Parallel tabu search for optimizing the OSPF weight setting problem

Parallel Tabu Search for Optimizing the OSPF Weight SettingProblem

Sadiq M. Sait, Mohammed H. Sqalli, and Syed AsadullahComputer Engineering Department

King Fahd University of Petroleum & MineralsDhahran 31261, Saudi Arabia

{sadiq,sqalli,sasad}@kfupm.edu.sa

Abstract: The problem of setting the Open Shortest Path First (OSPF) weights on links such that congestion canbe avoided is proved to be NP-hard. Many iterative heuristics have been applied to solve the OSPF weight setting(OSPFWS) problem. As the size of any combinatorial optimization problem increases, it becomes more diffi-cult to find an optimum solution using sequential algorithms. Parallelization of modern iterative heuristics hasbeen proven to produce improved solution precision and timing. In this paper, we investigate the parallelizationof Tabu Search and apply two variants of a Parallel Tabu Search (PTS) heuristic on the OSPFWS problem. It isshown through experimental results that both PTS approaches produced better solutions quality compared to thesequential heuristics; specifically for larger topologies. In one approach, we propose a new design for our parallelcooperative search algorithm, which performs better than the conventional parallel heuristic. The purpose of thisnew design is to induce diversification into the search to explore a larger search space. We also show that the newapproach performs better than the conventional parallel heuristic.

Key–Words: Open Shortest Path First (OSPF), OSPF Weight Setting Problem, NP-hard, Iterative Heuristics, Par-allel Tabu Search.

1 Introduction

Open Shortest Path First (OSPF) is an intra au-tonomous system routing protocol which computesthe shortest paths based on the weights assigned tothe links. Routing on the Internet defines the traf-fic flows over the selected shortest paths. Traffic en-gineering aims at providing the required Quality ofService (QoS) to the users by efficiently utilizing theavailable resources and managing these traffic flows.The rapid growth in Internet traffic underlines the im-portance of traffic engineering.

OSPF uses the link weights as its routing met-ric. The major networking vendor Cisco, assigns thelink weights inversely proportional to the link capac-ity. This is termed as inverse capacity OSPF in theliterature [1, 2]. Other methods of weight assignmentsuch as unit OSPF and random OSPF also exist. Givena set of traffic demands between each source and des-tination node, the OSPF weight setting problem con-sists of determining suitable OSPF link weights so asto optimize a certain criterion (cost function), aimingat avoiding congestion in the network. This Problemis NP-hard [1].

The application of iterative heuristics to solve theOSPFWS problem was first attempted by Fortz and

Thoroup [3, 4]. They applied tabu search using theirproposed cost function [1]. We call this cost functionFortzCF. Sqalli et al. proposed a new cost function(NewCF) and applied Simulated Annealing [5], Sim-ulated Evolution [6], and Tabu Search [7] using bothcost functions. They proved experimentally that thenew cost function minimizes the number of congestedlinks. Ericsson et al. attempted Genetic Algorithm [2]as well as hybrid GA [8] for the same problem.

Tabu Search has also been used for many otheroptimization problems such as power system restora-tion [9] and job shop scheduling problems [10]. Inaddition, Balicki [11] used an evolutionary algorithmbased on a tabu search procedure for multi-criteriaoptimization of distributed systems. Sadegheih [12]also discusses a global optimisation using evolution-ary algorithms, simulated annealing, and tabu search.Adaptive Tabu Search (ATS) has been used as wellin the works of Sujitjorn et al.[13] and Kluabwang etal. [14].

In this paper, we investigate parallelizing the TabuSearch iterative heuristic to solve the OSPFWS prob-lem which, to our knowledge, has not been attemptedyet. Enormous work has been done in the area of par-allelization of iterative heuristics in general and Paral-lel Tabu Search (PTS) [15, 16, 17, 18] in particular to

WSEAS TRANSACTIONS on COMMUNICATIONS Sadiq M. Sait, Mohammed H. Sqalli, Syed Asadullah

ISSN: 1109-2742 311 Issue 3, Volume 8, March 2009

solve a range of combinatorial optimization problems.Different implementation strategies are also proposedin the literature which include, using dynamic TabuSearch parameters [19] at different processors, usinga cluster in some hierarchical architecture [20, 21]to enhance the search, integration of different paral-lelization strategies [20], etc. A detailed survey ofvarious parallelization strategies and their applicationto one or more classical or specific optimization prob-lems can also be found in the literature [22, 23, 24].

