A Hybrid Genetic Algorithm for Routing Optimization in IP Networks Utilizing Bandwidth and Delay Metrics

A Hybrd Genetc Algorthm for Routng Optmzaton n IP Networks Utlzng Bandwdth and Delay Metrcs Anton Redl Insttute of Communcaton Networks, Munch Unversty of Technology, Arcsstr. 21, 80290 Munch, Germany E-mal: Anton.Redl@e.tum.de Abstract -- Routng optmzaton s an mportant ssue of IP traffc engneerng. Dependng on the routng protocol used n the network, varous approaches are possble. In ths paper, we dscuss the dfferent concepts of IP routng and ther mplcatons for routng optmzaton. Specfcally, we focus on destnaton-based routng protocols that compute routes based on bandwdth and delay metrcs. In order to optmze the metrc settng n networks wth these types of routng protocols, a hybrd genetc algorthm s presented. Keywords -- Traffc engneerng, genetc algorthm, bandwdth-delay senstve routng, destnaton-based routng, OSPF, EIGRP I. INTRODUCTION Routng optmzaton s a core concept of Internet traffc engneerng, whch encompasses all methodologes capable of provdng Qualty of Servce (QoS) n IP networks [1]. Based on a network topology wth capactated lnks, routng optmzaton tres to mprove QoS by fndng approprate routes for all traffc flows n the network. As there are dfferent notons of QoS, there s no unque defnton or formulaton for the objectve of the routng optmzaton process. Usually lnk utlzaton s taken as a measure of perceved QoS snce t correlates wth packet delay and packet loss wthn routers. Therefore, a common objectve of routng optmzaton, whch we also adopt n ths paper, s the mnmzaton of the maxmum lnk utlzaton n the network. It s qute ntutve and smple to determne throughout the optmzaton process. We focus on routng optmzaton n ndvdual network domans, whch correspond to autonomous systems (AS) or parts of them, and base the optmzaton process on the use of nteror gateway protocols (IGP). As we wll dscuss n secton II, varous protocols and routng strateges exst for the employment wthn a doman, havng dfferent mplcatons for the routng optmzaton process. In order to successfully allevate overload problems by routng optmzaton, some prerequstes need to be fulflled. Frst of all, the avalable network resources have to suffce to carry the total offered traffc wth the desred servce qualty. Whenever overloaded lnks exst n the network, traffc has to be shfted onto other routes. However, ths can only be done, f other lnks stll provde enough bandwdth to bear the excess traffc wthout becomng overloaded themselves. Another prerequste for routng optmzaton s the deployment of a routng protocol, whch actually allows the settng of paths through the network. Furthermore, f a metrc-based routng protocol s used, network operators must be wllng to gve up any physcally relevant meanng of lnk metrcs such as cost, delay, or bandwdth. Instead, these metrcs have to be used as generc means for the sake of routng optmzaton. Therefore, t s of great help f network management tools support ths noton of metrc settng and provde the approprate framework for routng optmzaton. The rest of the paper s organzed as follows. In secton II the dfferent concepts of routng and ther mplcatons for routng optmzaton are dscussed. We specfcally focus on destnaton-based routng protocols that consder bandwdth and delay metrcs. A hybrd genetc algorthm for the computaton of optmzed routng schemes s ntroduced n secton III and computatonal results and performance ssues are presented n secton IV. Secton V concludes the paper. II. FUNDAMENTAL PRINCIPLES OF ROUTING OPTIMIZATION IN IP NETWORKS The potental of routng optmzaton,.e., the possble gan n QoS that can be acheved, strongly depends on the flexblty of the deployed routng protocol. Therefore, we gve a short overvew of exstng routng concepts and dscuss ther mplcatons for routng optmzaton. A. Destnaton-Based vs. Source/Flow-Based Routng Two fundamentally dfferent routng concepts exst, whch strongly nfluence the optmzaton procedure and the achevable results: destnaton-based routng and source- or flow-based routng. Conventonal routng protocols such as OSPF [2], EIGRP [3], or IS-IS [4], follow the next-hop destnaton-based routng paradgm. Wthn each router the forwardng decson for an IP packet s based solely on the destnaton address specfed n the packet header. A router looks up the prefx of the destnaton address n ts routng table, determnes the outgong nterface, and sends the packet to the approprate neghbor. No nformaton about the orgn or any other context of the packet s taken nto account. As a consequence, ths routng procedure s smple and qute effcent. However, t mposes lmtatons on routng optmzaton, as llustrated n Fgure 1. Whenever two traffc flows wth the same destnaton cross each other s way they are merged and sent out over the same nterface. Ths mght cause traffc overload on some lnks, whle other lnks are stll only lghtly utlzed.

