MULTI-LEVEL GROUPING GENETIC ALGORITHMFOR LOW CARBON VIRTUAL PRIVATE CLOUDS

Fereydoun Farrahi Moghaddam, Reza Farrahi Moghaddam and Mohamed CherietSynchromedia Laboratory, Ecole de Technologie Superieure, Montreal, QC, Canada

fffarrahi, rfarrahig@synchromedia.ca, mohamed.cheriet@etsmtl.ca

Keywords: Cloud Computing, Virtual Private Cloud, Green IT, Carbon Footprint, Genetic Algorithm, Multi-levelGrouping.

Abstract: Optimization problem of physical servers consolidation is very important for energy efficiency and cost reduc-tion of data centers. For this type of problems, which can be considered as bin-packing problems, traditionalheuristic algorithms such as Genetic Algorithm (GA) are not suitable. Therefore, other heuristic algorithms areproposed instead, such as Grouping Genetic Algorithm (GGA), which are able to preserve the group featuresof the problem. Although GGA have achieved good results on server consolidation in a given data center, theyare weak in optimization of a network of data centers. In this paper, a new grouping genetic algorithm is in-troduced which is called Multi-Level Grouping Genetic Algorithm (MLGGA), and is designed for multi-levelbin packing problems such as optimization of a network of data centers for carbon footprint reduction, energyefficiency, and operation cost reduction. The new MLGGA algorithm is tested on a real world problem in asimulation platform, and its results are compared with the GGA results. The comparison shows a significantincrease in the performance achieved by the proposed MLGGA algorithm.

1 INTRODUCTION

Global warming and its impacts on our life is one ofthe biggest twenty-first century’s challenges for hu-man societies. There are different reasons for globalwarming, but one of main reasons is known to be ex-cessive Green House Gases (GHG) emissions. Nowa-days, the share of ICT sector in the total GHG emis-sions is not greater than 2% (McKinsey, 2007). How-ever, according to rapid growth of ICT sector withinthe ICT enabling effect (Webb, 2008), in near future,GHG emission reduction in ICT sector will be veryimportant.

After introduction of virtualization technology,physical server consolidation plays an important rolein energy efficiency and GHG emission reduction indata centers (Beloglazov et al., 2010)(Gmach et al.,2009)(Liu et al., 2009). In this type of problems, theobjective is fulfilled by minimizing the energy con-sumption, carbon footprint, cost, or a mixture of them.Considering the locations of VMs as variables of theproblem and one of the aforementioned cost func-tions, the consolidation problem can be written as abin-packing optimization problem. Bin packing algo-rithms such as improved First Fit Decreasing (FFD)and Least Loaded (LL) (Ajiro and Tanaka, 2007) as

well as heuristic optimization algorithms can be usedin order to solve this type of problems.

Because of high complexity of this kind of op-timization problems, heuristic algorithms are goodcandidates for them. But traditional general heuris-tic algorithms such as GA are not able to provide agood solution for the special case of server consoli-dation (Xu and Fortes, 2010). Particular genetic op-erators which take advantage of the group-orientedstructure of cost function, could lead the genetic al-gorithm to better results compare to the non-groupingheuristic algorithms which are not aware of that struc-ture. For example, the GGA has been used to achievemore efficient results in various works (Xu and Fortes,2010)(Agrawal et al., 2009)(Wilcox et al., 2011).These new methods are proven to have better resultsthan traditional methods and global heuristic algo-rithms.

Ability to migrate virtual machines in a livelymanner from one data center to another datacenter without service interruption (Clark et al.,2005)(Van der Merwe et al., 2010)(Wood et al.,2010)(Wood et al., 2009)(Farrahi Moghaddam andCheriet, 2010), opens the door to more complex archi-tectures and behaviors of connected data centers andbrings higher opportunity for GHG, and mainly car-

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bon footprint reduction (Farrahi Moghaddam et al.,2011). Higher complexity of new designs requiresbetter and more efficient optimization algorithm in or-der to reduce the GHG emissions as much as possiblein real-time in response to the unpredicted variationsin the workload and energy sources. In these net-works, not only server consolidation should be con-sidered, but also for each VM the best data centershould be chosen while meeting all the constrains.

