Expert Systems with Applications 38 (2011) 7179–7185

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Expert Systems with Applications

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A comparative study of the multi-objective optimization algorithmsfor coal-fired boilers

Feng Wu, Hao Zhou ⇑, Jia-Pei Zhao, Ke-Fa CenState Key Laboratory of Clean Energy Utilization, Institute for Thermal Power Engineering, Zhejiang University, Hangzhou 310027, People’s Republic of China

a r t i c l e i n f o a b s t r a c t

Keywords:CombustionMulti-objective optimizationSupport vector regressionSPEA2OMOPSOAbYSSMOCell

0957-4174/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.eswa.2010.12.042

⇑ Corresponding author. Tel.: +86 571 87952598; faE-mail address: zhouhao@cmee.zju.edu.cn (H. Zho

Combustion optimization has been proved to be an effective way to reduce the NOx emissions andunburned carbon in fly ash by carefully setting the operational parameters of boilers. However, thereis a trade-off relationship between NOx emissions and the boiler economy, which could be expressedby Pareto solutions. The aim of this work is to achieve multi-objective optimization of the coal-fired boi-ler to obtain well distributed Pareto solutions. In this study, support vector regression (SVR) wasemployed to build NOx emissions and carbon burnout models. Thereafter, the improved Strength ParetoEvolutionary Algorithm (SPEA2), the new Multi-Objective Particle Swarm Optimizer (OMOPSO), theArchive-Based hYbrid Scatter Search method (AbYSS), and the cellular genetic algorithm for multi-objec-tive optimization (MOCell) were used for this purpose. The results show that the hybrid algorithms bycombining SVR can obtain well distributed Pareto solutions for multi-objective optimization of the boiler.Comparison of various algorithms shows MOCell overwhelms the others in terms of the quality of solu-tions and convergence rate.

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1. Introduction

Thermal power is China’s dominant power generating capacityand accounts for three quarters of the total capacity. Of the thermalgenerating capacity, more than 90% is coal-fired (Lam & Shiu, 2004).The emission of nitrogen oxides (NOx) during coal combustion is asignificant pollutant source to the environment. As environmentalproblems become more serious, the problem of NOx emission isreceiving increasing attention. On the other hand, the level ofunburned carbon in fly ash is an important factor affecting the effi-ciency of pulverized coal-fired boilers, especially those equippedwith low NOx burners (Zhou, Cen, & Fan, 2004). High carbon con-tent of fly ash will cause excessive heating of superheater andreheater tubes at the furnace outlet and may cause tube explosion.

There are many old-designed coal-fired utility boilers in China.These boilers with low thermal efficiency generate rather high NOxemissions. The NOx emissions of these boilers may be reduced byinstalling the flue gas treatment equipment such as SelectiveCatalytic Reduction (SCR) and Selective Non-Catalytic Reduction(SNCR), however, the costs are high.

Recently, combustion optimization has been proved to be aneffective way to reduce the NOx emissions (Zheng, Zhou, Wang,& Cen, 2008; Zhou et al., 2004; Zhou, Cen, & Mao, 2001) andunburned carbon in fly ash (Chen & Liu, 2005; Zhao, Wang, Lu, &Yue, 2005) in coal-fired utility boilers by carefully setting the

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operational parameters of boilers. Some achievements are madein their work, however NOx emissions and carbon burnout are con-sidered in isolation in their studies. It is well known that the airdistribution implemented in low NOx burners would induce highlevels of unburned carbon in fly ash. Therefore, NOx emissionsand carbon burnout should be taken into account simultaneously.Consequently multi-objective optimization for the coal-fired utilityboiler is imperative. More recently, multi-objective optimizationfor the coal-fired utility boiler was developed by Wu, Zhou, Tao,Zheng, and Cen (2009).

Over the last decade, a number of multi-objective evolutionaryalgorithms (MOEAs) have been proposed (Deb, 2001; Deb, Partap,Agarwal, & Meyarivan, 2002; Fonseca & Fleming, 1993). The pri-mary reason for this is their ability to find multiple Pareto-optimalsolutions in one single simulation run (Deb et al., 2002). Amongvarious multi-objective algorithms, the SPEA2 proposed by Zitzleras a classical genetic algorithm, has been widely accepted as thebenchmark in multi-objective evolution algorithms (MOEA). Morerecently, some modern algorithms such as new Multi-ObjectiveParticle Swarm Optimizer (OMOPSO) (Sierra & Coello, 2005),Archive-Based hYbrid Scatter Search (AbYSS) (Nebro, Luna, Alba,Beham, & Dorronsoro, 2006), and cellular genetic algorithm formulti-objective optimization (MOCell) (Nebro, Durillo, Luna,Dorronsoro, & Alba, 2006) have yielded good performance innumerical experiments, and received increasing attention.