Flow 1 Flow 2 Fgure 1 Lmtatons of destnaton-based routng To overcome these lmtatons, new flow-based routng technologes such as Multprotocol Label Swtchng (MPLS) [5] have been developed. MPLS makes t possble to establsh an overlay routng structure wthn the IP network - ndependently of the used routng protocol - and to set up explct paths for ndvdual traffc flows. Each MPLS-routed IP packet s marked wth a specal label, whch the routers along the way consder for forwardng decsons. Thus, the routng pattern does not depend on the underlyng routng protocol, but rather on the label and forwardng nformaton that s stored n the MPLS routers. Instead of determnng the path of a packet based on the destnaton address n a hop-by-hop manner, the path s now fxed by the router, whch marks the packet wth the approprate label. Ths ntroduces a hgh degree of routng freedom as any desred routng pattern can be reached. B. Sngle-Metrc vs. Multple-Metrc Routng In the case of destnaton-based routng protocols a router determnes an outgong nterface based on metrc values, whch quanttatvely descrbe the dstance to a destnaton node. Most commonly, sngle addtve metrcs are assgned to every lnk, and a shortest-path algorthm s used to determne the preferred path from each node to every other node n the network ( sngle-metrc routng ). Whle lnk metrcs often have physcally relevant meanngs such as propagaton delay or cost, they can also be used n a generc way purely for the sake of routng optmzaton. By settng approprate lnk metrc values, one can mplctly nfluence and, thus, optmze the routng scheme. In addton to sngle-metrc protocols, routng schemes exst, whch allow more than one metrc taken nto account when computng the length of a path towards a destnaton node ( multple-metrc routng )[6][7]. One example s Csco s routng protocol EIGRP, whch ncorporates four metrc types. However, only two of them are used by default: one addtve metrc ( delay ) and one concave metrc ( bandwdth ). In the followng, we wll focus on these two metrc types and show how they can be used for routng optmzaton. The dstance to a destnaton node s now computed by the normalzed metrc formula M 1 = + d = max( cm ) + d mn(bw ). Parameter bw denotes the bandwdth of a lnk, whle d refers to ts delay value. Thus, a router takes the sum of all delay values towards the destnaton node and adds a bandwdth component, whch s the nverse of the smallest bandwdth along the path ( bottleneck ). From all possble path optons t selects the one wth smallest path metrc M. For further consderatons we wll refer to the bandwdth component as nverse capacty metrc cm and take the maxmum along the path nstead of the recprocal value of the bandwdth mnmum. Fgure 2 llustrates the concept of bandwdth-delay senstve routng. If only the delay metrcs d were taken nto consderaton, flow 1 would take the upper path along nodes B-C-E. However, lnk C-E has a smaller normalzed bandwdth of 0.25 and, therefore, contrbutes to M wth an nverse capacty metrc of 4. Thus, the cost value assocated wth path A-B-C-E s 7 (delay sum of 3 plus bandwdth component of 4), whle path A-D-E has only an overall metrc of 5. Therefore, router A would choose router D as ts next-hop neghbor. Flow 1 A d = 3 cm = 1 cm = 1 Flow 2 D B cm = 1 cm = 1 C bw = 0.25 cm = 4 Fgure 2 Multple-metrc routng Dependng on the values for d and cm, emphass s ether put on small overall delay, on hgh throughput, or on a mxture of both. In case delay metrcs are substantally larger than nverse capacty metrcs, the overall path metrc s manly determned by delay values. Only when there are several alternatves wth equal smallest delay sum, the bandwdth component really matters. The router then selects the outgong nterface wth the largest possble throughput ( wdest-shortest path ). In the opposte case (cm >> d), hgh throughput paths are preferred, and delay s manly used to break tes ( shortest-wdest path ). Whenever