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Energy 36 (2011) 2440e2449

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Energy

journal homepage: www.elsevier .com/locate/energy

Multi-objective optimization of HVAC system with an evolutionarycomputation algorithm

Andrew Kusiak*, Fan Tang, Guanglin XuDepartment of Mechanical and Industrial Engineering, 3131 Seamans Center, The University of Iowa, Iowa City, IA 52242-1527, USA

a r t i c l e i n f o

Article history:Received 24 July 2010Received in revised form15 January 2011Accepted 20 January 2011Available online 26 February 2011

Keywords:Data-driven modelsEvolutionary computation algorithmHVAC system optimizationEnergy savings

* Corresponding author. Tel.: þ1 319 3355934; fax:E-mail address: andrew-kusiak@uiowa.edu (A. Ku

0360-5442/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.energy.2011.01.030

a b s t r a c t

A data-mining approach for the optimization of a HVAC (heating, ventilation, and air conditioning)system is presented. A predictive model of the HVAC system is derived by data-mining algorithms, usinga dataset collected from an experiment conducted at a research facility. To minimize the energy whilemaintaining the corresponding IAQ (indoor air quality) within a user-defined range, a multi-objectiveoptimization model is developed. The solutions of this model are set points of the control system derivedwith an evolutionary computation algorithm. The controllable input variables d supply air temperatureand supply air duct static pressure set points d are generated to reduce the energy use. The resultsproduced by the evolutionary computation algorithm show that the control strategy saves energy byoptimizing operations of an HVAC system.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Reducing the energy consumption of HVAC (heating, ventilatingand air conditioning) systems is essential, as it constitutes over 50%of the building energy consumed in the US [1]. The operation ofHVAC system is a critical activity in terms of optimizing the controlsettings to reduce the energy consumption, improving the systemefficiency, and preserving the thermal comfort for the occupants.The performance of the existing HVAC system can be largelyimproved by adjusting the control set points to maximize the overallsystem capacity and efficiency.

This has intensified the research inmodeling and optimization ofenergy use by HVAC systems. Analytical approaches [2] and simu-lation-basedmethods [3]were studied tomodel thermal behavior ofbuildings. Different control strategies, including experimentaldetermination and intelligent control were applied [4,5]. Zheng andZaheer-Uddin [6] formulated the thermal process in a VAV (variableair volume) box with constraints on zone humidity. This provideddaily operating strategies achieving optimal outdoor air-flow ratesand energy savings. Wang and Jin [7] proposed a control strategybased on a genetic algorithm to search for the optimal settings ofmultiple variable processes. Differing from the data-driven models,the optimization algorithmwas applied on the incremental models,

þ1 319 3355669.siak).

All rights reserved.

with self-tuning ensuring the accuracy of the models. Fong et al. [8]discussed energy reduction by using an evolutionary programmingapproach to suggest optimal settings in response to the dynamiccooling loads and changing weather conditions. Ke and Mumma [9]studied the impact of tuning the supply air temperature set point ina VAV on energy consumption. Based on the steady-state models,Nassif et al. [10,11] applied evolutionary algorithms to one- and two-objective optimization of an HVAC system, and the supervisorycontrol strategies resulted in energy savings. Mossolly et al. [12]examined three control strategies developed by a genetic algo-rithm. Significant energy saving were achieved by varying systemparameters. Kusiak and Li [13] applied an evolutionary strategyalgorithm to solve a bi-objective optimization model to minimizethe cooling output while maintaining the corresponding thermalproperties.

An HVAC system is a complex, nonlinear, discrete system con-taining numerous variables and constraints. Therefore, themodeling and optimization of an HVAC system is a challenge fortraditional mathematical models [14] and simulation approaches[15]. In this study, several data-mining algorithms are applied tobuild the predictive models. A multi-objective evolutionarycomputation algorithm is proposed for generating optimal controlstrategies of an existing HVAC system. Extensive test runs havebeen performed to determine the accuracy of the models. Theoptimized set points are used to minimize the energy consumptionby maximizing the HVAC system efficiency. Different controlstrategies are given by weighting the objective functions to satisfy

Fig. 2. The schematic diagram of a single-room VAV box.

A. Kusiak et al. / Energy 36 (2011) 2440e2449 2441

the preference of management operations. The energy use requiredfor actual operations, along with the predictive results obtainedfrom the trained and validated models, is compared to the oneattained through the optimization controller set points. Theresulting energy savings are presented.

2. HVAC system structure and description

The HVAC system being investigated is operated by the ERS(Energy Resource Station) in Ankeny, Iowa. It consists of twoindependent AHUs (air handling units) with the same zone loadsand outside weather conditions. Each AHU serving four differentthermal zones is set as a test area. Fig. 1 provides a schematicdiagram of the existing AHU. For each thermal zone, a VAV box isconnected to the AHU to maintain the comfort temperature of thethermal zone. The structure of the VAV box is shown in Fig. 2.