Due to the complexity of boiler systems, theoretical models areextremely difficultly to build so far. However, Alternative modelscould be obtained by using the artificial intelligence methods.

A

B

C

D

E

F

8 x

675m

m

12900mm

560 mm

Fig. 1. Burner arrangement of the boiler (Wu et al., 2009).

7180 F. Wu et al. / Expert Systems with Applications 38 (2011) 7179–7185

Among them, the support vector regression (SVR) method, whichhas the advantages of global optimum, simple structure and goodgeneralization properties, has attracted wide spread attention(Bloch, Lauer, Colin, & Chamaillard, 2008; Li, Cui, He, & Wang,2008; Mehta & Lingayat, 2008; Trebar & Steele, 2008).

In this study, SVR was employed to build the NOx emissions andcarbon burnout models, respectively. Subsequently, SPEA2, AbYSS,OMOPSO and MOCell were combined with the SVR model respec-tively to search the optimal parameters for Pareto-based multi-objective optimization of a boiler. Comparisons on the availabilityand the convergence rate with various algorithms were thusconducted.

The structure of this paper is organized as follows. Section 1presents the introduction. Section 2 describes the multi-objectiveproblem of the coal-fired boiler, and the experimental setup. Addi-tionally, the NOx emissions and carbon burnout models built bySVR and the performance metrics of Pareto solution are also in-cluded in Section 2. In Section 3, the multi-objective optimizationalgorithms used in this work are presented. Section 4 presents theresults on NOx emissions and carbon burnout predictions by SVRmodels. Comparisons of different algorithms through the metricsmentioned in Section 2 are conducted. Finally, conclusions aredrawn in Section 5.

2. Multi-objective problem of the coal-fired boiler

2.1. Outline of the multi-objective problem of the coal-fired boiler

In this study, the utility coal-fired boiler is optimized to simul-taneously minimize the NOx emissions and the unburned carbonin fly ash. Unburned carbon in fly ash is an index that when mini-mized can maximize the boiler efficiency. There are many opera-tional parameters of the boiler that can affect the NOx emissionsand carbon content in fly ash, such as boiler load and coal qualities.All of these parameters are used as input variables of SVR models(see Section 2.3 for more details). However, not all inputs of theSVR models can be considered as optimized variables. The boilerload and coal properties are generally determined by the operatingcondition, and should not be taken as adjustable parameters. Thespeeds of coal feeders are determined by the boiler load, andshould not be considered as adjustable parameters as well. Undera determined unit load, the primary and secondary air velocitiesare the targeted parameters to be optimized.

Multi-objective optimization problems of the coal fired boilercan adopt the following objective functions:

Minimize y ¼ ðfNOxðxÞ; fUCðxÞÞSubject to xmin

i 6 xi 6 xmaxi

where x ¼ ðx1; x2; . . . ; x10Þ 2 X

y ¼ ðfNOxðxÞ; fUCðxÞÞ 2 Y

8>>><>>>:

ð1Þ

where, x stands for the ten parameters to be optimized, i.e. fourvariables for primary air and six variables for secondary air veloci-ties. fNOx(x) represents NOx emissions, fUC(x) is the unburned carbonin fly ash. The inequality constraint for the problem states that theparameters to be optimized must be in the optimal range. The opti-mal range of primary air velocities is 25–30 m/s, which is con-strained by pulverized coal transportation. The optimal range ofthe A–E levels of secondary air velocities is 25–45 m/s and F levelof secondary air velocities is in the optimal range of 0–20 m/s.