In this type of complex problems, even algorithmssuch as the GGA, are not able to discover all the re-lations between VMs, servers and data centers to leadto the best optimal solution. As a bin-packing algo-rithm, GGA is able to benefit from consolidation ofVMs on servers, while it cannot discover the possiblebenefits of data center consolidation. Therefore, evena more complex heuristic algorithm is needed in orderto discover these relations and behaviors.

In this paper, a new genetic algorithm is proposedas multi-level grouping genetic algorithm (MLGGA),and we argue that this algorithm is useful for thosetypes of problems which deal with different levels ofbin packing. This new algorithm will consider notonly the relation of individuals as groups, it also con-siders the relation of groups of groups in order toachieve the best possible solution for the optimizationproblem. As a use case in this work, a network of datacenters is optimized for carbon footprint reduction. itis worth noting that the concept of the MLGGA couldbe used in any optimization problem which deals withgroups of groups in different levels and their relations.

The paper is organized as follows. In the firstsection, different works on using heuristic algorithmsfor server consolidation, energy efficiency and carbonfootprint reduction are reviewed. In the next section,the principle of the proposed algorithm is explained.In the next section, a case study is planned for com-parison of the proposed algorithm with GGA. Finally,in the last section, the conclusion and some prospectsfor future works are discussed.

2 RELATED WORKS

2.1 Grouping Genetic Algorithm

In (Falkenauer and Delchambre, 1992), Falkenauerand Delchambre proposed a new version of genetic al-gorithm known as grouping genetic algorithm. Theyargue that normal genetic crossover and mutation op-erators are not able to preserve the group features ofthe parent chromosomes. In the straightforward en-coding scheme, each item (for example, a VM) is rep-resented by a gene in the chromosome, and its label is

its group (for example, a server) which that item be-longs to. For example, the chromosome ADEBFFBCencode a solution for 8 VMs where the first VM ison server A, the second VM is on server D, and soon. Basically, when there are two parents with goodgroups defined in their chromosomes, there is no wayfor normal genetic crossover operator to create anoffspring in which those good groups are preserved.A part of a child chromosome comes from one par-ent, and the rest comes from the other parent, well-defined groups in both parents will break in parts, andthe probability of having an offspring with strongergroups is very low. Therefore, they proposed a newcrossover and mutation operators in their new algo-rithm, which perform on groups instead of individualgenes.

In their crossover operator, the groups presentedin the chromosomes are lined up (keeping one geneper group), and the crossover will happen on thesetwo group representations of the parents. For ex-ample, for the chromosome ADEBFFBC, the grouplineup will be ADEBFC. It is worth noting that, inthe group representation the chromosomes could beof variable length. Two crossover points will be se-lected in each parent group-lineup randomly. And,the groups in middle part of the second parent group-lineup will be inserted in first parent group-lineup atthe first crossover point. For example, the group-lineup of the parents are as follows:

P1 : ADEjBFjC (ADEBFFBC)P2 : bdjcaj (bbdcabba)

where the groups with same alphabetic character butwith different cases (upper and lower cases) are samebut represent that group in first and second parent, andcrossover points are marked as j. Also, the straight-forward encoding of the chromosome is provided inparentheses.

After insertion, the offspring group lineup of theoffspring will look like (ADEcaBFC). Because thegroups “c” and “a” are inserted from the second par-ent, their matched groups in first parent “C” and “A”,are no longer valid and these two groups and all theirassignments to individual genes will be removed fromthe offspring; remaining the offspring group lineup as(DEcaBF). For our example, the straightforward en-coding of the offspring will be: (?DEcaFBa). ”?”symbol shows that the first individual gene has nogroup assigned to it any more because group A is re-moved from the chromosome. In a same way, thereare some individuals which are in groups “c” and “a”in second parent while they are in other groups infirst parent. The group of these individuals will bereplaced with inserting groups from second chromo-some. The groups of replaced individuals need to

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be removed with all assignment to individual geneswhich are groups “B” and “F” in the first parent. Forour example, the straightforward encoding of the off-spring will be: (?DEca??a). Now, there are some in-dividuals which their group assignments are removedfrom chromosome in previous actions which needsto be reinserted in the offspring chromosome. FirstFit Descending algorithm (Garey and Johnson, 1979)is used in order to reinsert the removed individualsinto the chromosome. The priority is with the groupswhich are almost full.

