Computers and Chemical Engineering 30 (2006) 1019–1025

Multiobjective optimization of synthesis gas production usingnon-dominated sorting genetic algorithm

Swati Mohanty ∗Regional Research Laboratory, Bhubaneswar 751013, India

Received 8 November 2004; received in revised form 9 December 2005; accepted 17 January 2006Available online 18 April 2006

Abstract

Synthesis gas finds wide applications in various chemical industries. Various routes for manufacture of synthesis gas have been reported such assteam reforming of methane, carbon dioxide reforming of methane, partial oxidation of methane and combination of both carbon dioxide reformingand partial oxidation of methane. However, very few studies have been reported on optimization of process parameters for synthesis gas production.These processes have multiple objective functions that are conflicting in nature and hence use of single objective optimization technique is notsuitable. In this study therefore real parameter non-dominated sorting genetic algorithm has been used to obtain a Pareto optimal set of processpTmm©

K

1

kocgRcN1S1o2osw

0d

arameters for production of synthesis gas from combined carbon dioxide reforming and partial oxidation of natural gas over a Pt/�-Al2O3 catalyst.he objectives are to maximize the conversion of methane, maximize the selectivity of carbon monoxide and maintain the hydrogen to carbononoxide mole ratio at approximately 1. The variables that have been taken are temperature, gas hourly space velocity and the oxygen to methaneole ratio. The results have been compared with that reported by other authors.2006 Elsevier Ltd. All rights reserved.

eywords: Non-dominated sorting genetic algorithm; Synthesis gas; Multi-objective optimization

. Introduction

Mixtures of carbon monoxide and hydrogen, commonlynown as synthesis gases, are produced for the manufacturef ammonia, hydrogen, liquid hydrocarbons, alcohols and otherhemicals. The most common method of production of synthesisas is by steam reforming of natural gas (Bartholomew, 1982;ostrup-Nielsen, 1984; Trimm, 1977). Other methods includearbon dioxide reforming of methane (Song, Choi, Yue, Lee, &a, 2004), partial oxidation of methane (De Groote & Froment,996; Hayakawa et al., 1997; Nakagawa, Ikenaga, Kobayashi, &uzuki, 2001; Nakagawa, Ikenaga, Teng, Kobayashi, & Suzuki,999; Ritchie, Richardson, & Luss, 2001; Takehira et al., 1995)r combination of both (Larentis, de Resende, Salim, & Pinto,001). Combination of steam reforming and partial oxidationf methane has also been reported (Gosiewski, 2001). Besides,ynthesis gas from coal (Frolov et al., 1993; Qiu et al., 2004),aste and biomass (Panigrahi, Dalai, Chaudhari, & Bakhshi,

∗ Tel.: +91 674 2581635; fax: +91 674 2581637.

2003; Tomishige, Asadullah, & Kunimori, 2004) gasificationhas also been reported. Synthesis gas is produced in differentratios of H2/CO viz. 1, 2 or 3, depending on the purpose forwhich it has to be used. Larentis et al. (2001) have optimizedthe process conditions for production of synthetic gas so as toobtain a H2/CO ratio close to 1. This ratio is suitable for man-ufacture of oxygenated hydrocarbons, heavy hydrocarbons byFT process and polycarbonated products.

Although a number of papers on production of synthesisgas are available, very few have tried to optimize the processconditions to get the maximum benefit. From among these fewstudies on optimization, most of them are qualitative in nature(Asadullah et al., 2003; Coetzer & Keyser, 2003; Marnasidou,Voutetakis, Tjatjopoulos, & Vasalos, 1999). Coetzer and Keyser(2003) have developed response surface models using designof experiment technique for optimizing the process variablesto maximize the pure gas yield for coal gasification to pro-duce synthesis gas. The second objective function, i.e. O2/puregas yield ratio was not considered for optimization. Use ofmulti-objective optimization technique in this case could helpin obtaining more realistic optimized parameters. Similarly,