The OSPFWS problem, like any other combina-torial optimization problem, requires high computingwhich grows exponentially with the problem dimen-sion [25]. Parallelism has obvious advantages dueto the availability of more resources at hand. If ef-ficiently done, it not only achieves good results inrelatively lesser time compared to it sequential coun-terparts, but also can obtain superior solution qualitydue to more comprehensive and independent parallelsearch by multiple entities. In this paper, we presenta Parallelized Tabu Search (PTS) [26] heuristic usingtwo strategies to solve the OSPFWS problem by us-ing the two cost functions available in the literature.The objective is to achieve better solutions quality ina given time, which could not be achieved by sequen-tial heuristics; specifically for larger topologies andhigher traffic demands.

The rest of the paper is organized as follows; TheOSPFWS problem statement and the cost functionsproposed in the literature are presented in Section 2.The two Parallel Tabu Search algorithms are discussedin Section 3. This is followed by the experimentalresults and conclusion.

2 Problem Statement

The OSPF weight setting problem can be stated asfollows: Given a directed network of nodes and arcsG = (N, A), a demand matrix D, and capacity Ca foreach arc a ∈ A, determine a positive integer weightwa ∈ [1, wmax] for each arc a ∈ A such that theobjective function or cost function Φ is minimized.When routing is perfromed using OSPF, the assignedlink weights completely determine the shortest paths,and hence the traffic flows. Based on these trafficflows, the partial loads on each arc for a given des-tination are computed. This is done for all destina-tion nodes. The aggregated partial loads for all des-tinations on a particular arc give the total load la onthat arc. The cost of sending traffic through this arc isgiven by Φa(la). The cost value depends on the uti-lization of the arc and is given by the linear functionproposed by Fortz and Thoroup [1].

Φ′a(l) =

1 for 0 ≤ l/ca < 1/3,3 for 1/3 ≤ l/ca < 2/3,10 for 2/3 ≤ l/ca < 9/10,70 for 9/10 ≤ l/ca < 1,500 for 1 ≤ l/ca < 11/10,5000 for 11/10 ≤ l/ca < infinity

(1)

The Fortz cost function is given in equation 2.

Φ =∑

a∈A

Φa(la) (2)

The objective is to minimize Φ, subject to theseconstraints:

la =∑

(s,t)∈NXN

f (s,t)a a ∈ A, (3)

f (s,t)a ≥ 0 (4)

In constraint 3, for traffic between a source anda destination pair (s,t), f

(s,t)a indicates the amount of

traffic flow that goes over arc a. The detailed stepsshowing the formulation of this cost function can befound in the literature [1, 5].

The New cost function [5] is shown in equation 5,

Φ = MU +∑

a∈SetCA (la − ca)E

(5)

This function contains two terms. The first termis the maximum utilization (MU) in the network. Thesecond term represents the extra load on the networkdivided by the number of edges present in the networkto normalize the entire cost function.

We have applied our proposed parallel heuristicson both cost functions presented in this section.

3 Parallel Tabu Search (PTS)

In conventional parallel implementations of tabusearch, all the processors including the master inde-pendently generate an initial solution and compute itscost. After searching its part of the current neighbor-hood, repeatedly for a certain number of iterations,each slave process reports its best move back to the



master. The master process selects the best among thereceived best moves (subject to tabu conditions). If thestopping criteria are met then the search stops; other-wise the master broadcasts the selected move back tothe slaves. The selection criterion for the best moveand also the slaves to which this best move is broad-casted, depend on the implementation strategy. Thesearch continues, where each processor sets the re-ceived solution from the master as its current solu-tion and explores the neighborhood. The master alsobroadcasts the tabu list pertaining to the selected solu-tion and all slaves update their individual tabu lists.