In mutation operator of grouping genetic algo-rithm, the lineup of groups will be created in a similarway of the crossover operation. Then, some groupswill be chosen by random and those groups with theircontaining individuals will be removed from the chro-mosome. Then, there are some individuals, whichhave been removed in previous action, and are neededto be reinserted into the chromosome. A similar ac-tion as that of the crossover operator will be takenhere in order to reinsert the removed individuals intothe chromosome.

2.2 GGA in Server Consolidation

Xu et al. used Grouping Genetic Algorithm (GGA)in (Xu and Fortes, 2010) in order to achieve multi-objective goals in placement of virtual machines invirtualized data center environments. They claimedthat normal GGA crossover operator is not efficientand they modified it to achieve better results. Theyproposed a ranking-crossover instead, and claimedthat new crossover is able to inherit good featuresfrom parents more efficiently. They evaluated all theindividuals based on three evaluation functions whichthey used to represent their three optimization objec-tives. These three objectives were resource usage ef-ficiency, power consumption efficiency, and thermalefficiency. They represented some evaluation func-tions for each of these objectives. The evaluation re-sults were some numbers in the range of [0,1]. Insteadof random selection of crossover points, the selectedgroups for insertion to the first chromosome are mostlikely selected from groups with higher rank in rank-ing evaluation of three objectives. They claimed thatthis way, the high quality groups will most probablyremain intact and optimizer will reach to better so-lutions faster. They also combined GGA with fuzzyconcepts in order to achieve the best solution for theirseveral objectives problem.

Shubham Agrawal et al. used the GGA algorithmfor a server consolidation problem in (Agrawal et al.,2009). They modeled the server consolidation prob-lem as a vector packing problem with conflicts. In

their mathematical model, they tried to differentiatebetween efficiency of bin packing and number of binswhich are packed. Their model was designed to preferthe bin-packing efficiency over bin number optimiza-tion. They used the original version of the GGA inorder to solve the optimization problem.

In another work, David Wilcox et al. introducedanother type of GGA algorithm known as Reorder-ing Grouping Genetic Algorithm (RGGA) (Wilcoxet al., 2011). They describe the multi-capacity bin-packing problem in data center server consolidationas bins (servers) with multiple capacities (CPU, mem-ory, network, storage, and etc.) and VMs with mul-tiple weights. In their proposed grouping genetic al-gorithm, each individual has several representations,and they claim these multiple representation will leadto better solution in more efficient time frame. Parentchromosomes are chosen with a higher probability formore fit individuals. In their approach, they combinedall the bins from both parent chromosomes and sortthem by fitness. The fuller a bin is, it is on top ofthe list, and less full bins are at the bottom of the list.From the top of the list, some bins will be selectedand the rest of the bins will be discarded. If there is abin which contain an individual belongs to already se-lected bins, that bin will be discarded as well. For theindividuals which are discarded, they will be orderedby their fitness and first fit descending algorithm willbe used in order to reinsert them to the offspring chro-mosome.

Because the algorithm always prefers tightlypacked bins over other bins, they added a Gaussiannoise to the fitness function of the individuals in orderto escape the local minimums. Respectively, in theirmutation operator, the mutation take place more onless fit bins than good bins. This will assure that thestructure of good groups does not intact often. Theyused three mutation operator. First, normal GGA mu-tation while some bins will remove randomly andtheir individuals will reinsert into the chromosome.Second, two items in the order list will be swapped,and third, one item will be randomly relocate in theorder list.

3 MULTI-LEVEL GROUPINGGENETIC ALGORITHM

In the GGA, a new crossover and mutation operatorswere introduced in order to save the group relationsbetween individual genes. In a similar way, here, theMLGGA crossover and MLGGA mutation operatorsare introduced in order to preserve the relations be-tween groups. These operators substitute the normal

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GA crossover and mutation operators and work alongwith the other GA operators as shown in lines 6 and 7of the following MLGGA pseudocode:

1: Choose initial population.2: Evaluate each individual’s fitness.3: repeat4: Select individuals to reproduce.5: Mate pairs at random.6: Apply MLGGA crossover operator.7: Apply MLGGA mutation operator.8: Evaluate each individual’s fitness.9: until terminating condition