2.2. Experimental setup

The experiments were carried out in a 300 MW tangentiallyfired dry bottom boiler with large dual furnaces of 17 m �8.475 m cross section and 45.5 m high. The boiler is one of the

units of the JianBi power plant, manufactured by Shanghai BoilerCo. Ltd. in the 1980s. Four primary air ports and six secondaryair ports (represented by A–F) were arranged on each corner ofthe furnace, as shown in Fig. 1. Four medium-speed coal pulveriz-ers supplied coal for combustion. Coal-air two-phase flow was di-rected at the circumference of an imaginary horizontal circle of500 mm diameter at the furnace center. The bituminite was com-busted by the concentric firing system. The characteristics of thecombusted coal are listed as follows: ash content 11.06 wt%, mois-ture content 13.60 wt%, volatile content 31.96 wt%, and heating va-lue 23.49 MJ/kg.

A total of 119 tests have been conducted with this boiler toinvestigate the effects of boiler parameters on NOx emissionsand carbon burnout characteristics. During the experiments, NOxconcentrations were continuously monitored at the boiler outletprior to the air heater by using continuous emission monitoringsystem (Rosemount, Emerson Process Ltd.). The maximum NOxemissions reported for the old-designed utility boiler was up to404.65 ppm; the unburned carbon was measured through the solidsamples retracted from the flue gas and was varied from 1.51% to2.96%. In all tests, coal quality remained constant, and otherparameters of the boiler varied in the following ranges: the pri-mary air velocities, 24.11–29.8 m/s; secondary air velocities atthe A–E elevations, 24.69–39.03 m/s and F elevation of secondaryair velocities 2.19–9.87 m/s due to a restriction in the air ductarrangement; boiler load, 243.19–331.03 MW.

2.3. Modeling NOx emissions and carbon burnout

As a modeling technique, the Support Vector Machine (SVM)methodology was used to produce mathematical expressions usinga set of inputs–output data (Zheng et al., 2008). Moreover, SVMcould be extended to solve nonlinear regression problems throughintroducing the insensitive loss function e, called support vectorregression (SVR). The complete SVR equations could be obtainedin reference Smola and Scholkopf (2004).

In this paper, NOx emissions and carbon burnout models werebuilt by SVR separately as mentioned in Section 2.1. Identical inputparameters were used for both models. The parameters were boilerload, speeds of the four mills, coal quality, four levels of primary airvelocities and six levels of secondary air velocities, respectively.Oxygen concentration in the flue gas and the total air flowrateare also important parameters to the boiler, however, they arenot independent design variables and their contributions to NOx

F. Wu et al. / Expert Systems with Applications 38 (2011) 7179–7185 7181

emissions formation and carbon burnout, have been reflected byprimary and secondary air velocities (Zheng et al., 2008).

Among the 119 cases obtained in the experiments, 89 caseswere chosen as the training subset, the remaining as the testingsubset. In order to eliminate the unit influence upon various oper-ating parameters of the boiler, the inputs were scaled into therange [�1, 1] through Eq. (2)

xscal ¼xinput � rangemin

rangemax � rangemin� 2� 1 ð2Þ

where, rangemax and rangemin are upper and lower limits of the testrange mentioned in Section 2.2, respectively; xinput and xscal areoperating parameters before and after scaling, respectively.

As for SVR, the parameters (g, C) have a significant influence onthe models built by SVR, and should be set carefully. The grid-search method (Chang & Lin, 2001) has been proved to be an effec-tive way to determine (g, C) (Zheng, Zhou, Cen, & Wang, 2009).Additionally, the application of cross-validation in searching theoptimal (g, C) could avoid over fitting, and obtain a better general-ization ability for SVR models. In this study, the fivefold cross-vali-dation combined with grid-search method was used to determinethe optimum parameters. Pairs of exponentially growing sequenceswere tried, i.e. g = 2�10, 2�9.9, . . ., 23; C = 20, 20.1, . . ., 210. The optimal(g, C) thus obtained should reduce the Mean Relative Error (MRE) inthe samples after fivefold cross-validation to a minimum.

2.4. Performance metrics of Pareto solution

In multi-objective optimization, several performance metricshave been adopted to evaluate the algorithms (Deb et al., 2002;Nebro, Durillo, Coello, Luna, & Alba, 2008; Zitzler, Deb, & Thiele,2000). Evaluation of the solution set obtained is essential, andthe solution set obtained was expected as: (1) proximity to the truePareto-optimal front, the closer to the true Pareto-optimal front ofthe solution set, the more accurate; (2) breadth against the entiretrue Pareto-optimal front; (3) equal distribution within the Pare-to-optimal front.