E-mail address: swati mohanty@yahoo.com. Asadullah et al. (2003) have reported the optimum equivalence

098-1354/$ – see front matter © 2006 Elsevier Ltd. All rights reserved.oi:10.1016/j.compchemeng.2006.01.002

1020 S. Mohanty / Computers and Chemical Engineering 30 (2006) 1019–1025

Nomenclature

CCH4 methane conversion (%)CO2/CH4 carbon dioxide/methane feed ratio (gmol/gmol)dij normalized Euclidean distance between i and jfi ith dummy fitness functionf

′i ith shared fitness value

Fi ith objective function, i = 1, 2, 3GHSV gas hourly space velocity (h−1)�H298 K heat of reaction at 298 K (kJ/gmol)H2/CO hydrogen/carbon monoxide ratio (gmol/gmol)HC hydrocarbon (gmol)O2/CH4 oxygen/methane feed ratio (gmol/gmol)mi niche count for ith solutionnk number of solutions in the kth rankp probabilityp′ cumulative probabilityP number of decision variablesSCO carbon monoxide selectivity (%)Sh sharing functionTEMP temperature (◦C)x

(j)i ith decision variable of jth gene

Greek lettersα a parameter for extending the variable rangeλ a parameter in cross-over operator (Eq. (8))σshare a parameter in sharing function

ratio, defined as (supplied oxygen weight)/(dry biomassweight)/(stoichiometric oxygen weight/dry biomass weight forcomplete combustion), and biomass feeding rate, to maximizethe rate of gaseous product formation and carbon-based con-version to gas (defined as (A/B) × 100, where A is the rate offormation of (CO + CO2 + CH4) and B is the supplying rate oftotal carbon from biomass) and minimize the formation of car-bon which deposit on the catalyst surface, for production ofsynthesis gas from biomass. They have used an experimentalapproach to process parameter optimization. This method maynot actually lead to the global optimum and therefore one shouldadopt multi-objective optimization techniques for optimizing theparameters. Marnasidou et al. (1999) have only given a quali-tative reasoning for maximizing the conversion of methane tosynthesis gas by partial oxidation in a spouted-bed reactor byoptimizing the parameters such as the freeboard design, % Ni inthe catalyst, bed depth and the particle size. Larentis et al. (2001)have used design of experiment technique for developing empir-ical models and then optimized the process parameters. Theyhave however used single objective optimization technique foroptimizing the parameters, although there are multiple (three)objective functions. These objective functions are conflictingin nature and can be better handled using a multi-objectiveoptimization technique. In general, it is noticed that there is alacunae in the area of process parameter optimization for mostof the studies reported on synthesis gas manufacture. In thisp

al. (2001) have been used to optimize the process parametersusing real parameter non-dominated sorting genetic algorithm(NSGA) and the results compared with that reported by them.

2. Synthesis gas production method

Although there are various routes for production of synthesisgas, the experimental method reported by Larentis et al. (2001)has been described here. They have used a combined methodof carbon dioxide reforming and partial oxidation of natural gasover a Pt/�-Al2O3 catalyst for production of synthesis gas havinga H2/CO ratio of approximately 1. This method of productionof synthesis gas results in a very low H2/CO ratio and it is eas-ier to control the reactor temperature as it is a combination ofhighly exothermic reaction of methane oxidation and moderatelyendothermic reaction of carbon dioxide reforming of methane.The experiments were carried in a micro U-shaped tubular reac-tor built of quartz and the catalyst placed in it. The reactantswere natural gas, consisting of 79% CH4, 17% C2H6 and 4%C3H8, compressed dried air over molecular sieve consisting of20% O2, 79% N2 and 1% Ar and ultra pure CO2 (99.99%).