The experiment conducted in ERS was designed to investigatethe impacts of AHU set points on the total energy consumption,since the HVAC system consumes a majority of the energy ina particular office building. Two set points, namely, AHU supply airtemperature set point and static pressure set point, were adjustedfor both air handling units, AHU-A and AHU-B. The supply airtemperature set point varied from 52 �F (11.11 �C) to 63 �F (17.22 �C)with 1 �F (0.56 �C) increments. The supply air static pressure variedfrom 1.2 WG (0.3 kPa) to 1.8 WG (0.45 kPa) with 0.2 WG (0.05 kPa)increments. To simulate the impact of people and the lighting in thethermal zones, the internal load was divided into four stagesreflecting the different thermal states at different time. The purposeof this experiment was to find the optimal set points minimizing theenergy consumption while maintaining an acceptable level of IAQ.

The total energy consumed by the HVAC system includes twoparts: the AHU and the VAV box. For the energy consumed in theAHU, three major categories, namely heat energy, fan energy, andpump energy, account for the total energy consumption. Since allthree categories come from electricity, they can be calibrated by themeters originally installed in the system.

In the VAV box, the reheat load accounts for the maximumconsumed energy. The VAV box supplies the conditioned air fora specific thermal zone tomeet the comfort temperature of the zoneenvelope. By tuning the valve position and the dampers in the VAVbox, the hot water flows through the coils adjusting to the actualrequirements of the zone comfort. The reheat load is computed fromequation (1) [16].

Exhaustair

Outsideair

Damper

Damper

Damper

Returnair

Supplyair

Supplywater

Returnwater

Supplywater

Returnwater

Valve Valve

Returnfan

Supplyfan

Mixedair

Fig. 1. The schematic diagram of the AHU system.

QReheat ¼ cm�TVAVEAT

� TVAVDAT

�(1)

where c is the heat capacity of the hot water,m is themass flow rateof the hot water, and TVAV EAT and TVAV DAT represent the enteringand leaving water temperatures of the hydronic reheat coil,respectively.

The total energy consumed by the system is expressed inequation (2).

ETotal ¼ EHeat þ EFan þ EPump þ QReheat (2)

where EHeat is the energy consumed by the heat coil, EFan is theenergy consumed by the fan, EPump represents for the energy use ofwater pump, and QReheat is the energy consumed during the reheatprocess in the VAV box.

The inherent nonlinearity and complexity of a typical HVACsystem is difficult to accurately represent by a mathematical ora physics-based model. However, it can be easily captured by theempirical models developed from the process data. The data-drivenmodels often outperform the traditional models of dynamicprocesses and prediction of performance metrics [17e19]. In thisstudy, different data-mining algorithms are applied to derive thetemporal process models.

To minimize the total energy ETotal, the function yEnergyðtÞ ¼f ðx1; x2Þ should be established between the output ETotal and theinput variables of the HVAC system. The function f(�) represents theAHU process, x1 is a vector ofm controllable variables, x2 is a vectorof n uncontrollable variables, and y is the output variable. Bothcontrollable and uncontrollable variables are used to represent theunderlying dynamic process. Tomaintain the desired IAQ level, bothroom humidity and room comfort temperature are considered.

Table 2Five different algorithms of the wrapper evaluator.

A. Kusiak et al. / Energy 36 (2011) 2440e24492442

Let yEnergyðtÞ ¼ f ðx1; x2Þ be an objective function reflecting theenergy consumption to be optimized with an evolutionarycomputation algorithm. The same parameters are used formodeling the indoor room temperature y2ðtÞ ¼ f ðx1; x2Þ andhumidity y3ðtÞ ¼ f ðx1; x2Þ, representing the IAQ at an acceptablelevel. The global optimal settings are achieved by minimizing theenergy objective yEnergy while ensuring y2(t) and y3(t) vary withintheir constraint range. The optimization model proposed in thisresearch is presented next.

Min�yEnergyðtÞ

�subject to:y2ðtÞ ¼ f ðx1; x2Þy3ðtÞ ¼ f ðx1; x2Þ

x1˛R1yj˛Rj j ¼ 2;3

(3)

An evolutionary computation algorithm has been modified tosearch for the optimal control settings of the HVAC system. The twocontrollable variables, the AHU supply air temperature and thesupply air static pressure, are considered to vary in a restricted rangemeeting the requirements of HVAC system. The room temperatureand humidity are treated as constraints with their values changingin a certain range, so as not to sacrifice the environmental comfortwhile the output is minimized to reduce the energy consumption.

3. HVAC system modeling

The model proposed in this study has been tested on the datacollected from February 4 to 15, 2010 at ERS. More than 300 vari-ables have been captured reflecting the different characteristics ofthe HVAC system. The frequency of the original dataset is 1 min. Toreduce the error produced by time delay and system error, theoriginal 1 min data has been aggregated to 1 h interval data bycalculating the mean value. In total, there are 576 observations (2variables, twelve days of 1 h interval data) recorded in this dataset.Because of the existence of system and sensor errors, someabnormal data exist and will affect the accuracy of the experiment.After the pre-processing of the whole data, the dataset with 500observations was randomly sampled and roughly divided intoa training set (85% of dataset) and a testing set (15% of dataset). Thedataset description is presented in Table 1.

3.1. Parameter selection and data dimensionality reduction

Some of the parameters collected are irrelevant or redundant inthe modeling process. Therefore, parameter selection is essentialbefore building the predictive model. The presence of irrelevant orredundant parameters in data mining may mask primary patterns.Redundant parameters also duplicate much or all of the informa-tion contained in one or more other parameters, making themodeling task much more difficult than it should be. Eliminatingparameters that are less important or related may improve theaccuracy, scalability, and comprehensibility of the resulting modelsand decrease the dimensionality which may greatly reduce thecomplexity of a model [20].