Two strategies, namely, PTS-Star and PTS-Ringwere implemented to parallelize Tabu Search. Theimplementation aspects of the two strategies mainlydiffer in the way the processors coordinate during theperiodic solution exchanges. From the functional as-pect, they differ in the search space each processorworks on after each solution exchange. In this sec-tion, we discuss the two strategies in detail.

3.1 PTS-Star

In the PTS-Star strategy, the parallel cluster consistsof n + 1 processors with 1 master and n slave proces-sors/nodes. Each processor starts by generating a ran-dom initial solution. Due to the independent randomnumber generation by each entity the initial solutiongenerated by a processor is different from the other.Each slave processor starts Tabu Search and contin-ues for K iterations. After each move the current andbest cost are computed. At the end of the Kth itera-tion, the best cost and solution are sent to the master.The master waits to receive the cost and solution fromall slaves, after which it compares the received costsand picks the best cost among the n slaves. Once thecomparison is done and the best cost is selected, themaster broadcasts the corresponding best solution toall slaves. Each slave processor receives the new bestsolution from the master and sets this received solu-tion as the current solution. With this current solution,Tabu Search is started for another K iterations.

This process of parallel Tabu Searches with pro-cessor coordination by periodic solution exchangecontinues until the termination criterion is met. Themaster is the central point of coordination betweenall slaves, which means that all communications gothrough the master and each processor is directly con-nected only to the master. The processor arrangementresembles a star topology and hence the name PTS-Star. The structure of the PTS-Star algorithm is shownin Figure 1.

With multiple processors working on the solutionand exploring the search space, the convergence is ex-pected to be faster and the final solution quality is also

Algorithm: PTS-Star

Begin:Slave:1: Generate Initial Solution.2: Continue TS for K Iterations.3: Send the bestsol and bestcost to master.Master:4: Receive individual bestcost from each slave.5: Compare the received costs.6: Select the bestsol among all slaves.7: if termination criteria is met: then

Save the results.Stop.

8: else:Broadcast bestsol to all slaves.

9: GoTo: 4Slave:10: Receive the solution from master.11: Update current solution based on the received solution.12: if termination criteria is met: Stop.13: else: GoTo: 2

End:

Figure 1: Structure of the PTS-Star algorithm

expected to be better by visiting more points (solu-tions) in the search space.

This technique however has the limitation that,after every periodic solution exchange, all processorsstart Tabu Search with the same current solution, andhence searching in similar regions of the search space.To prevent this redundant search, some technique isrequired where different processors can coordinate toexplore a larger search space. The next strategy PTS-Ring addresses this issue.

3.2 PTS-Ring

The primary objective of devising this new strategyis to improve the solution quality by making the pro-cessors work in different regions of the search space.This is done by making different set of processorsstart the search from different starting points (solu-tions) after each solution exchange, thereby diversify-ing the search considerably. It is practically importantto search a new region when the neighborhood searchfails to improve the best solution for a while; and di-versification techniques can help achieve this goal. Inthe PTS-Ring strategy, the parallel cluster consists ofn+1 processors with 1 master and n slaves. Each slavenode Si has a rank i associated with it. A node ex-changes its solution only with its neighbors. Neigh-borhood is defined as a set of three nodes with ranksi − 1, i, i + 1; hence the neighbors of node Si are(Si−1, Si+1). Further, the neighbors of the last nodeSn are (Sn−1, S1) while the neighbors of the first node



S1 are (Sn, S2). This arrangement of nodes, with thefirst and last node being neighbors, completes a ringstructure. The implementation logic of the PTS-Ringstrategy is explained below.