More details can be found elsewhere (Larentis et al., 2001).To obtain maximum information with minimum number ofexperiments, the experiments have been carried out using threelevel full factorial design at temperatures (TEMP) 600, 850 and1 ◦aaccc

t

smtw

2

ssmtfitmootm

aper therefore, the objective functions given by Larentis et

100 C, gas hourly space velocity (GHSV) of 10,000, 15,000nd 20,000 h−1 and oxygen to methane feed mole ratio (O2/CH4)t 0.25, 0.4 and 0.55, i.e. at combinations of lower, upper andentral points. Replicates of eight experiments have also beenarried out for estimating the pure error. Therefore, they havearried out a total of 35 experiments.

The combined reaction of carbon dioxide reforming and par-ial oxidation of natural gas is given as:

2CH4 + CO2 + 12 O2 → 3CO + 4H2,

�H298 K = 211 kJ/gmol (1)

To theoretically analyse the effect of the various parametersuch as gas hourly space GHSV, TEMP and O2/CH4 ratio onethane conversion, carbon monoxide selectivity and hydrogen

o carbon monoxide mole ratio, both first principle models asell as empirical models have been developed by them.

.1. Genetic algorithm for optimization

Conventional optimization methods are grouped as directearch method, which uses the objective function and the con-traints for finding the optimum and the other is the gradientethod, which use the first or the second derivative of the objec-

ive function and/or the constraints to reach the optimum. Therst method is slow and the second method cannot be applied

o discontinuous and non-differentiable functions. In addition,ost of the real life problems require optimization of several

bjective functions and hence require use of multi-objectiveptimization techniques. Traditionally, multi-objective func-ions are reduced to a single objective function by various

ethods and then solved as a single objective optimization tech-

S. Mohanty / Computers and Chemical Engineering 30 (2006) 1019–1025 1021

nique. The various methods are weighting method, �-constraintmethod, goal programming method, modified game theory, etc.(Sunar & Kahraman, 2001). All these methods depend on theuser’s decision to specify weights to the different objective func-tions and therefore dependent highly on the judgment of theuser. Thus the user must have good knowledge on fixing thepriority for the different objective functions to form a singleobjective function from multiple objective functions. The usermay change the priorities and solve the problem to get a numberof solutions. The set of all the solutions is known as the Pareto-optimal set and the corresponding objective value vectors areknown as Pareto-optimal front, but the Pareto optimal set cannotbe obtained simultaneously in a single run. Genetic algorithm(GA), which works on the principle of natural genetics has theadvantage of obtaining the Pareto optimal set in a single run asit works with a population of points rather than with a singlepoint. In the simplest form, the basic working principle of GAconsists of random selection of values for the variables (codedor real), which constitutes the population, calculation of the fit-ness value and then subjecting the population to reproduction,crossover and mutation so as to obtain a new population. Thisnew population is also evaluated and checked to see whetherit meets the termination criteria. The concept of GA was firstintroduced by Prof. John Holland of University of Michiganand since then a number of modified forms of this simple GAhave been reported by several authors. Some of them includeS((PiA(scUlpaautasir(rBtcacchdo

flotation circuit. Optimal design and operating parameters foran industrial ethylene reactor using NSGA-II has been carriedout by Tarafder, Lee, Ray, and Rangaiah (2005). These studiestestify that GA is a useful tool for multi-objective optimizationproblems.

In the present study a real parameter NSGA with blendcrossover is used for optimizing the temperature, oxygen tomethane mole ratio and gas hourly space velocity for maximiz-ing the conversion of methane and carbon monoxide selectivitywhile maintaining the hydrogen to carbon monoxide ratio closeto 1. Real parameter GA is more suitable to handle continuousfunctions, as number of difficulties has been noticed when usingbinary coded parameter. Firstly, it is not possible to achieve anyarbitrary degree of accuracy in the optimal solution and accu-racy depends on the length of the binary string. Secondly, certainbinary strings may be associated with Hanning cliffs so that anytransition to a neighbouring solution may necessitate changingmany bits of the string. The various steps involved in NSGA areas follows.