the two lnk metrcs are of the same order, no clear preference s gven to ether one of them. Lnk metrcs are then used n ther most generc form as means of routng optmzaton, wthout any physcally relevant meanng. Routng optmzaton based on the multple-metrc concept has some advantages over the pure shortest-path approach, as can be demonstrated on the network scenaro n Fgure 3. Flow 1 Flow 2 Fgure 3 A d = 2, cm = 1, cm = 4 B C d = 2, cm = 1, cm = 4 D E d = 2, cm = 1, cm = 4 Fsh-pattern routng wth multple metrcs Assume we have two traffc flows wth dfferent destnatons, whose paths have several nodes n common. Let A be the frst node where the two flows come together and D be last common node on ther way. Whle shortestpath routng would merge the flows at node A and send both of them ether over B or over C, multple-metrc routng protocols can acheve the flow pattern gven n the fgure. For flow 1, the chosen path has a total metrc of 7, E F

whle the lnk metrcs along the route va C would sum up to 8. For flow 2 the stuaton s dfferent. The total metrcs of the upper and the lower path are 9 and 7, respectvely. The trck s to use the nverse capacty metrc to make one path opton appear more costly for one traffc flow, whle for the other flow a larger cm value has no extra effect (snce t experences already hgh cm values on other lnks along the path, whch the two flows do not share). From ths small scenaro we can conclude that routng optmzaton based on multple-metrc routng protocols s superor to ts sngle-metrc counterpart as t can realze addtonal routng patterns. C. Equal-Cost Mult-Path ECMP Another possble feature of routng protocols, whch nfluences the optmzaton process, s load sharng. In destnaton-based routng protocols ths capablty s often mplemented n form of the equal-cost mult-path concept. Whenever a router can reach a destnaton node va several paths wth equal metrc sums, t splts up the traffc evenly across all correspondng outgong nterfaces. If multple-metrc routng protocols are used, equal cost does not necessarly mean that all metrc components are the same on all load-sharng paths. Ths s llustrated n Fgure 4. Whle the metrc combnatons of both paths from B to C are equal, ther delay and bandwdth portons are qute dfferent. A bw = 0.25 cm = 4 B bw = 0.25, cm = 4 d = 4, cm = 1 Fgure 4 Load sharng example Followng pecularty has to be consdered, when usng multple-metrc protocols together wth load-sharng: In order to compute the route from A to C, router A needs to know the metrcs d and cm of the path from B to C. Therefore, B has to choose one representatve nterface among the outgong nterfaces, whose metrc set t then passes on to the upstream routers. Although both paths have equal costs the choce of metrc par that B reports to A affects the cost value of A towards C. Recevng the metrcs of the upper path results n a total cost value of 6, whle the lower path metrcs gve a value of 9. To allow unambguous route computaton we defne a prmary outgong nterface, whose metrcs are reported to neghbor routers. Among all outgong nterfaces, the prmary nterface s the one wth the hghest throughput value. In the gven example, ths would be the lower path wth. D. Routng Optmzaton Classes and Soluton Approaches Based on the concepts dscussed n the precedng paragraphs varous categores of IP routng optmzaton can be dfferentated. Source and flow-based routng protocols ( MPLS ) certanly provde the greatest potental for routng optmzaton. Assumng that there are no specal restrctons concernng the routes through the network, we C can try to fnd a global optmum by solvng a mxed-nteger program for the multcommodty flow problem. However, as we focus on destnaton-based routng protocols, we are manly nterested n the lnear programmng (LP) soluton as t provdes a lower bound for the routng optmzaton process. The category of destnaton-based routng optmzaton s further dvded nto sngle-metrc ( OSPF ) and multplemetrc ( EIGRP ) models, each havng a verson wth and wthout load-sharng ( ECMP ). Most of the lterature about ths type of IP routng optmzaton deals wth OSPF as the underlyng protocol [8][9][10][11][12]. A mxednteger programmng formulaton of the routng optmzaton process for bandwdth-delay senstve protocols can be found n [13]. However, snce t s not possble to solve the mxed-nteger program for medumsze and large networks, approprate heurstcs are necessary. III. GENETIC ALGORITHM FOR ROUTING OPTIMIZATION A. Genetc Algorthm Bascs Genetc algorthms are based on the dea of natural selecton. It s suggested that an ndvdual s strength to survve n the world s determned by ts gene structure and that over many generatons only good genes preval, whereas bad ones are rejected. Furthermore, t s expected that brngng together ndvduals wth good gene combnatons produces agan good or even better ones. Genetc algorthms apply ths prncple to optmzaton problems by representng possble soluton alternatves through approprate gene strngs and performng operatons of natural selecton on these strngs[14]. At frst, a random set of strngs s generated ( Generaton 0 ). Then, the three basc operators reproducton, crossover, and mutaton are carred out repeatedly untl some termnaton crteron s reached. At each teraton ( generaton ) the exstng strngs are transformed nto solutons and ther qualty ( ftness ) s evaluated. Fgure 5 llustrates the general procedure of genetc algorthms. Fgure 5 mutaton crossover reproducton + selecton no Generaton 0 (generated randomly) perform local search evaluate solutons assgn ftness values max. generaton? Genetc algorthm flow chart yes hybrd GA return best soluton The reproducton process creates a new generaton. Startng from an exstng generaton, strngs are reproduced wth a probablty proportonal to the qualty of the correspondng soluton. Strngs, whch represent solutons wth good propertes, have a hgher chance to survve than strngs depctng soluton ponts wth bad characterstcs ("survval of the fttest"). The crossover operator chooses pars of strngs, breaks up ther gene sequence at random

places, and exchanges the genetc nformaton. Fnally, the mutaton operator ntroduces new genetc materal by randomly selectng and changng sngle genes. Mutaton s mportant to partally shft the overall search process to new locatons n the soluton space. Otherwse, the search process would converge to a local optmum wthout havng the chance to consder any further ponts. As ndcated n Fgure 5, we extend the pure genetc algorthm framework and perform a local search heurstc before evaluatng the solutons (therefore, hybrd GA ). In the lterature, ths combnaton of genetc algorthms wth a local search process s also referred to as memetc algorthm. B. Implementaton of the Algorthm Strng Representaton A crucal pont of every genetc algorthm s the strng representaton of possble soluton alternatves. After every crossover and mutaton step, one has to be able to turn the resultng strngs nto vald solutons. Our approach s analog to the ones presented n [11][12][15]. We enumerate all lnks n the network and assocate lnk weghts wth each of them. A specfc gene strng contans the weghts of all lnks n the order of ther enumeraton. For the sngle-metrc routng case, we have one strng representng a routng scenaro (one metrc assocated wth every lnk), whle n the bandwdth-delay case a genetc representaton of a certan soluton requres two strngs (one for d and one for cm). From the metrc strngs, a specfc soluton can be deduced by applyng the respectve routng computaton algorthms for shortest-path routng or bandwdth-delay routng. Lnk weghts are ntegers rangng from 1 to a maxmum value. In practce, routng protocols allow qute large maxmum values (e.g., n case of OSPF up to 65535). However, for traffc engneerng and routng optmzaton purposes the metrc values can be kept much smaller. Intal Populaton The ntal populaton