3.1 MLGGA Crossover

In the virtual cloud problems, the positions of VMsare the variables of the problem. In these problems,grouped variables, such as server consolidation, lowerthe cost function. However, normal GA crossoverbreak the existing groups in parent genes, and prob-ability of preserving the good grouping features pre-sented in parent genes is very low. Although the GGAcrossover provides a way to preserve the groupingfeatures in parent genes, there are relations betweengroups that the GGA crossover is not able to preserve,and most probably it breaks these relations. In the net-work of data centers, the GGA is good to consolidateVMs on servers, but it is not able to identify that thereare benefits in choosing servers from only one datacenter. For example, the GGA may consolidate VMson different servers which allow us to turn off some ofthe servers and save energy, but it is not aware that ifit consolidate all servers on less number of data cen-ters as well, it may save a lot more by turning off anintermittent data center.

For example, assuming parent genes P1 and P2and their groups are as follow:

P1 : ACDEGIJB(ACDEGAIJDCBACDEAGIA)

P2 : bcghieda(bcghieddaccccehigha)

If each group is assigned to a higher level group (abigger bin) as follows:

W=fAg X=fB,Cg, Y=fD,E,Fg, Z=fG,H,I,Jgw=fag x=fb,cg, y=fd,e,fg, z=fg,h,i,jg

The genes group lineup can be rewritten as theirhigher level groups as follows by replacing the grouprepresentations (for example, ACDEGIJB for P1) bytheir higher level group labels:

P1 : WXYYZZZX ACDEGIJBP2 : xxzzzyyw bcghieda

As it is shown above, some higher level groupsare repeated in the group lineup. Here, we create a

higher level group lineup (level 2 group lineup), andwe keep only one gene per higher level group similarto what we did in group lineup in lower level. Now,the chromosome could be written as below:

P1 : WXYZ WXYYZZZX(ACDEGAIJDCBACDEAGIA)

P2 : xzyw xxzzzyyw(bcghieddaccccehigha)

where the first column is the new level 2 grouplineup representation of the chromosomes. Thecrossover will be done on the level 2 group lineup rep-resentation of the genes: (WXYZ) and (xzyw). Likethe GGA, two crossover point will be chosen ran-domly on each gene:

P1 : WXjYjZ WXYYZZZX(ACDEGAIJDCBACDEAGIA)

P2 : xjzyjw xxzzzyyw(bcghieddaccccehigha)

and the middle part of second gene will be insertedto the first gene, and similar higher level groups infirst gene with their assigned groups and containingindividuals will be removed from the gene.

Offspring : WXjzyYjZ

As it is shown in above, higher level groups (z) and(y) are inserted from second parent to the first parent.This means that their matching higher level groups(Z) and (Y) are not any more valid and their contain-ing groups (D,E,F,G,H,I,J) and their containing in-dividuals should be removed from the chromosome;which remains the offspring chromosome as below:

Offspring : WXzy (ACghiedd?CBACehighA)

Genes number 3-8, and 14-18 in second parent (P2)are belongs to groups (d,e,f,g,h,i,j) which are belongsto higher groups (y,z) and they are transferred directlyfrom second chromosome to the first chromosome.Gene number 9 is in group (D) in first parent whichbelongs to higher level group (Y) which needs to beremoved as mentioned above.

For the genes in first parent, which are replacedwith genes from second parents, there are some indi-viduals which are belongs to some groups and higherlevel groups which are not yet removed from the chro-mosome. For our example, genes number 6 and 16 arebelong to group (A) in first parent chromosome whichare replaced with (e) and (i) from the second parentchromosome. These individuals with their co-groupand co-higher-group individuals need to be removedfrom the chromosome as well. Co-group individualsof an individual are those genes which are in the samegroup, and co-higher-group individuals of and indi-vidual are those genes which are in the same higher

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group. For our example, all individuals in higher levelgroup (W) which is higher level group of (A) need tobe removed from the offspring chromosome. For ourexample, the offspring chromosome will be like this:

Offspring : Xzy (?Cghiedd?CB?Cehigh?)

As it is shown in above, higher level groups (X) fromfirst parent, and (z) and (y) from the second parent arepreserved in the offspring chromosome intact whichis the goal of the crossover operator.