In this paper, as the true Pareto-optimal front was unknown forthe complexity of the boiler, the ratio of non-dominated individu-als (RNI) was used to evaluate the accuracy of the set obtained.Cover rate was used to evaluate the breadth of solution set andhow evenly the solutions were distributed.

2.4.1. The ratio of non-dominated individuals (RNI)This performance measure is derived by comparing two solu-

tions from two methods. By RNI, the accuracy of the solutionscan be compared.

The RNI is defined as follows: suppose S1 and S2 are the solutionsets obtained by two different methods, and they could be com-bined to form a new solution set SU. From SU, the non-dominatedsolutions are selected to form SP. Then, the ratios of S1 and S2

against SP were calculated, respectively. The higher ratio demon-strates the corresponding method outperform the other in termsof the accuracy of the solutions.

2.4.2. Cover rateThe diversity of the solutions is discussed here. Generally, the

distribution of the solutions could be evaluated through general-ized co-variance value. However, the co-variance value is not suit-able for the solutions having multiple peaks (Hiroyasu, Nakayama,& Miki, 2005). Therefore, cover rate was used to evaluate the diver-sity of the solutions instead of co-variance in this study.

The following procedures should be taken to derive the coverrate (Hiroyasu, Miki, & Watanabe, 2000). Firstly, the maximumand the minimum values were obtained by searching one objectivefunction fk. The distance between the minimum and the maximum

was divided into N divisions, where N was any positive integernumber. The number of the area containing Pareto optimum indi-viduals was counted as Nk. Then, the cover ratio CRk against theobjective fk could be obtained by Eq. (3)

CRk ¼Nk

Nð3Þ

Next, the above steps were conducted for every object function. Fi-nally, the cover rate CR could be obtained by Eq. (4), where n wasthe number of the objective functions

CR ¼ 1n

Xn

k¼1

CRk ð4Þ

Cover rate was in the range 0–1. The closer the value was to 1,the more evenly distributed the solution set would be. In the pres-ent study, the Pareto solutions obtained by each algorithm showed100 points for one object function, so the number of divisions was100.

3. Multi-objective algorithms

There are a large number of multi-objective optimization algo-rithms as indicated in the Introduction. In this paper, SPEA2, OMO-PSO, AbYSS and MOCell were respectively employed to optimizethe NOx emissions and carbon burnout simultaneously. The focusis on the feasibility of their application to multi-objective optimi-zation of coal-fired utility boiler and comparisons of their perfor-mance. The performance metrics have been mentioned in Section2.4. Prior to application, a brief description of the three multi-objective optimization approaches is presented in the followingsubsection.

3.1. SPEA2

SPEA (Zitzler & Thiele, 1999) has been widely used in manyapplications. However, some shortcomings such as inaccuracyassignment of the fitness and the poor diversity of the resolutionsare reported in previous research. SPEA2 (Zitzler, Laumanns, & Thi-ele, 2000) is proposed to overcome these shortcomings. In SPEA2,the fine-grained fitness assignment strategy is used to replacethe former one and a nearest neighbor density estimation tech-nique is incorporated to allow a more precise guidance of thesearch process. Additionally, an enhanced archive truncationmethod is adopted to guarantee the preservation of boundarysolutions.

Compared with SPEA, SPEA2 is faster in convergence rate andthe Pareto optimal solutions obtained by it have a more uniformdistribution. So far the integral performance of SPEA2 has im-proved significantly. The detailed process of SPEA2 is presentedin reference Zitzler, Laumanns, et al. (2000).

3.2. OMOPSO

The swarm strategy for optimization is first introduced by Ken-nedy and Eberhart (1995) and the particle swarm optimization(PSO) algorithm is based on the simulation of the social behaviorof birds within a flock. The PSO algorithm has been applied inmany single objective optimization problems. To handle multi-objective problems, however, PSO algorithm must be obviouslymodified.

In the OMOPSO algorithm, a crowding factor (Deb et al., 2002) isused to establish a second discrimination criterion (additional toPareto dominance). For each particle, the leader is selected by abinary tournament based on the crowding value of the leader,and the maximum size of the set of leaders is equal to the swarm

260 280 300 320 340 360 380 400 420

260

280

300

320

340

360

380

400

420 Training samplesVerifying samples

Mod

el P

redi

ctio

ns (

ppm

)

Measurement data of NOx emissions (ppm)

Fig. 2. Modeling error of NOx emissions model built by SVR.