2.2. Selection operator

An initial population N is chosen randomly within the rangeof the decision variables. The objective functions are calculatedfor each of the member of the population. The dominating mem-ber is that, which satisfy the conditions that it is not worse inatofiitmwaIpovmvEou

d

wa

σ

wh

chaffer’s (1985) vector evaluated GA, Fonseca and Fleming’s1993) multi-objective GA, Horn, Nafploitis, and Goldberg’s1994) niched Pareto GA, Zitzler and Thiele’s (1998) strengthareto approach, Srinivas and Deb’s (1994) non-dominated sort-

ng genetic algorithm (NSGA), the elitist NSGA-II (Deb, Pratap,garwal, & Meyarivan, 2002) and NSGA-II with jumping gene

Kasat & Gupta, 2003). In the last one decade, a number oftudies on optimization of operating and design parameters forhemical processes using GA have been reported in literature.preti and Deb (1997) have used GA for optimizing the reactor

ength for ammonia synthesis with respect to the top reactor tem-erature so as to maximize the profit. Rajesh, Gupta, Rangaiah,nd Ray (2001) have used NSGA to maximize the export steamnd hydrogen production rate in a hydrogen production plantsing steam reforming of methane by optimizing gas tempera-ure, pressure and composition in the steam reformer as wells temperature of the high temperature and low temperaturehift converters. Optimization of substrate feed rate and switch-ng time for maximizing the performance index in a fed batcheactor using GA has been carried out by Sarkar and Modak2003). The two case studies include, production of secretedecombinant protein and biphasic growth of yeast. Silva andiscaia (2003) have used GA to obtain a Pareto optimal set of

emperature and initiator feed so as to maximize the monomeronversion and minimize the residual initiator concentration forbatch styrene polymerization process. Optimization of pro-

ess parameters to maximize yield of gasoline and minimizeoke formation using NSGA-II with jumping genes for a FCCUas been reported by Kasat and Gupta (2003). Guria et al. (2005)emonstrate the use of NSGA-II with jumping gene to obtainptimal solutions to maximize recovery and grade in a two-cell

ll the objectives than the dominated member and at least betterhan the dominated member in one objective. Thus the membersf the population are ranked according to their domination. Therst set of non-dominated members is ranked one. After exclud-

ng these members from the population the procedure is repeatedo find the second set which has rank two and so on till all the

embers in the population are ranked. The non-dominated set,hich has the lowest rank, has the highest fitness value, as they

re the best solution. Fitness values are assigned in two stages.nitially they are assigned dummy fitness values based on theopulation size and in the second stage based on the crowdingf the solutions at the front, fitness values are assigned to indi-idual using a sharing function (Srinivas & Deb, 1994). Theembers in the lowest rank are first assigned a dummy fitness

alue (fi) equal to the size of the population. Next the normalizeduclidean distance (dij) between each member i, and all of thether non-dominated members, j, in the same rank is calculatedsing the equation

ij =

√√√√√P∑

p=1

(x(i)p − x

(j)p )

2

xup − x1

p

, (2)

here x is the decision variable, P the number of decision vari-bles and u and l refer to the upper and lower limit, respectively.

The sharing function depends on a pre-specified parameter,

share ≈ 0.5P√

q, (3)

here q is the number of Pareto optimal solutions. However, itas been reported that q ≈ 10 works well in many cases (Deb).

1022 S. Mohanty / Computers and Chemical Engineering 30 (2006) 1019–1025

A sharing function Sh(dij) based on the difference betweendij and σshare is defined as

Sh(dij) =

⎧⎪⎨⎪⎩

1 −(

dij

σshare

)2

, if dij < σshare

0, if dij ≥ σshare

(4)

The niche count, mi, for each member, i, is calculated fromthe sharing function as:

mi =nk∑

j=1

Sh(dij)2 (5)

where nk is the number of members in the kth rank.The shared fitness value (fi

′) is then calculated as:

fi′ = fi

mi

(6)

The shared fitness is calculated for all the members in the low-est rank. Next a dummy fitness value is assigned to the membersin the next higher rank so that it is less than the minimum fitnessvalue of the members in the lower rank, and the steps repeatedto obtain the shared fitness value. The procedure is repeated tillshared fitness value for all the members and all the ranks areobtained.