At the end, there are some individuals which arenot assigned to any group and higher level group.These individuals will fit in the chromosome by us-ing the First Fit Descending algorithm or more ad-vanced fitting techniques. Higher level groups whichare fuller will chosen first, and also fuller groups arein more priority for first fit algorithm.

3.2 MLGGA Mutation

The MLGGA mutation is very similar to the MLGGAcrossover concept. From a selected chromosome:

P1 : WXYZ WXYYZZZX(ACDEGAIJDCBACDEAGIA)

Some higher level groups will be randomly cho-sen, and all co-group and co-higher-group individualgenes will be removed from the chromosome. For ourexample, if higher level group (Z) is selected to be re-moved, the remaining chromosome will be as below:

P1 : WXY WXYY???X(ACDE?A??DCBACDEA??A)

Then, the First Fit algorithm will be used to reinsertthem to the chromosome as described in crossover op-erator section.

3.3 Extensions of the MLGGACrossover and Mutation

In the GGA, the concept of group of individual genesis introduced. In previous section, we described a sit-uation where there are some relations between groupsof groups in a problem. We can extend this solutionfor cases in which there are several level of group-ing involved. For example, if, in a problem, individ-uals are grouped by some criteria, the problem hasgrouping relations at level 1. If the groups of level1 are grouped by some other criteria, there will thenbe a grouping of level 2. And similarly, we can havegrouping of level n for a problem.

For a problem with the grouping of level n, a leveln MLGGA crossover and mutation should be used.The concept of the level-n MLGGA crossover and

mutation is similar to what we described in previoussubsections which was a level-2 MLGGA crossoverand mutation. For the level-n MLGGA crossover, in-dividual genes will be represent by their level 1, level2, ..., level n groups. Two crossover point will be se-lected randomly in parents level-n groups representa-tion, and the second part of second chromosome willbe inserted to the first chromosome. The matchinglevel-n groups in first chromosome with all their indi-viduals will be removed from the offspring chromo-some. For those individual genes in first parent whichare replaced with transferring genes from second par-ent, all their co-level-n-group individual genes will beremoved as well. Co-level-n-group individuals of anindividual are those genes which are in the same leveln group. At the end, all removed individuals will beinserted to the chromosome with using an First Fit al-gorithm or more advanced algorithms as described inprevious subsections. According to this definition, theGGA algorithm is a level-1 MLGGA.

Level-n mutation operator will be defined in avery similar way with randomly selecting some level-n groups and removing their individuals and reinsert-ing them.

4 VIRTUAL PRIVATE CLOUDUSE CASE

In order to examine the performance of new algorithmon energy efficiency and Carbon footprint reduction,we test it in a simulation platform. A Virtual Pri-vate Cloud (VPC) (Van der Merwe et al., 2010)(Woodet al., 2010)(Farrahi Moghaddam et al., 2011) is sim-ulated and tested under two heuristic algorithms: theGGA and the proposed MLGGA. Different case stud-ies are considered to test the proposed algorithm asfollows:� Medium-scale network under normal load (Case

study 1):In this case study, a network of 7 data centers in7 cities around the world is simulated and car-bon footprint and energy consumption of the net-work is measured under different optimization al-gorithms. Initial utilization of servers are about60% in this case study. This case study showshow the proposed algorithm competes with theother algorithm in a medium-scale network undermedium utilization. This case study is the base-line case study for this research. Some parametersis changed in this case study to create new casestudies. For example, in order to see the effect ofhigh utilization on the algorithms, the followingcase study is considered.

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� Medium-scale network under heavy load (Casestudy 2):In this case study, A network similar to case study1 is simulated and Carbon footprint and energyconsumption of the network is measured underdifferent optimization algorithms. Initial utiliza-tion of servers are about 90%. This case studyshows how the proposed algorithm outperformsthe other algorithm in a medium-scale networkunder heavy utilization.Another important parameter is the network sizewhich is considered in the following case studyin which a large-scale network is defined in orderto show the effect of the size of network on thealgorithms.

� Large-scale network under normal load (Casestudy 3):In this case study, A network of 20 data centers in11 cities are simulated and carbon footprint andenergy consumption of the network is measuredunder different optimization algorithms. Initialutilization of servers are the same as case study 1.This case study compares the performance of thenew algorithm compete with other algorithm in aLarge-scale network under medium utilization.