For example, the mixed air temperature was important in thisexperiment for prediction, as it directly reflected how much energy

Table 1Data description.

Dataset Description No. of instances

1 Model training; A random sample of 85% of the data 4272 Model test; The remaining 15% of the data 73

should be consumed to reheat the air up to the comfort temperature.However, it had almost the same distribution of the supply airtemperature, and thus it could be discarded as duplicate information.

Wrapper algorithms [21,22] that use induction learning as eval-uation functions were applied to select the most importantparameters. A wrapper algorithm searches the space of all thepossible parameters and evaluates each subset of parameters bybuilding amodel on each subset. The subset of parameters providinghighest prediction accuracy is selected. Considering high computa-tional cost, three widely used search methods, namely geneticalgorithm, greedy, and linear forward, were used in the wrapperapproach. Four different classifiers, namely linear regression, paceregression, SVM (support vector machine) regression, and MLP(multi-layer perceptron), were also used.

Since a single wrapper algorithmmight dominate the features insome aspects, a vote method that is more robust to select theappropriate parameters than a single method, was applied tobalance the selection of parameters by combining five differentwrapper evaluation functions (Table 2) with 10-fold cross-valida-tion. For each wrapper evaluator, the number of each candidateselected within the 10-fold iterative cross-validation was summedup. Then the results of the five different wrapper evaluators wereaggregated to determine the importance of each parameter bycounting the total number of times selected.

The parameter getting the more votes indicates the largerimpact on the output of the HVAC system. The results of the fivedifferent combinations of wrapper evaluators are presented inTable 3.

Based on both domain knowledge and the results of the wrapperalgorithm, the top 12 variables were selected for the potentialcandidates to construct the energy consumption model. The corre-lation coefficient [23] matrix was then applied to the selectedparameters to reduce the linearity relationships among these vari-ables, since some parameters may contain similar information andproduce the same impact on the outputs. The results of the corre-lation coefficient are presented in Table 4.

From the matrix shown above, if we set the value of the linearrelationship as 0.8, the parameter MA-Temp has a highly linearrelationship with SA set point, and SA-Temp and OA-Temp are alsohighly correlated. Therefore, SA set point and OA-Temp are selectedto represent the characteristic of the two parameters, respectively.Ten significant parameters have been ultimately selected as inputsof the model of the HVAC system including both controllablevariables, i.e., the supply air temperature and supply air duct staticpressure set points, and uncontrollable variables such as internalload, supply air humidity and all the weather patterns.

Table 5 lists all the final inputs of the model. The internal load (t)has four basic states determined by the HVAC system itself tosimulate the actual activity in the test rooms. The system delay isimportant in modeling the AHU system; therefore, the parameterinternal load (t � 1) was selected. For instance, past values of thesystem internal load may have more impact on the output of theHVAC system than its current value. The other uncontrollableparameters reflecting the outside weather conditions should alsobe taken into consideration. The operation of the AHU system is

Evaluator Classifier Search method

Wrapper Linear regression GeneticPace regression Linear forwardLinear regression GreedySVM regression GeneticMLP Genetic

Table 3The results of parameter selection by voting-based wrapper algorithm.

Wrapper ¼Linear regressionþ Genetic search

Wrapper ¼Pace regression þLinear forward

Wrapper ¼Linear regression þGreedy

Wrapper ¼SVM regression þGenetic search

Wrapper ¼MLP þGenetic search

Rank

No. of times selected No. of times selected No. of times selected No. of times selected No. of times selected Total

Internal load (t � 1) 10 10 10 10 10 50SA set point 10 10 10 9 10 49MA-Temp 10 10 10 10 9 49OA-Hum 10 10 5 10 8 43SPSP set point 10 10 10 3 9 42BAR-Pres 10 10 7 10 4 41OA-Temp 3 10 8 8 10 39SOL-Beam 10 7 5 10 7 39Internal Load (t) 5 5 4 9 10 33SA-Hum 9 9 4 6 3 31IR-Rad 8 9 5 2 5 29SOL-Hor 2 7 5 3 10 27WIND-Dir 8 5 5 7 1 26WIND-Vel 2 8 9 1 5 25OA-CO2 0 2 2 3 4 11

A. Kusiak et al. / Energy 36 (2011) 2440e2449 2443

impacted by the weather patterns. The two controllable parame-ters, the AHU supply air temperature and the supply air duct staticpressure set points, directly account for the system energyconsumption. They are optimized in the next section, and thecontrol strategy to generate them is discussed.

3.2. Construction and validation of the energy consumption model

After parameter selection and dimensionality reduction, theenergy consumption model of the HVAC system is expressed inequation (4).

yEnergyðtÞ ¼ f�xSAT Spt; xSASP Spt ;xLoadðtÞ; xLoadðt�1Þ; xSA Humd;

xSOL Horz; xIR Radia; xBar Pres; xOA TEMP; xSOL Beam

�ð4Þ

where yEnergy (t) is the energy to be optimized; x represents all theinputs of this predictive model.