Each processor starts by generating a random ini-tial solution. Each slave processor starts Tabu Searchand continues for K iterations (moves). After everymove, the current and best cost are computed and atthe end of K moves, the best cost and solution are sentto the master. The master receives the cost and solu-tion from all slaves. For each slave processor, the mas-ter compares the slave’s cost with its neighbors andsends the best solution in its (slave’s) neighborhoodto this slave processor. Hence, any slave Si receivesthe best solution among the three processors (Si−1,Si, Si+1). Each slave processor receives the new bestsolution from the master and sets this received solu-tion as the current solution. With this current solu-tion, Tabu Search is started for another K iterations.The process continues until the termination criterionis met. The effect of this approach is that, with everysolution exchange, different sets of processors startwith a different solution as their starting point; unlikethe PTS-Star approach where the solution exchangebrings all processors to the same initial point for thatinstance in the search.

The structure of the PTS-Ring algorithm is shownin Figure 2.

4 Results

In this section, we present the experimental resultsfor the two Parallel Tabu Search algorithms. The testcases and demand matrices are the same as used in theliterature [1, 4]. The generation of these test cases isdone using GT-ITM generator [27], based on a modelof Calvert [28] and Zegura [29].

Experimental results have been recorded for thefollowing four performance metrics:

1. Cost

2. Maximum Utilization (MU)

3. Percentage of Extra Load (PXLoad)

4. Number of Congested Links (NOCL)

The utilization of the link is the ratio of load onthe link to its capacity. If the utilization of the link ismore than one, the link is congested. The MaximumUtilization is the utilization of the maximum utilizedlink in the network. In other words, it is the utilizationof the link having the highest degree of congestion.The extra load on a particular link is the load present

in excess to its capacity. If the load on the link is lessthan its capacity (utilization < 1), then the extraload on that link is zero. The percentage of extra loadis the sum of the extra load present in the network di-vided by the sum of capacities of congested links. Asexplained earlier, congested links are the links whichhave a utilization greater than 1 (i.e., load on the linkexceeds its capacity). The statistics for these perfor-mance metrics are plotted with respect to both parallelstrategies PTS-Star and PTS-Ring, using the two costfunctions: FortzCF and NewCF.

Algorithm: PTS-Ring

Begin:M=Master.S={ S1, S2,...Sn }; n=No. of Slave Processors.N(s): Neighbour of s.Ring Arrangement:N(Si)=(Si−1, Si+1).N(S1)=(Sn, S2).N(Sn)=(Sn−1,S1).Slave:1: Generate Initial Soln.2: continue TS for K Iterations.3: Send the bestsol and bestcost to M.Master:4: Receive costs from all slaves.5: if termination criteria is met: then

Save the results.Stop

6: else:for each slave Si. do

7: Compare cost of Si and N(Si).8: Select the best solution.9: Send the bestsol to Si.

EndForEndIf GoTo: 4

Slave:10: Receive the solution from master.11: Update current solution based on the received solution.12: if termination criteria is met: Stop13: else: GoTo: 2

End:

Figure 2: Structure of the PTS-Ring algorithm

4.1 PTS-Star

In this section, we first present the results of the PTS-Star strategy in which we show the Cost comparisonversus the number of processors for four test cases.In Figure 3, the results for the maximum demand areshown. It can be seen here that the cost improves withthe number of processors for all cases but this im-provement for the cases h100N360a and w100N476ais very minimal. The total demand and also the aver-



age load per arc (Total Demand/Number of Links) onthese topologies is less when compared to the randomgraphs (r100N403a, r100N503a). The cost of a solu-tion is dependent on the utilization of the links, andlower input demands lead to lesser utilization. Hence,when the input demands are low, a large set of solu-tions (weight combinations) will result in links withlow utilization and hence, a lower cost. These solu-tion sets representing a good solution, form a slightlybigger fraction of the search space and can also beexplored by sequential heuristics. Hence, for topolo-gies with lower input demands, the improvement dueto parallelization is not significant when compared tosequential heuristics.

The other two cost curves for r100N403a andr100N503a graphs show a significant improvement incost with the increase in the number of processors.The same trend is also observed for Demand-11, ascan be seen in Figure 4. The random graphs used inthis work are the graphs with large sizes and higherdemands when compared to any other topology. Noneof the sequential heuristics mentioned in this paperhave achieved results close to PTS for these topolo-gies. The final costs achieved using PTS are evenupto one third of the best achieved using the sequen-tial Tabu Search heuristic (TS). TS has also the bestresults among all sequential heuristics [7].