4.1 Simulation Platform Specifications

Simulation platform is designed in Matlab environ-ment. In this platform, a set of components are sim-ulated such as data centers, servers, VMs, VM mi-grations, and weather conditions. It is possible to de-fine more than one data centers in each selected citiesin this simulation platform. Each data center can beconnected to a source of renewable energy and alter-native non-green source of energy. Renewable sourceof energies which are simulated in this environmentincludes solar, wind, hydro, and nuclear source of en-ergies. There is battery bank in each data center whichstores extra green power to be used when the source ofgreen energy is not available. The simulator estimatesthe energy used in each data center based on the num-ber of running servers and other utilities, and calcu-lates the extra green power. Knowing the extra greenpower at a moment, the simulator will update the bat-tery charge of each data center. Not all source of greenpower are the same, and each renewable source ofenergy has its own cleanness measured as the g fac-tor (Farrahi Moghaddam et al., 2011). The g factorchanges according to the availability of source of en-ergy and charge of batteries in each node. For exam-ple, for solar and wind energy, if there is enough en-ergy stored in the batteries, the g is high. In contrast,when the batteries are discharged and data center is

using the grid energy the g factor is low. For hydroand nuclear energy, if energy exist, g factor is alwayshigh, and for grid energy powered by coal, g factor isalways low.

4.2 Optimization Algorithms

To evaluate the efficiency of the proposed algorithm,the MLGGA algorithm is compared with the GGAalgorithm which is used in other works for energy ef-ficiency in virtualized data center environments. car-bon footprint and energy consumption of the networkare also measured when there is no optimization inorder to have a baseline in the comparison of the re-sults of the GGA and the MLGGA. This will showhow much energy and carbon these two algorithm cansave. As shown in the previous works section, thereare things which can be done to improve the resultof the GGA in energy efficiency in virtualized datacenter environment. Here, we use the same improve-ments for both GGA and MLGGA as described inprevious works. The only differences between the twoalgorithms implementation are the crossover and mu-tation operators, and the rest of the algorithms are ex-actly the same, and both algorithms benefit from theenhancements.

4.3 Carbon and Energy Measurement

One of very important parts of the new algorithm eval-uation is the carbon and energy measures which areused to show the carbon/energy footprint of the wholenetwork. For this research, a measurement tool whichis developed for virtual private clouds is used to mea-sure the Carbon and energy footprint of the whole net-work of data centers (Kansal et al., 2010)(Economouet al., 2006)(Farrahi Moghaddam et al., 2011). ForCarbon footprint the following formulation is used:

C(t;Dt) =Cm(Dt)+CDCon=o f f (Dt)

+rmax åd Od(1�gd(t))�

Pcd (t)+PPd (t)+ås2d Os(acpus

µcpus+amems µmems

+aios µdisks + gs)

Dt

(1)

where C(t;Dt) is the total carbon footprint of the net-work in time t for time period of Dt . For more detailsplease see (Farrahi Moghaddam et al., 2011).

And for energy measurement, the following for-mulation is used:

E(t;Dt) =Cm(Dt)=rmax+CDCon=o f f (Dt)=rmax+åd Od

�Pcd (t)+PPd (t)

+ås2d Os(acpusµcpus

+amems µmems

+aios µdisks + gs)

Dt

(2)

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where E(t;Dt) is the total energy consumption of thenetwork in time t for time period of Dt . For moredetails please see (Farrahi Moghaddam et al., 2011).

The objective of this work is to reduce the car-bon footprint and emissions. As shown in (FarrahiMoghaddam et al., 2011), Carbon optimization andenergy optimization are not equivalent in VPC envi-ronments. When the Carbon is optimized, energy isnot necessary optimized. Here, the energy is mea-sured just as a reference, and no optimization with re-spect to energy is performed. There are many worksthat deal with energy efficiency in the literature suchas dynamic CPU speed, energy-aware job scheduling,server consolidation (Zhang et al., 2008).

4.4 Results

The algorithms are tested on medium-scale and large-scale networks in a simulation environment1 whichare shown in Figure 1 and Figure 2.

Figure 1: Medium-scale network of data centers (case study1).

Figure 2: Large-scale network of data centers (case study3).