Five data-mining algorithms were used to extract the mappingbetween inputs andoutputs: ExhaustiveGeneral CHAID (Chi-squareAutomatic Interaction Detector) [24], Boosting Tree [26], RandomForest [27], SVM (Support Vector Machines) [28], and MLP [29].

The Exhaustive CHAID algorithm is derived from the standardCHAID [25], which is a type of decision tree allowing multiple splitsof nodes and can be used for detection of interaction betweenvariables in regression and classification analysis. It allows for morecomprehensive merging than standard CHAID.

Boosting tree is a typical machine learning meta-algorithm forperforming supervised learning. Boosting is an iterative procedure

Table 4The results of the correlation coefficient matrix.

Internal load (t) Internal load (t � 1) SA set point SASP set poin

Internal load (t) 1.00 0.45 0.01 �0.02Internal load (t � 1) 0.45 1.00 �0.02 �0.01SA set point 0.01 �0.02 1.00 �0.02SP set point �0.02 �0.01 �0.02 1.00MA-Temp 0.02 0.00 0.99 �0.06SA-Hum 0.02 0.00 �0.54 0.00BAR-Pres �0.06 �0.06 �0.72 0.03IR-Rad 0.06 �0.02 0.04 0.00OA-Hum �0.07 �0.05 0.13 �0.35OA-Temp 0.05 0.00 �0.18 0.13SOL-Beam 0.01 �0.04 �0.29 0.20SOL-Hor 0.08 �0.12 0.00 0.57

used to adaptively modify the distribution of training examples sothat the base predictors will mostly concentrate on learninginstances misclassified by the previous biased examples.

Random Forest is a class of ensemble methods consisting ofmultiple decision trees, where each tree is generated based on thevalues of an independent set of random variables. Unlike theadaptive approach used in Boosting, the random variables aregenerated from a fixed probability distribution.

SVM is a supervised learning algorithm based on kernel func-tions, and it is applied to binary classification and regression. Usingspecific kernel functions, the original vector space is transformedinto a higher-dimensional space where a separated hyperplane isconstructed with the maximum margin.

The MLP Ensemble method presents a combination of multiplemodels to leverage the strengthofmultipleMLPmodels in achievingbetter prediction accuracy than any individual model does.

The five different data-mining algorithms have been tested forthe construction of predictive models. In order to evaluate theperformance of different algorithms, the following four metrics(see equations (5)e(10)) have been used to measure the predictionaccuracy of the model: the MAE (mean absolute error), the Std_AE(standard deviation of absolute error), the MAOE (mean absolutepercentage error) and the Std_APE (standard deviation of absolutepercentage error) [30]:

AE ¼���~y� y

��� (5)

MAE ¼Pn

i¼1 AEiN

(6)

t MA-temp SA-Hum BAR-Pres IR-Rad OA-Hum OA-Temp SOL-beam SOL-Hor

0.02 0.02 �0.06 0.06 �0.07 0.05 0.01 0.080.00 0.00 �0.06 �0.02 �0.05 0.00 �0.04 �0.120.99 �0.54 �0.72 0.04 0.13 �0.18 �0.29 0.00

�0.06 0.00 0.03 0.00 �0.35 0.13 0.20 0.571.00 �0.54 �0.71 0.04 0.15 �0.18 �0.28 �0.03

�0.54 1.00 0.13 0.65 0.32 0.80 �0.09 �0.10�0.71 0.13 1.00 �0.19 �0.53 0.06 0.38 0.120.04 0.65 �0.19 1.00 0.38 0.77 �0.34 �0.060.15 0.32 �0.53 0.38 1.00 0.10 �0.47 �0.46

�0.18 0.80 0.06 0.77 0.10 1.00 �0.05 0.09�0.28 �0.09 0.38 �0.34 �0.47 �0.05 1.00 0.51�0.03 �0.10 0.12 �0.06 �0.46 0.09 0.51 1.00

Table 5Parameter description.

Parameter Type Parameter name Description Unit

Controllablevariables

SAT set point AHU supply airtemperature set point

�C

SASP set point Supply air duct staticpressure set point

kPa

Uncontrollablevariables

Internal load (t) System internal load /

Internal load (t � 1) The previous state ofsystem internal load

/

SA-Hum Supply air humidity % RHSOL-Hor Solar normal flux B/HFt2IR-Rad Infrared radiation B/HFt2BAR-Pres Barometric pressure

(normalized to sea level)mBar

OA-Temp Outside air temperature �CSOL-Beam Solar beam intensity B/HFt2

Table 6Prediction performance of the energy consumption models built by five different-mining algorithms.

Dataset Algorithm MAE Std_AE MAPE (%) Std_MAPE (%)

Training MLP ensemble 659.13 645.63 10.20 9.40Testing 720.92 642.52 13.00 9.50Training MLP 628.28 569.67 9.80 7.60Testing 700.29 780.71 11.10 8.50Training SVM 1464.34 1312.41 25.90 24.50Testing 1396.86 1370.59 25.30 21.10Training Boosting tree 2012.51 1824.92 32.60 27.30Testing 1736.34 1711.62 30.20 31.40Training Random forest 3061.98 2614.16 49.60 39.00Testing 4328.04 3488.01 83.40 57.50Training Exhaustive CHAID 1471.81 1905.16 20.50 24.10Testing 2236.16 2296.80 36.00 26.30

0

5000

10000

15000

20000

25000

30000

35000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73

]Jk[noitp

musnocygren

E

Time [h]

Observed energy consumption Predicted energy consumption

Fig. 3. Test results produced by the model.