s chosen randomly. However, t s possble to use the hop-based shortest-path routng scenaro as one startng pont for the optmzaton process. Ths s acheved by settng all weghts of one strng of generaton 0 to equal values. Ftness Functon and Power Scalng As we would lke to mnmze the maxmum lnk utlzaton n the network, we choose the nverse of ths value as our ftness functon. Ths way, routng solutons wth smaller maxmum lnk utlzaton values receve hgher ftness values and, thus, have a hgher chance to be reproduced when settng up a new generaton. However, to avod that n some cases good solutons are reproduced too fast and weaker ones de out too quckly, we apply power scalng to the ftness functon: 1 ftness = max( utlzaton ) lnks p p > 0. Wth p = (0,1) we can acheve that ftness values of bad solutons ncrease relatvely to the best ones wthn a generaton, thus, avodng that the optmzaton process converges to a local optmum too fast. C. Local Search Heurstc In order to mprove the performance and the speed of the genetc algorthm, the evaluaton step shown n Fgure 5 s preceded by a local search process. Before evaluatng each routng soluton, smple heurstcs are used to dvert traffc from the lnk wth the hghest utlzaton. Ths s done repeatedly untl no further mprovement can be acheved. As the search heurstc s determnstc, a certan metrc strng always results n the same routng soluton. Thus, t s sutable for the use wthn the genetc algorthm framework. Sngle-Metrc Heurstc In case of shortest-path routng, traffc can be dverted from a lnk by ncreasng ts metrc. Therefore, we ncrement the metrc of the hghest-utlzed lnk and reroute all traffc flows. If ths step leads to a hgher utlzaton value n the network t s reverted and the local optmzaton heurstc ends. Otherwse, the procedure s repeated for the lnk, whch now shows hghest utlzaton. Ths search heurstc s analog to the one n [12], where a computatonally optmzed verson s presented. Multple-Metrc Case For routng protocols wth bandwdth and delay metrcs there are some more possbltes of dvertng traffc from ndvdual lnks. We can ncrease ether the delay metrc or the nverse capacty metrc. Furthermore, combnatons are possble that mght also result n a change of the path structure: the delay metrc can be ncreased whle at the same tme the cm metrc s decreased, or vce versa. Thus, the search heurstc teratvely apples these metrc modfcatons to the hghest-utlzed lnk. Each metrc change s accepted f t does not lead to an ncrease of the maxmum utlzaton. If no further mprovements can be obtaned, the heurstc stops. IV. FIRST RESULTS AND ALGORITHM EVALUATION A. Comparson of GA and Hybrd GA At frst, we would lke to demonstrate the benefts of the local search heurstc. In the graph of Fgure 6 the best maxmum utlzaton value of each generaton s shown over tme for a sample run of the pure genetc algorthm GA and of the hybrd verson. The total tme s about 10 mnutes on a Lnux PC. For GA, the populaton sze was set to 2000, whle the hybrd algorthm works wth a populaton sze of 500. Snce GA s less complex, t proceeds faster from generaton to generaton even though ts populaton sze s four tmes larger. In 10 mnutes t has produced about 150 generatons, whle the hybrd verson only reaches about 100 generatons. However, from the begnnng on, the maxmum utlzaton values of the hybrd algorthm le below the values of pure GA.