As it is depicted in Figures 1 and 2, each data cen-ter is illustrated with a red or green filled circle. Redcircle means that data center is using a source of en-ergy with a g factor less than 0:5, and green circlemeans that data center is using a source of energy with

1http://www.greenservices.info/2011/10/simulation-environment.html

g factor greater than 0:5. The type of source of energyfor each data center is illustrated as an icon in the mid-dle of the circle. Available source of energies in thissimulation are solar, wind, hydro, nuclear, and grid(coal). As it is shown, hydro and nuclear source ofenergies are always green, and grid source of energyis always red. For solar and wind source of energies,it depends on existence of sun and wind, and also onthe amount of energy stored in the batteries. For ex-ample, in Figure 1, the solar power in Brazil is greeneven though at the moment the snapshot taken it ismidnight there. It is because of available solar powerstored in batteries of the data center. As it is shown,there is a battery indicator near the data center whichis reflecting the remaining battery charge in each datacenter. The battery indicator for data center in Brazilshows that there is not much battery left and the datacenter will soon switch to grid which is a non-greensource of energy. This has already happened for thedata center in South Africa and France. The data cen-ter in India is in day time, but it is still red. Thereare two reason for that. First, it is early morning inIndia, so the sun light is not direct, and solar powergeneration is low. Second, there is not enough energystored in data center batteries in order to enable thedata center to switch from grid power to solar power.

For case study 1, measured carbon and energy areshown in Figures 3 and 4.

Figure 3: Carbon measurement in case study 1.

Figure 4: Energy measurement in case study 1.

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In the legend of figures Figures 3 and 4, Carbonmeans that carbon is measured and Energy means thatenergy is measures, while [Carbon-opt] means thatfor all cases the optimizer was trying to minimize thecarbon and not the consumed energy. The tag [7x8-5source] shows the structure of the network which isa 7 data center with 8 server on each data center with5 different type of source of energy. [every1hour]means that the optimizations are done for every onehour, according to (Farrahi Moghaddam et al., 2011)this is an acceptable interval. [gga], [no-opt], and[mlgga] represent the optimization algorithm for eachgraph. All the graphs need to be summed with the off-set value in the title of each graph in order to achievethe real carbon or energy value.

As it is shown in Figure 3, the proposed algorithmhas a better performance compare to the GGA. Theassociated curve of the MLGGA is under the curve ofthe GGA in the most of time. This is not the case forthe energy as it is shown in Figure 4, and the energyfootprint of the MLGGA is not visually better thanthe GGA. As described in (Farrahi Moghaddam et al.,2011), carbon optimization and energy optimizationare not equivalent in network of data centers with dif-ferent energy and carbon footprint profiles, and herewe confirmed it again.

For case study 2, the measured carbon and en-ergy are shown in Figures 5 and 6. As it is shown,the MLGGA has a better performance compare to theGGA, but the difference in the performance is de-creased because of higher data center utilization.

Figure 5: Carbon measurement in case study 2.

For case study 3, measured carbon and energy areshown in Figures 7 and 8. The graph shows morecomplexity compared to case study 1 and 2 accordingto higher number of involved data centers in this casestudy. The better performance of the MLGGA is vi-sually recognizable on the carbon graph. Because theoptimization for each point is not isolated from previ-ous points, we cannot compare the two curves pointto point. To have a better understanding of the amountof carbon footprint and energy consumption, the ac-

Figure 6: Energy measurement in case study 2.

cumulated amount of emitted carbon is summarizedin Table 1 and Table 2, and accumulated amount ofconsumed energy is summarized in Table 3 and Table4.

Figure 7: Carbon measurement in case study 3.

Figure 8: Energy measurement in case study 3.

The ”No-opt”, ”GGA”, and ”MLGGA” columnsshow the exact measured emitted carbon of the net-work. the ”GGA %” and ”MLGGA %” columns showthe emissions percentage of the two optimization al-gorithms with respect to the no-optimization situa-tion. And the ”MLGGA perf. %” column show theperformance of ”MLGGA” over ”GGA”. As shownin the Table 1 and Table 2, the MLGGA has a betterperformance of 10.65 % over the GGA in case study1. The MLGGA has better performance compare to

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Table 1: 48 hour carbon footprint.

Case No-opt GGA MLGGAstudy

CO2kg CO2kg CO2kgCase 1 1009.56 719.79 612.30Case 2 1040.31 922.92 877.14Case 3 3202.28 2560.70 2369.49

Table 2: 48 hour carbon footprint.