A. Kusiak et al. / Energy 36 (2011) 2440e24492444

APE ¼�����~y� yy

����� (7)

MAPE ¼Pn

i¼1 APEiN

(8)

Std AE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPn

i¼1ðAEi �MAEÞ2N � 1

s(9)

Std APE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPn

i¼1ðAPEi �MAPEÞ2N � 1

s(10)

where AE in equation (2) represents the absolute error, ~y is thepredicted value obtained from the model, y is the actual targetvalue measured, and N is the number of data points used fortraining or testing.

Table 6 presents the prediction performance of the energyconsumption models derived by five data-mining algorithms bypresenting the respective training and testing errors. The compu-tational results listed in Table 3 demonstrate that the MLP neuralnetwork performs best on the four evaluation criteria. Therefore itis selected as the algorithm for constructing the energy consump-tion model.

The test results of the MLP neural network for this model areshown in Fig. 3. The chart shows that the predicted values closelytrack the observed ones at most of the points.

3.3. Construction and validation of the IAQ models

In this HVAC system examined, the value of room temperature ismaintained from 69 �F to 73 �F and the room humidity is controlledbelow 30% to ensure the thermal comfort. As the supply airtemperature and the supply air static pressure set points change,the room temperature and humidity are also affected by theimplementation of changeable settings. Models of room tempera-ture and humidity should be constructed so as to conform to theindoor air quality while minimizing the energy consumption. Usingthe same methodology introduced in Section 3.2, the IAQ modelcan be described as follows:

yTempðtÞ ¼ f�xSAT-Spt; xSASP Spt ;xLoadðtÞ; xLoadðt�1Þ; xSA-Humd;

xSOL-Horz; xIR-Radia; xBar-Pres; xOA-TEMP; xSOL-Beam�ð11Þ

yHumidityðtÞ ¼ f xSAT Spt;xSASP Spt ;xLoadðtÞ;xLoadðt�1Þ;xSA Humd;�

�xSOL Horz;xIR Radia;xBar Pres;xOA TEMP;xSOL Beam ð12Þ

where yTemp (t) and yHumidity (t) are constraints to meet the IAQ ofHVAC system; x represents all the inputs of this predictive model.

The MLP algorithm and the same dataset are used to constructthe two models. The test results can be seen in Fig. 4 and 5.

4. Optimization algorithm

4.1. Model formulation

The optimization process seeks the set point values minimizingthe total energy consumption of the HVAC system. This is done byapplying the evolutionary computation algorithm [31]; the setpoints were optimized to maximize the energy savings. The opti-mizationmodel is formed through the identification of the problemparameters, the objective functions, and the constraints.

4.1.1. Model parametersThe model parameters of the HVAC system have been deter-

mined by the wrapper algorithm described in Section 3.1. Table 5lists each parameter used for the optimization process. The twocontrollable parameters, the AHU supply air temperature and thesupply air duct static pressure set points, are to be varied to obtainthe optimal solutions. As uncontrollable input parameters areessentially independent of the controllable ones, the values ofuncontrollable variables, such as supply air humidity, outside air

18.00

19.00

20.00

21.00

22.00

23.00

24.00

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73

]C[

erutarepmet

mooR

Time [h]

Observed room temperature Predicted room temperature

Fig. 5. Test results for the room temperature model.

A. Kusiak et al. / Energy 36 (2011) 2440e2449 2445

temperature and other outside weather patterns, can be fixed inseeking the optimal control settings at each time stamp.

4.1.2. Objective functionsThe optimal control strategy determines two set points to

minimize the energy use. The total energy consumption, includingthe fan, pump, and reheat power, is computed from equation (2).The inputeoutput relationship was expressed by the HVAC systemmodel presented above in equations (3), (11) and (12). The energyobjective function is to be minimized while the other two e

temperature and humidity objective functions e are treated asconstraints to satisfy the indoor air quality of the AHU system.

4.1.3. ConstraintsThe constraints in the model are due to the upper and lower

limits imposed on the parameters of the HVAC system and the IAQmodels. The value of the supply air temperature set point, thesupply air duct static pressure set point, indoor room temperature,and room humidity are restricted within the limits:

� Supply air temperature must vary between 52 �F (11.11 �C) and63 �F (17.22 �C).

� Supply air duct static pressure must vary between 1.2 WG(0.3 kPa) and 1.8 WG (0.45 kPa).

� Room temperature must be maintained between 70 �F(21.11 �C) and 72 �F (22.22 �C).

� Room humidity must be controlled below 30%.

Consequently, the optimization model (13) is expressed asminimizing the objective function (4) with control parametersvarying within their bounds.