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.01.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2 Training samplesVerfying samples

Mod

el p

redi

ctio

ns (

%)

Measurement data of unburned carbon in fly ash (%)

Fig. 3. Modeling error of carbon burnout model built by SVR.

7182 F. Wu et al. / Expert Systems with Applications 38 (2011) 7179–7185

size. The set of the leaders and the corresponding crowding valuesare updated after each generation. This algorithm is featured bythat if the size of the set of leaders is greater than the maximumallowed, only the best leaders are retained based on their crowdingvalue, and the others are eliminated. The detailed process of OMO-PSO could be found in the study by Sierra and Coello (2005).

3.3. AbYSS

Scatter search has been successfully applied to a wide variety ofsingle objective optimization problems (Glover, Laguna, & Marti,2000). AbYSS is proposed by Nebro, Luna, et al. (2006), which isbased on the well-known scatter search template (Glover, 1997).However, the AbYSS can not be considered as scatter search buta hybrid of this algorithm with an evolutionary algorithm, becauseAbYSS combines ideas of state-of-the art evolutionary algorithmsfor solving multi-objective problems. In this algorithm, an externalarchive is used to store the non-dominated solutions founded dur-ing the search, following the scheme applied by PAES, however, theadaptive grid used by PAES is instead by using the crowding dis-tance of NSGA-II; on the other hand, the density estimation usedby SPEA2 is used to the selection of solutions from the initial setto build the reference set. The detailed process of AbYSS could befound in the study by Nebro, Luna, et al. (2006).

3.4. MOCell

It has been proved that the cellular models of genetic algorithms(cGAs) are very effective in solving a diverse set of single objectiveoptimization problems from both real world and classical settings(Alba & Dorronsoro, 2005). The cellular genetic algorithm for mul-ti-objective optimization (MOCell) is proposed by Nebro, Durillo,et al. (2006), which is an adaptation of a canonical cGA to the mul-ti-objective field. The additional feature of MOCell is to return anumber of solutions, from the archive to the population by ran-domly replacing existing individuals (Nebro, Durillo, et al., 2006).This makes MOCell distinct from other multi-objective evolution-ary algorithms. In MOCell, the individual is distributed accordingto a certain topology and only interacts with its nearby neighborsin the breeding loop. The most commonly used population topologyis 2-dimensional toroidal grids, which is adopted by this paper. Allthe individuals distribute in the grids, and each individual occupiesa certain grid, and its neighbors including eight individuals adjacentwith it in the east, south, west, north, southeast, southwest, north-east and northwest directions. The detailed process of MOCell mayfound in the study by Nebro, Durillo, et al. (2006).

4. Result and discussion

4.1. Estimation of NOx emissions and carbon burnout by SVR

In the present study, the optimal SVR parameters (g, C) for NOxemissions model and carbon burnout model are (2.64, 34.30) and(0.47, 238.86), respectively. With the optimal parameters, theSVR models for NOx emissions and carbon burnout could be builteasily. The comparison results between the SVR models and themeasurement data are present in Figs. 2 and 3. The average errorsof the NOx emission model and carbon burnout model were 1.62%and 3.79%, respectively. As for the NOx model, the maximum errorwas 11.32% in the 119th case, and 92% of the cases were less than6%; for the carbon burnout model, the maximum error was 8.37%in the 27th case, and 91% of them were less than 6%. It could beconcluded from the results that the predicted values showed com-paratively good agreement with the measured values and the SVRmodels were feasible and reliable.