Case GGA MLGGA MLGGAstudy perf.

% % %Case 1 71.30 60.65 10.65Case 2 88.72 84.32 4.40Case 3 79.96 73.99 5.97

the GGA in case study 2 and 3 too, but the better per-formance is decreased when network is more utilizedor the network is bigger. Overall, the table shows abetter performance for the proposed algorithm. Formore utilized network, it is much harder for the GGAand the MLGGA to group all the VMs on some datacenters with green energy and empty the one with nonrenewable energy due to high number of VMs in thenetwork.

Table 3: 48 hour energy footprint.

Case No-opt GGA MLGGAstudy

KWh KWh KWhCase 1 2587.20 2296.48 2299.63Case 2 3124.80 3027.88 3095.52Case 3 7392.00 6555.61 6466.39

As mentioned earlier, the gain on energy is littleor even negative as it is shown in Table 3 and Table4. With targeting on Carbon, this loss will pay off infuture with Carbon penalty/reward regulations.

5 CONCLUSIONS AND FUTUREWORK

According to the results, the level-2 MLGGA, intro-duced in this work, can provide better results in prob-lems such as VPC carbon optimization. The GGAwas able to reduce 28.7% carbon emission compareto no-optimization situation, while the MLGGA wasable to reduce 39.35% carbon emission compare tono-optimization case which shows that the MLGGAhas an overall 10.65% better performance comparedto the GGA. When the utilization of the network ofdata centers is increased, the MLGGA was able to re-duce 4.4% more in carbon emission compared to the

Table 4: 48 hour energy footprint.

Case GGA MLGGA MLGGAstudy perf.

% % %Case 1 88.76 88.88 -0.12Case 2 96.90 99.06 -2.16Case 3 88.69 87.48 1.21

GGA. The decrease in the relative performance com-pared to the low-utilization case is because of highernumber of VMs in the network. This lowers the pos-sibility of emptying a whole data center from virtualmachines. But, overall the MLGGA has a better per-formance in higher utilization compare to the GGA.In another test, when the network size increased from7 data centers to 20 data centers with the same rate ofutilization, again the MLGGA outperforms the GGAwith 5.97% extra Carbon emission decrease. Over-all, the MLGGA has a better performance comparedto the GGA in problems such as low-carbon virtualprivate cloud problem.

Beside the carbon footprint, the energy consump-tion of the network was measured. According to theresults the energy consumption for the MLGGA hasa little improvement or declination compared to theGGA over time. This is because of the nature of thevirtual private cloud problem. In VPC, which is dis-tributed over different locations and powered with dif-ferent source of energies, the carbon footprint reduc-tion and energy efficiency are not equivalent. Accord-ing to our objective, the carbon footprint was min-imized. According to the cost of renewable sourceof energies, carbon footprint optimization is costlynow, but with implementation of the expected carbonpenalty/reward regulations in the near future, carbonfootprint optimization could be used to minimize theoverall cost of the network as well.

For future works, the following suggestion mightbe considered: i) The MLGGA can be used on othertype of grouping problems and success of the al-gorithm can be compared with other heuristic algo-rithms, ii) The higher levels of MLGGA can be testedon problems with higher level of grouping, iii) Morereal world data can be used in the simulations in or-der to make the results more usable in real world VPCimplementations, iv) the energy consumption can bechosen as target and the indirect carbon footprint re-duction can be studied, and v) for having a good es-timation of cost in such a networks, the real cost ofoperating a virtual private network can be model andmeasured. The measured cost can be compared fordifferent inter- and intra-data center topologies withtheir constraints, such as pooling limits. The solutionwill be different for different load scenarios, and alsofor different application types running on the VMs.

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One scenario could be the comparison of costs of car-bon footprint optimization and energy consumptionoptimization. In additional, various penalty/rewardregulations for carbon footprint reduction, such ascarbon tax, can be model and simulated in order to es-timate the success rate of such networks in real worldconditions.

ACKNOWLEDGEMENTS

The authors thank CANARIE (Canadian Network forAdvanced Research in Education) for their financialsupport of the GreenStar Network project. The au-thors also thank the MDEIE (Ministry of EconomicDevelopment, Innovation and Export Trade) of Que-bec for their financial support.

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