0.00

5.00

10.00

15.00

20.00

25.00

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73

]%[

ytidimuh

mooR

Time [h]

Observed room humidity Predicted room humidity

Fig. 4. Test results for the room humidity model.

min�yEnergyðtÞ

�xSAT Spt;xSASP Spt

subject to :

yEnergyðtÞ ¼ f�xSAT Spt; xSASP Spt ;xLoadðtÞ; xLoadðt�1Þ; xSA Humd; xSOL H

yTempðtÞ ¼ f�xSAT Spt; xSASP Spt ;xLoadðtÞ; xLoadðt�1Þ; xSA Humd; xSOL H

yHumidityðtÞ ¼ f�xSAT Spt; xSASP�Spt ;xLoadðtÞ; xLoadðt�1Þ; xSA Humd; xSOL

11:11 � xSAT Spt � 17:220:3 � xSASP Spt�0:45

20:56 � yTempðtÞ � 22:785 � yHumdðtÞ � 25

Solving such a nonlinear multi-objective optimization problemis a challenge. For the typical HVAC system, the procedure ofcomputation is also complex and time-consuming, resulting in thedifficulty of getting the results for some large datasets. In order tosimplify the problem and reduce the calculation time, the twoconstraint functions yTemp (t) and yHumidity (t) are assigned into one-objective function shown in equation (14):

yConstraintsðtÞ ¼maxn0;20:56� yTempðtÞ

oþmax

n0; yTempðtÞ

� 22:78oþmax

n0;5� yHumidityðtÞ

oþmax

n0; yHumidityðtÞ � 25

oð14Þ

4594.7

4594.8

4594.9

4595

4595.1

4595.2

4595.3

4595.4

4595.5

4595.6

0 0.01 0.02 0.03 0.04 0.05 0.06

]Jk[noitp

musnocygren

E

IAQ constraints

Fig. 6. Feasible solutions obtained after 150 generations at some time stamp.

orz; xIR Radia; xBar Pres; xOA TEMP; xSOL Beam

�orz; xIR Radia; xBar Pres; xOA TEMP; xSOL Beam

�Horz; xIR Radia; xBar Pres; xOA TEMP; xSOL Beam

� (13)

Table 7Description of the eleven weight assignment scenarios.

Scenario Weight assignedto energy

Weight assignedto IAQ constraints

Description

1 w1 ¼ 1.0 w2 ¼ 0 No IAQ constraints2 w1 ¼ 0.9 w2 ¼ 0.1 Preference to energy saving3 w1 ¼ 0.8 w2 ¼ 0.2 Preference to energy saving4 w1 ¼ 0.7 w2 ¼ 0.3 Preference to energy saving5 w1 ¼ 0.6 w2 ¼ 0.4 Preference to energy saving6 w1 ¼ 0.5 w2 ¼ 0.5 Equal importance to both

objectives7 w1 ¼ 0.4 w2 ¼ 0.6 Preference to IAQ maintenance8 w1 ¼ 0.3 w2 ¼ 0.7 Preference to IAQ maintenance9 w1 ¼ 0.2 w2 ¼ 0.8 Preference to IAQ maintenance10 w1 ¼ 0.1 w2 ¼ 0.9 Preference to IAQ maintenance11 w1 ¼ 0 w2 ¼ 1.0 Maximization of thermal

comfort

A. Kusiak et al. / Energy 36 (2011) 2440e24492446

As the constraints are satisfied, each of the four terms in equa-tion (14) will remain 0 and the sum equals 0. However, since roomhumidity and temperature are not at the same scale, the constraintfunction may not accurately reflect the influences of them. It ispossible room humidity may dominate the result because of itshigh value. The values of room humidity and temperature are thennormalized to eliminate the deviation. The revised function isshown in equation (15).

min�yEnergyðtÞ

�xSAT Spt;xSASP Spt

subject to :

yEnergyðtÞ ¼ f�xSAT Spt; xSASP Spt ;xLoadðtÞ; xLoadðt�1Þ; xCHWC VLV; xSA Humd; xSOL Horz; xOA Humd; xOA TEMP

�yConstraintsðtÞ ¼ w1*

nmax

n0;20:56� yTempðtÞ

oþmax

n0; yTempðtÞ � 22:78

oo.�yTemp upperbound � yTemp lowerbound

�þ

w2*nmax

n0;5� yHumidityðtÞ

oþmax

n0; yHumidityðtÞ � 25

oo.�yHumidity upperbound � yHumidity lowerbound

�11:11 � xSAT Spt � 17:22

0:3 � xSASPSpt�0:45 (18)

yConstraintsðtÞ ¼nmax

n0;20:56� yTempðtÞ

o

þmax

n0; yTempðtÞ � 22:78

oo=�yTemp upperbound � yTemp lowerbound

�þnmax

n0;5� yHumidityðtÞ

oþmax

n0; yHumidityðtÞ � 25

oo=�yHumidity upperbound � yHumidity lowerbound

�ð15Þ

Table 8Weight assignment of 11 scenarios.