4.2. Multi-objective optimization by combining SVR and optimizationmethods

4.2.1. Parameter settings for various algorithmsA set of parameter settings were chosen to guarantee a fair

comparison of the algorithms. An internal population size equalto 100 was adopted by two evolutionary algorithms (SPEA2 andMOCell); OMOPSO was configured with 100 particles and with amaximum number of 100 leaders. AbYSS used a population sizeof 20, which was also the size of the reference Nebro, Luna, et al.(2006) set, and the size of external archive was 100. In MOCell, atoroidal grid of 100 individuals (10 � 10) was chosen to structurethe population and an archive of 100 individual was used. Simu-lated binary crossover (SBX) and polynomial mutation operatorswere respectively adopted as the crossover operator and mutationoperator by SPEA2 and MOCell. The distribution indices for theoperators were gc = 20 and gm = 20, and probabilities Pc = 0.9 andPm = 1/n, for crossover and mutation respectively, where n wasthe number of decision variables. Two types of mutation operators,uniform and non-uniform were used by OMOPSO. For AbYSS, poly-nomial mutation was used in the local search procedure and SBXwas used as the solution recombination method. For all the algo-rithms, 25,000 function evaluations were required to obtain 100

1.3 1.4 1.5 1.6 1.7 1.8 1.9324

326

328

330

332

334

336

338N

Ox

emis

sion

s (p

pm)

Unburned carbon in fly ash (%)1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

324326328330332334336338

NO

x em

issi

ons

(ppm

)

Unburned carbon in fly ash (%)1.3 1.4 1.5 1.6 1.7 1.8 1.9

324326328330332334336338

NO

x em

issi

ons

(ppm

)

Unburned carbon in fly ash (%)1.3 1.4 1.5 1.6 1.7 1.8 1.9

324326328330332334336338

NO

x em

issi

ons

(ppm

)

lleCOM)d(SSYbA)c(OSPOMO)b(2AEPS)a(Unburned carbon in fly ash (%)

Fig. 4. Pareto-optimal front obtained by algorithms.

Fig. 5. Comparison of SPEA2, OMOPSO, AbYSS and MOCell by RNI.

Fig. 6. Comparison of SPEA2, OMOPSO, AbYSS and MOCell by cover rate.

F. Wu et al. / Expert Systems with Applications 38 (2011) 7179–7185 7183

resolutions which were sufficient for convergence for the problemhere.

4.2.2. Performance comparisonsDuring the experiments, both NOx emissions and unburned car-

bon in fly ash of the 53rd case were returned in high values(352.8 ppm, 2.09%) compared with other cases. Therefore, the opti-mization procedures were executed on this case.

In this paper, all calculations were performed on a 2.01 GHz,AMD Athlon 64 X2 Dual PC with 2 GB of RAM under Window XP(32 bit). All the above algorithms were coded in the Java languageenvironment version 1.6.0 u6. The 100 resolutions obtained bySPEA2 costed 13469 ms CPU time, MOCell 3781 ms, AbYSS2391 ms, and OMOPSO only 2281 ms. It means that OMOPSO isthe fastest algorithm in the experiments, and AbYSS and MOCellare slightly slower than MOCell. SPEA2 is the slowest and its exe-cution time is one order higher than the others.

In order to calculate the cover rate of each algorithm, the max-imum and minimum values of each object function should be as-signed. The boiler load was determined by operating condition,and all the optimization procedures were performed on the 53rdcase with the boiler load of 303.1 MW. The maximum and mini-mum values of NOx emissions model were 375.40 ppm and323.02 ppm. These were equal to the maximum and the minimumvalues in the experiments where the boiler load was 303.1 MW.The maximum value of carbon burnout model was 2.4, whichwas also equal to the maximum value of unburned carbon in flyash in the experiments with the boiler load 303.1 MW. The mini-mum value of unburned carbon in fly ash was set as 1, which isan empirical value.

The Pareto-optimal fronts obtained by each algorithm areshown in Figs. 4. Fig. 5 shows the evaluation results of the obtainedsolution set using RNI and Fig. 6 shows the corresponding resultsusing the cover rate.

As shown in Fig. 4, the NOx emissions optimized by the algo-rithms vary in the following range: 325.2–337.7 ppm by SPEA2,324.9–337.6 ppm by OMOPSO, 324.8–337.7 ppm by AbYSS,324.9–337.7 ppm by MOCell; the corresponding unburned carbonin fly ash optimized vary in the following range: 1.3–1.8%, 1.3–1.9%, 1.3–1.9% and 1.3–1.9%. Due to the large size of the result, onlythe resolutions with small NOx emissions obtained by each algo-rithm are listed in Table 1. From Table 1, it could be concluded thatthe NOx emissions and unburned carbon in fly ash after optimiza-