PTS-StarCost vs No. of Processors (Demand12)

0

10

20

30

40

50

60

1 2 3 4 5 6

No. of Processors

Co

st

h100N280a

w 100N476a

r100N403a

r100N503a

Figure 3: Cost vs. # of Processors Using PTS-Star forD12.

Time comparison for the PTS-Star strategy isshown in Figure 5 and Figure 6 for Demand-12 andDemand-11 respectively. The target cost is the bestcost achieved by the sequential heuristic in 1 hour(3600 sec). The runtime for the parallel heuristics isalso 1 hour. With the increase in the number of proces-sors, the parallel heuristics generally take lesser timeto reach the target cost. The time taken by the parallelheuristic to achieve the target cost is recorded for dif-ferent number of processors. The h100N280a topol-

PTS-StarCost vs No. of Processors (Demand11)

0

2

4

6

8

10

12

14

16

18

1P 2P 3P 4P 5P 6P

No. of Processors

Co

st

h100N280a

w 100N476a

r100N403a

r100N503a

Figure 4: Cost vs. # of Processors Using PTS-Star forD11.

ogy shows an almost linear speedup with the increasein the number of processors. Other topologies showfaster convergence with the increase in the number ofprocessors when compared to the sequential heuristic,but the speedup is not linear. It was observed that theaverage time consumed in synchronization and mes-sage passing between processors was about 25% ofthe total time. Hence, the communication overheadcould be one of the reasons for not achieving fasterspeedups. However, further investigation is requiredto make a conclusive statement about the same.

PTS-StarTime vs No. of Processors (Demand12)

0

5001000

15002000

2500

30003500

4000

2P 3P 4P 5P 6P

No. of Processors

Tim

e (S

ec) h100N280a

w100N476a

r100N403a

r100N503

Figure 5: Time vs. # of Processors Using PTS-Starfor D12.

4.2 PTS-Ring

Cost comparison for the above mentioned four topolo-gies is shown here for the PTS-Ring strategy. Theresults for Demand-12 and Demand-11 are shown inFigure 7 and Figure 8 respectively. It can be seenthat, with the increase in the number of processors,the cost improves considerably for the two test casesr100N403a, r100N503a. The PTS-Ring strategy also



PTS-StarTime vs No. of Processors (Demand11)

0

500

1000

1500

2000

2500

3000

3500

2P 3P 4P 5P 6P

No. of Processors

Tim

e (S

ec) h100N280a

w100N476a

r100N403a

r100N503

Figure 6: Time vs. # of Processors Using PTS-Starfor D11.

could not achieve a linear speedup with the increasein the number of processors, but was again able toachieve costs which are about three times better thanthe sequential heuristics.

PTS-RingCost vs No. of Processors (Demand12)

0

10

20

30

40

50

60

1P 4P 5P 6P

No. of Processors

Co

st

h100N280a

w100N476a

r100N403a

r100N503a

Figure 7: Cost vs. # of Processors Using PTS-Ringfor D12.

4.3 PTS-Star Versus PTS-Ring

Results for the Fortz cost function show that the costsachieved by PTS-Ring are slightly better than PTS-Star for all the test cases and demands. This improve-ment is expected and can be attributed to the diversi-fication feature of the Ring approach. The slave pro-cessors, in PTS-Ring, start from slightly different so-lutions after every solution exchange; thereby cover-ing a wider search space and achieving better solu-tions when compared to the ring approach. The costcurves for the FortzCF are shown in Figure 9 and 10for Demand-12 and Demand-11 respectively.

Figure 11 and 12 shows the cost curves forDemand-12 and Demand-11 respectively using thenew cost function (NewCF). The PTS-Ring Strategy,with a better diversification mechanism, again pro-

PTS-RingCost vs No. of Processors (Demand11)

0

5

10

15

20

1P 4P 5P 6P

No. of Processors

Co

st

h100N280a

w100N476a

r100N403a

r100N503a

Figure 8: Cost vs. # of Processors Using PTS-Ringfor D11.