The roulette-wheel selection procedure is then followed tosNfitSlew

p

oott0tp

2

bv

x

bf

extending the range of the decision variable by an amount α

times the difference between the two parents on either side ofthe region bounded by the two parents. In many cases, α = 0.5 hasbeen found to give good results. Thus the range can be writtenas

[x(j)i − α(x(k)

i − x(j)i ), x(k)

i + α(x(k)i − x

(j)i )] (9)

2.4. Mutation operator

Mutation operation is carried out to maintain the diversityin the population. Different types of mutation operators areavailable in literature, but in the present study random muta-tion operator has been used. The decision variable of a parentto be mutated is assigned a random (uniform) number from therange of that decision variable.

The process of evaluation, selection, crossover and mutationrepresents one generation. These operations are carried out forpre-assigned number of generations to get the best set of solu-tions.

2.5. Model equations for process parameter optimisation

Larentis et al. (2001) have reported both pseudo-phenomenological as well as empirical models for combinedcTwntstamia

F

w

F

w

F

bGsmrcm

elect the N members. In this method the wheel is divided intodivisions, the size of the divisions being proportional to the

tness value of the members. The wheel is spun N number ofimes and the member to which the pointer points is selected.ince the size of the member with higher fitness value will be

arger, the probability of it being selected is also higher. Math-matically, the probability of ith member being selected can beritten as:

i = f ii∑N

j=1fij

(7)

The cumulative probability (p′i) of ith member can be

btained by adding the individual probabilities starting from topf the list till the ith member. The ith member is represented byhe cumulative probability value between p′

i−1 and p′i. In order

o choose N members, N random numbers are chosen betweenand 1 and the member in whose cumulative probability range

hese numbers lie are selected as the new N members of theopulation for further operation.

.3. Crossover operator

Crossover operator is responsible for searching of new mem-ers, which could possibly have better fitness. For two parentalues of the decision variable xi, x

(j)i and x

(k)i :

newi = (1 − λ)x(j)

i + λx(k)i , 0 ≤ λ ≤ 1 (8)

In the present paper, blend crossover operator, first suggestedy Eshelman and Schaffer (1993), is used in which a new valueor the decision value is created uniformly and randomly by

arbon dioxide reforming and partial oxidation of natural gas.hey found that predictions made by the empirical modelsere better than the phenomenological model as it had aumber of adjustable parameters. As the authors have usedhe empirical models for process optimization, in the presenttudy, the empirical models given by them have been used sohe results could be compared. The three objective functionsre the percent methane conversion (CCH4 ), percent carbononoxide selectivity (SCO) and hydrogen to carbon monox-

de mole ratio (H2/CO). These objective functions are defineds,

1 = CCH4 (%) =(

mol HCin − mol HCout

mol HCin

)× 100 (10)

here HC represents hydrocarbon.

2 = SCO(%) =(

mol COout∑mol of jout

)× 100 (11)

here j = CO, CO2, H2, H2O and CH4.