Maxmum Utlzaton 2.0 1.8 1.6 1.4 1.2 1.0 0.8 Fgure 6 Genetc Algorthm Hybrd GA lower bound 0 100 200 300 400 500 600 Tme n seconds Comparson of GA algorthms V. CONCLUSION In ths paper we have dscussed dfferent possbltes of routng optmzaton for IP networks. We have presented a hybrd genetc algorthm, whch consders smple-metrc as well as multple-metrc destnaton-based routng protocols and allows the use of the equal-cost load-sharng feature. Frst results show that the maxmum utlzaton n the network can be further decreased f a routng protocol wth two lnk metrcs s deployed. Whle the gan of around 5% mght not seem to be worth the extra effort, t could stll make a dfference when traffc s approachng some undesrable threshold. References B. Comparson of Routng Optmzaton Approaches The hybrd GA was appled to several network archtectures, each loaded wth varous traffc matrces (from lghtly loaded to overload stuatons). Table 1 descrbes three typcal scenaros. The networks are hghly loaded. If routng s done wth standard OSPF and all lnk metrcs are set to 1, several lnks are overloaded. Scenaro 1 Scenaro 2 Scenaro 3 nodes 11 20 50 lnks 40 60 170 flows 110 200 400 max. utl. 1.37 1.35 1.72 overloaded lnks 11 3 8 Table 1 Network parameters Table 2 summarzes the optmzaton results for the consdered topologes. Snce genetc algorthms do not guarantee to fnd the optmum soluton, the algorthms were run several tmes for each topology, and the best soluton was taken. Scenaro 1 Scenaro 2 Scenaro 3 Lower Bound 0.85 0.69 0.68 OSPF 0.970 0.716 0.780 OSPF ECMP 0.911 0.706 0.742 EIGRP 0.939 0.716 0.766 EIGRP ECMP 0.883 0.706 0.730 Table 2 Optmzed maxmum utlzaton values As expected, EIGRP s able to acheve lower utlzaton values than OSPF (scenaro 1 and 3), and load sharng (although t s qute lmted for destnaton-base routng protocols) also allows further QoS enhancement (all scenaros). However, dependng on the load stuaton, t s not always guaranteed that EIGRP optmzaton performs better than ts OSPF counterpart (scenaro 2). Snce n ths scenaro OSPF ECMP optmzaton already gets very close to the lower bound, no further mprovement can be expected by EIGRP ECMP. In most cases that we have nvestgated the gan from OSPF to EIGRP (and ther respectve ECMP versons) has been around 4%. [1] D. Awduche, J. Malcolm, J. Agogbua, M. O'Dell, J. McManus, Requrements for Traffc Engneerng Over MPLS, IETF RFC 2702, Sept 1999 [2] J. Moy, OSPF Verson 2, IETF RFC 2328, Aprl 1998 [3] Enhanced Interor Gateway Routng Protocol, Csco Whte Paper EIGRP, http://www.csco.com/warp/publc/103/egrp-toc.html [4] R. Callon, Use of OSI IS-IS for Routng n TCP/IP and Dual Envronments, IETF RFC 1195, December 1990 [5] E. Rosen, A. Vswanathan, R. Callon, Multprotocol Label Swtchng Archtecture, IETF RFC 3031, January 2001 [6] Z. Wang, J. Crowcroft, "Qualty-of-Servce Routng for Supportng Multmeda Applcatons", IEEE Journal of Selected Areas n Communcatons, Vol. 14, No. 7, pp. 1228-1234, 1996 [7] S. Chen, K. Nahrstedt, An overvew of Qualty-of-Servce Routng for the Next Generaton Hgh-Speed Networks: Problems and Solutons, IEEE Network Magazne, Specal Issue on Transmsson and Dstrbuton of Dgtal Vdeo, 12(6):64-79, November/December 1998 [8] A. Bley, M. Grötschel, R. Wessäly, Desgn of Broadband Vrtual Prvate Networks: Model and Heurstcs for the B- WN, Techncal report, Preprnt SC 98-13, Konrad- Zuse_zentrum für Informatonstechnk, Berln, 1998 [9] K. Holmberg, D. Yuan, Optmzaton of Internet Protocol Network Desgn and Routng, Research Report LTH-MAT- R-2001-07, Department of Mathematcs, Lnkopng Insttute of Technology, Sweden, 2001 [10] B. Fortz, M. Thorup, Internet traffc engneerng by optmzng OSPF weghts, Proceedngs of INFOCOM 2000, Tel-Avv, Israel, March 2000 [11] M. Ercsson, M.G.C. Resende, P.M. Pardalos, A Genetc Algorthm For The Weght Settng Problem n OSPF Routng, to appear n J. of Combnatoral Optmzaton [12] M.G.C. Resende et al., "A memetc algorthm for the weght settng problem n OSPF routng," presented at 6 th INFORMS Telecommuncatons Conference, Boca Raton, Florda, March 2002 [13] A. Redl, D.A. Schupke, A Flow-Based Approach for IP Traffc Engneerng Utlzng Routng Protocols Wth Multple Metrc Types, presented at 6th INFORMS Telecommuncatons Conference, Boca Raton, Florda, March 2002 [14] D.E. Goldberg, Genetc Algorthms n Search, Optmzaton & Machne Learnng, Addson-Wesley, Massachusetts, 1989 [15] A. Redl, A Versatle Genetc Algorthm for Network Plannng, n Proc. of EUNICE'98, Munch, September 1998