Cost Comparison - Star vs RingDemand-12

0

10

20

30

40

50

60

1P 4P 5P 6P

No. of Processors

Co

st (

Fo

rtzC

F)

r100N403a-Ring

r100N403a-Star

r100N503a-Ring

r100N503a-Star

Figure 9: Cost Results of PTS For FortzCF for D12.

Cost Comparison - Star vs RingDemand-11

0

5

10

15

20

1P 4P 5P 6P

No. of Processors

Co

st (

Fo

rtzC

F)

r100N403a-Ring

r100N403a-Star

r100N503a-Ring

r100N503a-Star

Figure 10: Cost Results of PTS For FortzCF for D11.



duced better results than the PTS-Star Strategy for theNewCF which can be seen from these results.

Cost Comparison - Star vs Ring Demand-12

0

5

10

15

20

1P 4P 5P 6P

No. of Processors

Co

st (

New

CF

)

r100N403a-Star-NC

r100N403a-Ring-NC

r100N503a-Star-NC

r100N503a-Ring-NC

Figure 11: Cost Results of PTS For NewCF for D12.

Cost Comparison - Star vs Ring Demand-11

0

1

2

3

4

5

6

1P 4P 5P 6P

No. of Processors

Co

st (

New

CF

)

r100N403a-Star-NC

r100N403a-Ring-NC

r100N503a-Star-NC

r100N503a-Ring-NC

Figure 12: Cost Results of PTS For NewCF for D11.

The comparisons of other performance metricsfor both cost functions are shown in the following sub-sections.

4.4 Number of Congested Links

The comparison of the Number of Congested Links(NOCL) for both cost functions for the topologyr100N403a is shown in Figure 13. It can be ob-served that for FortzCF, there is no improvement ofthe NOCL with the increase in the number of proces-sors. We have seen in previous results that there isa significant improvement in cost with the number ofprocessors. Hence, we can conclude that the improve-ment in cost is due to reducing the extra load on thenetwork at the expense of the number of congestedlinks. FortzCF attempts to load balance the conges-tion on the network among all links by reducing theload from the more congested links and placing it onthe lesser congested links. However, for the NewCF,there is a minimization in the NOCL. Similar resultsare displayed in Figure 14 for Demand-11. Amongthe two strategies, the PTS-Ring minimizes the NOCL

better than the PTS-Star for the same cost function, asit also minimizes the overall cost better for both costfunctions. The best results for the NOCL were ob-tained when optimizing weights using the NewCF andthe Ring Topology.

Number of Congested Links (r100N403a) Demand-12

0

20

40

60

80

100

120

1P 4P 5P 6P

No. of Processors

No

. o

f C

on

ges

ted

Lin

ks

Star-FC

Ring-FC

Star-NC

Ring-NC

Figure 13: NOCL Results of PTS Using Both CFs forD12.

Number of Congested Links (r100N403a) Demand-11

0

10

20

30

40

50

60

70

1P 4P 5P 6P

No. of Processors

No

. o

f C

on

ges

ted

Lin

ks

Star-FC

Ring-FC

Star-NC

Ring-NC

Figure 14: NOCL Results of PTS Using Both CFs forD11.

4.5 Percentage of Extra Load

We now discuss the results for the Percentage of extraload (PXLoad). In the case of Demand-12 as shownin Figure 15, and Demand-11 as shown in Figure 16the values of PXLoad are better for FortzCF when op-timized using the PTS-Ring strategy compared to theNewCF; and PTS-Ring performs better than PTS-Star.Hence, it can be said that when weights are optimizedusing the FortzCF, the links which are over-utilizedare not highly congested; while with the NewCF, alesser number of links are congested but each indi-vidual congested link has a higher load. However,from the results of NOCL and PXLoad, it is importanthere to note that when weights are optimized usingthe NewCF and the Ring topology, it is found to pro-duce comparable values of PXLoad and at the sametime give better results for the Number of congested



Links. Similar results for NOCL and PXLoad werealso achieved for the r100N503a topology.

