactionPPD ¼ Predicted percentage dissatisfiedPMV ¼ Predicted mean vote_T ¼ Rate of change of temperature within

the houseC ¼ The heat capacity of the material within

the roomR ¼ The thermal resistance of the roomPbulb ¼ Power flow inside the roomg(x) ¼ Gaussian cooling functionF(x) ¼ Objective function without constraintsf(x), fobj ¼ Objective function with constraints

includeda, b, c ¼ Gaussian model coefficientsx(lo), x(hi) ¼ Lower and upper bounds of the

objective functionx(1), x(2) ¼ Intermediate points of the objective

functionx(mid) ¼ Middle point for parabolic interpolationx(qu) ¼ Quadratic fit optimum pointa= 0.618 ¼ The golden ratioCGeni;j ;CGenþ1

i;j ¼ Current and future chromosomesb ¼ Weighting factorm ¼ Positive penalty multiplierpi ¼ Penalty functionsTo ¼ Set point or desired temperatureT ¼ Current temperature in the roomΔT ¼ Individual’s temperature toleranceECool ¼ Energy consumption of air condition

with cooling ONEFan ¼ Energy consumption of fanTON ¼ Air conditioner ON timeTOFF ¼ Air conditioner OFF time

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