tion have been reduced to different degrees; moreover, the trend ofair distribution obtained by each algorithm are almost the same.The primary air velocities change slightly, as they are mainly usedto transport the pulverized coal, which is limited by the mill feederand boiler load (Zheng et al., 2008). Compared with primary airvelocities, the secondary air velocities change significantly. Thedistribution of the A–E levels of secondary velocity after optimiza-tion is closer to inverse tower-like. This kind of air distributionscheme makes the secondary air more rigid and enhances its abil-ity to suspend the fuel powder, which reduces the unburned car-bon in fly ash and in turn reduces the thermal losses of theboiler, a conclusion consistent with the operation experience.Additionally, this kind of air distribution scheme forms high fuel/air stoichiometric ratio at lower location of the furnace resultingin lower NOx emissions. The analyses demonstrate the resolutionsobtained by the three methods are reasonable, and all the threemulti-objective methods are feasible.

As shown in Fig. 5, the accuracy of the solution set obtained byOMOPSO is the best, which is better than the others. Additionally,the accuracy of the solution set obtained by AbYSS is the lowest.From Fig. 6, it could be concluded that the range covered of theinterval of the solution set obtained by AbYSS is superior to others

Table 1Comparison of the 53rd case before and after executing optimizations.

NOx emissions(ppm)

Unburned carbonin fly ash (%)

Load (MW) Primary air velocities (m/s) Secondary air velocities (m/s)

A B C D A B C D E F

Field data before optimization 352.8 2.1 303.1 26.4 28.0 26.4 27.3 32.5 29.8 33.5 31.3 33.0 2.9SPEA2 325.2 1.8 303.1 26.2 28.2 26.7 27.1 31.2 28.9 24.8 32.0 35.4 7.2OMOPSO 324.9 1.9 303.1 26.2 28.1 26.9 27.1 31.1 28.4 24.8 31.9 34.8 7.4AbYSS 324.8 1.9 303.1 26.2 28.1 26.9 27.1 31.3 28.6 24.9 31.8 34.9 7.4MOCell 324.9 1.9 303.1 26.2 28.1 26.8 27.1 31.1 29.0 24.7 31.7 35.0 7.3

7184 F. Wu et al. / Expert Systems with Applications 38 (2011) 7179–7185

(the cover rate of SPEA2, OMOPSO, AbYSS and MOCell are 30%, 34%,34.5% and 35%, respectively). In addition, the range covered andcloseness of the interval of the solution set obtained by SPEA2 isthe lowest.

In summary, it is concluded that the OMOPSO algorithm, for thecases studied in this paper, shows much better results than otheroptimization approaches in terms of accuracy; at the same time,it takes less CPU time to execute than others. Considering thediversity, AbYSS is the best, but is just slightly better than OMOPSOand MOCell.

5. Conclusions

The present study aims at comparing various optimization algo-rithms applied in the coal-fired utility boiler for multi-objectiveoptimization. SVR was employed to build the models for NOx emis-sions and carbon burnout, and the predicted NOx emissions andcarbon burnout from the SVR models showed good agreement withthe measurement. Three multi-object optimization algorithmswere respectively presented for realizing Pareto-based multi-objec-tive optimization of the coal-fired boiler by carefully setting theoperational parameters. The results show that the method combin-ing SVR and multi-objective algorithms could effectively reduceNOx emissions and unburned carbon in fly ash of the coal-fired boi-ler simultaneously. Detailed comparisons among the three algo-rithms were made in terms of accuracy, diversity and theconvergence rate. The results show that OMOPSO algorithm is thebest in terms of the accuracy and convergence rate. AbYSS has a bet-ter diversity but the worst accuracy. SPEA2 is the slowest algorithmand its execution time is one order higher than other algorithms.Therefore, OMOPSO and MOCell are the proposed algorithms foronline multi-object optimization of coal-fired boilers.

Acknowledgements

This work was supported by the National Natural Science Foun-dation of China (60534030), Zhejiang Provincial Natural ScienceFoundation of China (R107532), Program for New Century Excel-lent Talents in University (NCET-07-0761), a Foundation for theAuthor of National Excellent Doctoral Dissertation of China(200747) and Zhejiang University K.P. Chao’s High TechnologyDevelopment Foundation (2008RC001), the Program of IntroducingTalents of Discipline to University (B08026) and National Basic Re-search Program of China (2009CB219802).

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