Percentage of Extra Load (r100N403a)Demand-12

0

2

4

6

8

10

1P 4P 5P 6P

No. of Processors

PX

Lo

ad

Star-FC

Ring-FC

Star-NC

Ring-NC

Figure 15: PXLoad Results of PTS Using Both CFsfor D12.

Percentage of Extra Load (r100N403a)Demand-11

0

1

2

3

4

5

6

1P 4P 5P 6P

No. of Processors

PX

Lo

ad

Star-FC

Ring-FC

Star-NC

Ring-NC

Figure 16: PXLoad Results of PTS Using Both CFsfor D11.

4.6 Maximum Utilization

The results for the Maximum Utilization (MU) areshown in Figure 17 and Figure 18. From this figure, itcan be seen that the Maximum Utilization in the caseof FortzCF is better than that of the NewCF.

From the above results it was observed that thePTS-Ring strategy produced better results for bothcost functions and the NewCF produced very good re-sults for minimizing the Number of congested links.The percentage of extra load was found to be best(Minimum) using the FortzCF and the Ring topology.However, in many cases, the NewCF also producedvalues close to the FortzCF. For both topologies, a sig-nificant improvement in the performance metrics wasobserved using parallelization.

As the size of any combinatorial optimizationproblem increases, not only its search space increasesexponentially but also it becomes more complex as thefraction of solutions that are close to the optimal one

Maximum Utilization (r100N403a)Demand-12

0

0.5

1

1.5

2

1P 4P 5P 6P

No. of Processors

Max

imum

Util

izat

ion

Star-FC

Ring-FC

Star-NC

Ring-NC

Figure 17: MU Results of PTS Using Both CFs forD12.

Maximum Utilization (r100N403a)Demand-11

1.041.061.08

1.11.121.141.161.18

1.2

1P 4P 5P 6P

No. of Processors

Max

imum

Util

izat

ion

Star-FC

Ring-FC

Star-NC

Ring-NC

Figure 18: MU Results of PTS Using Both CFs forD11.

becomes smaller. Sequential heuristics often fail toexplore this small fraction from the huge search space.Having seen the results of sequential heuristics, PTS-Star, and PTS-Ring in terms of speedup and final cost,it is evident that, as the size and routing complexity ofthe network increases, there is a significant improve-ment in the solution quality with parallelized heuris-tics.

5 Conclusion

Two different Parallel Tabu Search iterative heuristicswere implemented on several networks using two costfunctions. Results for four performance metrics arereported for FortzCF and NewCF. Both PTS heuris-tics produced the desired results in the case of largetopologies in terms of cost. The PTS-Ring strategywhich was designed to induce diversification into thesearch was found to achieve better cost than any otherapproach including the PTS-Star for the same runtime. However, linear speedup could not be achievedin any strategy. Both the strategies produced better re-sults for smaller topologies also, but did not providea significant improvement in cost as achieved for thelarger topologies. Hence, it can be concluded that if



the problem size is large, parallel Tabu Search or anyother parallel algorithm can be efficiently applied tothe OSPFWS problem to achieve a solution qualitywhich can not be achieved by using sequential algo-rithms within the same or comparable time frame.

Acknowledgements: Acknowledgement goes toKFUPM for supporting this research work. This ma-terial is based in part on work supported by a KFUPMproject under Grant No. SAB-2006-10. The authorswish to thank Bernard Fortz and Mikkel Thorup forsharing the test problems.

References:

[1] Bernard Fortz and Mikkel Thorup. Increasinginternet capacity using local search. TechnicalReport IS-MG, 2000.

[2] M Resende Ericsson and P Pardalos. A ge-netic algorithm for the weight setting problem inospf routing. Combinatorial Optimisation con-ference, 2002.

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Parallel tabu search for optimizing the OSPF weight setting problem

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