3 = H2

CO= mol H2 out

mol COout(12)

The empirical models for the objective functions were builtased on analysis of variance (ANOVA) with decision variables,SHV, TEMP and O2/CH4. Those terms that were statistically

ignificant within 95% confidence level were included in theodels and others eliminated. Therefore, models obtained were

educed quadratic and reduced cubic models. Table 1 lists theoefficients of the terms when the decision variables are in nor-alized form (Larentis et al., 2001). In this problem it is desired

S. Mohanty / Computers and Chemical Engineering 30 (2006) 1019–1025 1023

Table 1Co-efficients for the objective functions

Objective function

F1 = CCH4 F2 = SCO F3 = H2/CO ratio

Constant 86.74 39.46 1.29(O2/CH4)n 14.6 5.98 –(GHSV)n −3.06 −2.40 –(TEMP)n 18.82 13.06 −0.45(O2/CH4)n(GHSV)n 3.14 2.50 −0.112(GHSV)n(TEMP)n – 1.64 −0.142(O2/CH4)2

n −6.91 −3.90 0.109(TEMP)2

n −13.31 −10.15 0.405(GHSV)2

n(O2/CH4)n – −3.69 –(TEMP)2

n(GHSV)n – – 01.67

to maximize F1 and F2 while keeping F3 close to 1.0. The con-straints are:

0.25 ≤ O2

CH4≤ 0.55 gmol/gmol (13)

10, 000 ≤ GHSV ≤ 20, 000 h−1 (14)

600 ≤ TEMP ≤ 1100◦C (15)

The three decision variables i.e. GHSV, TEMP and O2/CH4in normalized form can be represented by

(xi)n = xi − xi,min

xi,max − xi,min(16)

where (xi)n is the normalized ith decision variable and xi,min andxi,max are the minimum and maximum value for the ith decisionvariable, respectively. The normalized decision variable has thevalue between 0 and 1.

3. Results and discussions

The objective functions were optimized fulfilling the con-straints given in Eqs. (13)–(15). As stated earlier the NSGAalgorithm was used for obtaining the Pareto optimal solutions.A MATLAB code for real-parameter NSGA described in earliersection has been used to optimize the parameters. A popula-tion size of 20 was chosen with crossover probability of 0.9 andmfosdgc1ogowbIaw

Table 2Non-dominated Pareto optimal solutions after 200 generations

No. O2/CH4

mole ratioGHSV(h−1)

Temperature(◦C)

H2/COmole ratio

CCH4

(%)SCO

(%)

1 0.5088 15993 920.2 1.18 ∼100.0 45.232 0.3983 17968 868.5 1.13 97.33 44.163 0.4417 18374 856.4 1.13 98.51 44.104 0.5125 13159 926.3 1.21 ∼100.0 45.865 0.3886 15636 911.0 1.15 97.65 44.926 0.4823 17169 913.4 1.15 ∼100.0 44.897 0.5161 18565 840.5 1.14 99.98 43.758 0.3986 14461 896.8 1.16 98.08 45.199 0.4075 13398 892.5 1.17 98.47 45.42

10 0.4454 18197 899.0 1.13 98.97 44.4411 0.4648 12526 902.3 1.20 99.95 45.8612 0.4335 16729 895.4 1.14 98.78 44.8813 0.5109 18609 962.0 1.16 ∼100.0 44.3014 0.4138 11597 920.2 1.19 99.02 45.7115 0.4777 17892 877.4 1.14 99.64 44.4516 0.3521 18550 861.7 1.12 95.41 43.5917 0.4506 14109 915.1 1.18 99.58 45.6218 0.4571 16381 892.6 1.15 99.41 45.0419 0.4011 17965 896.4 1.13 97.64 44.3420 0.4190 17440 908.6 1.14 98.35 44.65

Fig. 1. 3D Pareto optimal front after two generations.

Fig. 2. 3D Pareto optimal front after 50 generations.

utation probability of 0.1. The different operations were per-ormed for 200 generations to obtain the non-dominated Paretoptimal solutions. The non-dominated Pareto optimal solutionets after 200 generations are shown in Table 2 and the 3D non-ominated Pareto optimal front after 2, 50, 100, 150 and 200enerations are shown in Figs. 1–5 respectively. In some of theases where the estimated methane conversion was slightly over00%, which could be due to model error, have been roundedff to 100% in Table 2. It can be seen from Fig. 1 that after twoenerations, 11 non-dominated Pareto optimal solutions werebtained. With successive generations the dominated solutionsere eliminated and replaced by better solutions so that the num-er of non-dominated Pareto optimal solutions increased to 20.t is also seen that with the increase in the number of gener-tions, better solutions are obtained i.e. F1 and F2 increases,hereas F3 approaches 1. The solutions listed in Table 2 show

1024 S. Mohanty / Computers and Chemical Engineering 30 (2006) 1019–1025

Fig. 3. 3D Pareto optimal front after 100 generations.