Scenario Total energy Recommended SA setting Recommen

1 26061.89 14.76 0.452 26063.17 14.97 0.453 26065.49 15.03 0.454 26076.04 15.19 0.455 26103.45 15.42 0.456 26185.11 15.84 0.457 26249.09 16.07 0.458 26450.17 16.53 0.439 26450.17 16.53 0.4310 26450.17 16.53 0.4311 26450.17 16.53 0.43

In the practical operation of HVAC system, it is possible thatsome constraint is of more importance or at least over than someother constraint. In different time period of the year, managers mayemphasize on different objectives. For example room temperatureshould be paid more attention to room humidity inwinter since theair humidity is really low and is not a big issue. Taking the effects ofdifferent constraints, weights should be assigned to each constraintto meet the specific preference of HVAC system. The final constraintfunctions are presented in eqs. (16) and (17).:

yConstraintsðtÞ ¼w1*nmax

n0;20:56� yTempðtÞ

oþmax

n0; yTempðtÞ � 22:78

oo=�yTemp upperbound � yTemp lowerbound

�þw2*

nmax

n0;5� yHumidityðtÞ

oþmax

n0; yHumidityðtÞ � 25

oo=�yHumidity upperbound � yHumidity lowerbound

�ð16Þ

w1 þw2 ¼ 1 (17)

Based on discussion above, the optimization problem wastransformed into a bi-objective model. Finally the optimization canbe modified to equation (18):

4.2. Evolutionary computation algorithm

In this study, a modified SPEA-LS (Strength Pareto EvolutionaryAlgorithm with Local Search) is used to solve the model (12). Thealgorithm is presented below:

Step 1: Initialize a population P and create an empty externalpopulation P* to store elite solutions.

Step 2: Find non-dominated solutions in P and copy them into P*.Step 3: Find non-dominated solutions in P and update the elite

population P*.

ded SASP setting Temperature Humidity IAQ violation

20.63 22.90 0.2620.67 23.14 0.2420.69 23.21 0.2320.72 23.39 0.2120.78 23.66 0.1820.90 24.13 0.1120.97 24.39 0.0721.10 25.11 0.0121.10 25.11 0.0121.10 25.11 0.0121.10 25.11 0.01

Table 9Comparison of the solutions for the weights of the 11 scenarios.

Scenario Averageoptimizedenergy used

Averageenergysavings

Averagepercentageenergy savings (%)

IAQviolation

1 6781.64 1976.36 22.57 0.15182 6781.93 1976.07 22.56 0.13503 6782.83 1975.17 22.55 0.12834 6783.19 1974.81 22.55 0.12715 6784.20 1973.80 22.54 0.12256 6824.26 1933.74 22.08 0.10877 6861.81 1896.19 21.65 0.01778 6866.99 1891.01 21.59 0.00979 6869.99 1888.01 21.56 0.007910 6875.36 1882.64 21.50 0.006611 6879.75 1878.25 21.45 0.0060

45

50

55

60

65

70

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

]F°[erutarep

meT

Original SAT setpoint Optimized SAT setpoint (Scenario 11)

Fig. 7. The observed and recommended supply air temperature settings.

A. Kusiak et al. / Energy 36 (2011) 2440e2449 2447

Step 4: Assign fitness values to each individual in P and P*.Step 5: Select a set of Pparent of size Nparent from P þ P* using the

binary tournament selection scheme with replacement.Step 6: Randomly select two individuals and add a better one to

Poffspring. Apply recombination and mutation operators toPoffspring.

Step 7: Local Search: Apply the modified local search procedure toall Noffspring solutions in the current population. The currentpopulation is replaced with the Noffspring solutionsimproved by the local search.

Step 8: Stopping Criterion: The maximum number of generations.If not exceeded, return to Step 2.

The local search procedure is as follows:

Step 1: Specify an initial solution x.Step 2: Examine n neighborhood solutions y ¼ {x1, x2,., xn} of the

current solution x.Step 3: Evaluate all the neighborhood solutions in y and find the

best one. If a solution which is better than x is found,replace the current solution x with the better one.

Step 4: Return to Step 1 until all the individuals are examined.

In the process of assigning the fitness for individuals P and P*,two different functions are applied to ensure the elite solution andretain the variety of the population. For individuals in elite pop-ulation P*, the fitness function is:

Si ¼ni

N þ 1(19)

where Si is the fitness value of ith elite individual in non-dominatedpopulation P*, ni is the number of individuals in P that solution idominates, and N is the population size of P.

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

]G

W[erusserp

citatS

Original SASP setpoint Optimized SASP setpoint (Scenario 11)

Fig. 8. The observed and recommended supply air static pressure settings.

For the individuals in current population P, thefitness function is:

Sj ¼ 1þXi˛F

Si (20)

where Sj is the fitness of jth individual in the current population P, Fis the elite set from P*.

The control parameters of the evolutionary computation algo-rithm must be adjusted to provide the best performance, i.e.,minimum energy consumption of the HVAC system with the leastsacrifice of air quality. Themutation operator in Step 6 is realized byadding noise Δxi (from a Gaussian distribution with zero mean andstandard deviation s) to the ith controllable variable xi. The newlygenerated solution is xi* ¼ xi þ N(0,s). In global search, the noisevalue for x1(t) and x2(t) is set to 0.5 and 0.05, respectively. In localsearch, the noise is set to 0.1 and 0.01, respectively. The populationsize is pz ¼ 100. The stopping criterion is set at 150 generations.

4.3. Optimization results and discussion

The proposed evolutionary computation algorithm was appliedto solve the optimization model at each time stamp. Optimizedcontrol settings of the existing HVAC system, namely the supply airtemperature and the supply air duct static pressure set points, wereobtained. The performance of the HVAC system model has beenvalidated. The bounds set for supply air temperature and supply airstatic pressure may be slightly violating the constraints during thegenerations.