Fig. 4. 3D Pareto optimal front after 150 generations.

that each of the solutions is better than the other in at least oneof the objective functions. In most of the solutions, the methaneconversion is almost complete with a minimum of 95.4%. TheCO selectivity varies between 43.59% and 45.86%, and H2/COmole ratio varies between 1.13 and 1.21. From Table 1 it can

Fig. 5. 3D Pareto optimal front after 200 generations.

be seen that although GHSV has no effect on F3, interactions ofGHSV and TEMP as well as GHSV and O2/CH4 are significant.Other significant interactions between the decision variables forthe objective functions can be also seen in the table.

When comparing the operating conditions, the O2/CH4 moleratio varies between 0.35 and 0.52 the GHSV varies between11,597 and 18,609 h−1, and temperature between 840.5 and962.0 ◦C. In order to get higher carbon monoxide selectivitya higher temperature, higher O2/CH4 and lower GHSV have tobe adopted whereas to get H2/CO mole ratio approximately 1,a lower temperature, lower O2/CH4 and higher GHSV has tobe adopted. Conversion of methane is almost complete in mostof the cases. These show the conflicting nature of the objectivefunctions. Thus the user has to decide on the operating conditionsbased on the ease of operation, experience, the cost involved andalso the quality of the product.

Larentis et al. (2001) have optimized each of the objectivefunctions individually using single objective optimization tech-nique. They have arrived at a solution that at O2/CH4 moleratio of 0.55 and at temperature of 950 ◦C, the conversion ofmethane is complete, carbon monoxide selectivity is 43% andthe H2/CO mole ratio is 1.3. They have also reported that themodels are not sensitive to GHSV and can be operated at anyvalue and have therefore not reported any optimum value ofGHSV. But the present study shows that in order to increasethe carbon monoxide selectivity, a lower GHSV is desirableaossitspgt

4

hcfsi41aennttrbap

nd to maintain the H2/CO at 1, a higher GSHV is better. Inrder to arrive at these solutions, the authors have carried outeveral runs which is not only cumbersome but also time con-uming. Also they have reported only a single solution whereasn multi-objective optimization with conflicting objective func-ions, a number of optimal solutions are possible each beingomeway better than the other. This has been shown in theresent study. The solutions obtained by using NSGA alsoive better results than that using single objective optimizationechnique.

. Conclusions

The real parameter non-dominated sorting genetic algorithmas been used to optimize the process parameters for combinedarbon dioxide reforming and partial oxidation of natural gasor production of synthesis gas. Twenty optimal non-dominatedolutions have been obtained so that the conversion of methanes between 95.4% and 100%. The CO selectivity is between3.59% and 45.86%, and H2/CO mole ratio between 1.13 and.21. The solutions obtained by non-dominated sorting geneticlgorithm have been compared with that reported by Larentist al. (2001) who have used single objective optimization tech-ique for optimizing the objective function individually. Sinceon-dominated sorting genetic algorithm deals with a popula-ion of points, spread over the search region, simultaneously,he chances of obtaining the global optimal solution is high. Theesults obtained in the present study are better than that reportedy Larentis et al. (2001). Thus non-dominated sorting geneticlgorithm can be used effectively for multi-objective processarameter optimization.

S. Mohanty / Computers and Chemical Engineering 30 (2006) 1019–1025 1025

Acknowledgement

The author acknowledges the Director, Regional ResearchLaboratory, Bhubaneswar, for permission to publish this paper.

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