Fig. 6 shows the values of the objective function of model (18)generations of the evolutionary computation algorithm. A decreasein constraints indicating the better air quality requires an increase in

0

5000

10000

15000

20000

25000

30000

35000

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

]Jk[ygrenelato

T

Original energy use Optimized energy use (Scenario 11)

Fig. 9. The observed and optimized total energy consumption for Scenario 11.

65

66

67

68

69

70

71

72

73

74

75

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

]F°[erutarep

meT

mooR

Original room temp Optimized room temp (Scenario 11)

Fig. 10. The observed and optimized room temperature for Scenario 11.

0.0000

0.0200

0.0400

0.0600

0.0800

0.1000

0.1200

0.1400

0.1600

6720.00

6740.00

6760.00

6780.00

6800.00

6820.00

6840.00

6860.00

6880.00

6900.00

1 2 3 4 5 6 7 8 9 10 11

noitaloivQ

AI

]Jk[noitp

musnocygren

E

Scenario

Average optimized energy use IAQ violation

Fig. 12. The optimized energy consumed versus IAQ violation.

A. Kusiak et al. / Energy 36 (2011) 2440e24492448

energy demand.When the constraints are satisfied (the left point onthe boundary), the system consumes more energy than at otherpoints. If the decision is to save more energy, the consequence mustbe the sacrifice of the thermal comfort and air quality. According tothe different preferences of management, the results will largelydiffer if different weights are assigned to each objective function. Atrade-off must be considered to meet the specific requirements ofdifferent systems. If we assign w1 to objective function one whichconsiders the energy, andw2 for objective function two representingthe violation of air quality, the different combination of w1 and w2will give the different preferences. The optimal solution is selectedfromthefinal elite set by theweightednormalizedobjective function(17). The following two equations show the following process.

Objective ¼ w2*ðobjective1� objective1minÞ

ðobjective1max � objective1minÞ

þw2*ðobjective2� objective2minÞ

ðobjective2max � objective2minÞ(21)

wherew1 andw2 represent the user-defined weights indicating theimportance of objective1 and objective2, respectively; objective1represents the energy consumption and objective2 represents theviolation of air quality. Note that w1 þ w2 ¼ 1.

Let w1 varies from 1 to 0 with 0.1 decrement while w2 variesfrom 0 to 1 with 0.1 increment. Eleven scenarios representingdifferent assignments of weights to the objectives have beencreated in Table 7. Table 8 lists the optimal solutions for each of the11 scenarios at some time stamp. After assigning different weightsto the objectives, the bi-objective optimization model is trans-formed into a single objective model to be minimized with the

0

5

10

15

20

25

30

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

]%

HR[

ytidimu

Hmoo

R

Original room humidity Optimized room humidity (Scenario 11)

Fig. 11. The observed and optimized room humidity for Scenario 11.

objective function shown in (21). Scenario 1 has the lowest totalenergy consumption as the air quality is not considered. As theweight assigned to the IAQ increases, the total energy saving isreduced.

To compare the optimal solutions with the actual energyconsumption, Scenario 11 is selected. Figs. 7 and 8 compare theoriginal and recommended control settings of the supply airtemperature and the static pressure.

Based on the optimal control settings, the corresponding totalenergy and the room air quality metrics are estimated using theenergy and the IAQ models of Section 3. Figs. 9e11 compare theoriginal and optimized energy as well as the IAQ indexes.

Fig. 9 presents that the total energy consumption is reducedafter the recommended control settings are implemented. Thecorresponding values of IAQ indexes are presented in Figs. 10 and11. At times, minimization of the energy is compromised in orderto maintain the required IAQ indexes. The total energy saved forScenario 11 is 21.4% compared to 22.6% Scenario 1 with no IAQconstraints included.

The results discussed above represent only the two extremesituations of weights assignments. Different trade-off can be foundby changing the weights to the corresponding objective. Table 9presents the final optimal solutions after assigning differentweights to the objectives. As the larger weight is assigned to IAQconstraints, more energy is consumed while the air quality isimproved. Fig. 12 shows the gradient trend of optimized energy useand IAQ violations.

Fig. 12 demonstrates that when the weight associated with theenergy objective decreases from 0.6 to 0.4, the energy consumptionincreases and the adherence of IAQ indexes improves. Both, theenergy consumption and IAQ indexes are minimally affected whenthe twoweights change from 1 to 0.6 and 0 to 0.4, respectively. Thesolution zone when the values of the weights are close to eachother is sensitive. By changing the weights, the model allows forincorporation of user’s preferences.

5. Conclusion

The proposed data-mining and optimization approach wasapplied to an existing HVAC system at the ERS. A predictive modelof energy consumption, room temperature, and humidity weregenerated by a MLP algorithm and aggregated into a model opti-mizing energy consumption. The model constructed in the paperwas solvedwith an evolutionary computation algorithm to produceoptimized set points of the supply air temperature and the supplyair static pressure of the HVAC system. The optimized set pointsdetermined by solving a model with two-objectives resulted in

A. Kusiak et al. / Energy 36 (2011) 2440e2449 2449

energy saving of 21.4% without violating the indoor air qualityconstraints. When occasional violations of air quality were allowedthe energy savings increased to 22.6%.

The approach presented in the paper, is suitable for imple-mentation of different control strategies based on user’s preferences.

The results produced in the study indicated that optimization ofcontrol settings is a valid strategy for reduction of energyconsumption of the existing HVAC systems.

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