This work explores the optimization of a real-valued parameter, assigned to each network node running the Distributed Exponentially-weighted Flow SpliTting (DEFT) routing protocol, in order to address changes on traffic conditions. This new proposal avoids the need to alter link weights and forwarding paths, by adjusting traffic splitting. In this context, we explore the use of Evolutionary Algorithms both in single and multi-objective optimization problems, to obtain solutions that minimize network's congestion.We thank the Portuguese FCT under the scope of the strategic funding of UID/BIO/04469/2013 unitand COMPETE 2020(POCI-01-0145-FEDER-006684) and BioTecNorte (NORTE-010145-FEDER-000004) funded by European Regional Development Fund (Norte2020-ProgramaOperacionalRegionaldoNorte).info:eu-repo/semantics/publishedVersio

Pereira, Vitor

Rocha, Miguel

Sousa, Pedro

Universidade do Minho: RepositoriUM

Evolutionary Computation at work for the optimization of linkstate routing protocolsVitor PereiraCentro Algoritmi / Dept. Informatics,University of MinhoPortugalvitor.pereira@algoritmi.uminho.ptPedro SousaCentro Algoritmi / Dept. Informatics,University of MinhoPortugalpns@di.uminho.ptMiguel RochaCentre of Biological Engineering /Dept. Informatics,University of MinhoPortugalmrocha@di.uminho.ptABSTRACTis work explores the optimization of a real-valued parameter, as-signed to each network node running the Distributed Exponentially-weighted Flow SpliTting (DEFT) routing protocol, in order to ad-dress changes on trac conditions. is new proposal avoids theneed to alter link weights and forwarding paths, by adjusting tracspliing. In this context, we explore the use of Evolutionary Algo-rithms both in single and multi-objective optimization problems,to obtain solutions that minimize network’s congestion.KEYWORDSEvolutionary Computation, Trac EngineeringACM Reference format:Vitor Pereira, Pedro Sousa, and Miguel Rocha. 2017. Evolutionary Com-putation at work for the optimization of link state routing protocols. InProceedings of GECCO ’17 Companion, Berlin, Germany, July 15-19, 2017,2 pages.DOI: hp://dx.doi.org/10.1145/3067695.30761101 INTRODUCTIONe Distributed Exponentially-weighted Flow SpliTting (DEFT)[1, 2] is a link-state routing protocol built around the well-knownshortest path algorithm from graph theory. Using topological infor-mation broadcast by all nodes on the network, each router calculatesthe shortest path to all others, which minimizes the sum of weightsassigned to links. While most implementations use Equal-CostMulti-Path (ECMP) [4] to equally distribute trac along shortestpaths, DEFT enables routers to forward portions of the trac overnon shortest paths, and thus enables a beer use of paths whichmay otherwise be underutilized.is work explores the utilization of distinct values for the pa-rameter p in DEFT, assigned to each node, and their optimizationby means of Evolutionary Algorithms (EAs). We show that by opti-mizing such values it is possible to accommodate trac variationswithout the need to recongure the installed link weights, andtherefore without changing the network routing paths. e EAs areused both to optimize link weights, for single and multi-objectiveproblems, as well as p values.Permission to make digital or hard copies of part or all of this work for personal orclassroom use is granted without fee provided that copies are not made or distributedfor prot or commercial advantage and that copies bear this notice and the full citationon the rst page. Copyrights for third-party components of this work must be honored.For all other uses, contact the owner/author(s).GECCO ’17 Companion, Berlin, Germany© 2017 Copyright held by the owner/author(s). 978-1-4503-4939-0/17/07. . .$15.00DOI: hp://dx.doi.org/10.1145/3067695.30761102 MATHEMATICAL MODEL AND PROBLEMDEFINITIONNetwork topologies are modeled as directed graphs G (N ,A), withcapacity constrains ca , for each arc a ∈ A. Considering a givenweight congurationw and a trac matrix D, the distribution oftrac among the available resources is achieved using the DEFTrouting protocol. DEFT assigns ows to a next-hop with a prob-ability that exponentially decreases with the extra length of thepath when compared with the shortest path. e distance from anode u to a node t , when trac is routed thought a node v , canbe expressed as dtv +wu,v , where dtv is the shortest distance fromthe next-hop v to t , andwu,v is the weight of the link (u,v ). eextra length of the path from u to t through v , when comparedto the shortest path from u to t , is htu,v = dtv + wu,v − dtu . eow proportion on the outgoing link (u,v ) destined to t , at u , iscomputed by Equation 1:P(htu,v)=Γ(htu,v)∑(u,i )∈A Γ(htu,i) , (1)where the exponential function Γ, Equation 2, maps the extra lengthhtu,v of a path into the [0; 1] range.Γ(htu,v)=e− htu,vp , if dtv < dtu0, otherwise(2)As the extra length htu,v is an integer value, the parameter p wasinitially thought as a constant to scale the penalizing function Γ toa range [wmin,wmax] of possible link weights. is work considersthe values of p to be distinct variables assigned to each node u, thatcan be optimized to improve trac distribution. To evaluate thenetwork resources utilization and congestion level we resort to thepiecewise linear cost function Φ, proposed by Fortz and orup [3],that also serves as main objective function.Given a network topology and one or more trac matrices, forwhich an optimal link weights conguration is already installed, weaim to nd a conguration ofp values whichminimizes the networkcongestion Φ when new trac requirements are imposed, withoutany change to the installed link weights. e problem requires apre-optimization of link weights, performed by a single-objectiveEA (SOEA), for a single trac matrix (Scenario A), or with NSGAII[5], when two trac matrices are provided (Scenario B).299GECCO ’17 Companion, July 15-19, 2017, Berlin, Germany Vitor Pereira, Pedro Sousa, and Miguel RochaTable 1: P-values Optimization - Scenario A: Single previously known trac matrixMeasureRand302 Rand502D0 D1 D2 D0 D1 D2Opt. Before Aer Opt Before Aer Opt. Opt. Before Aer Opt Before Aer Opt.Congestion 1.39 8.61 3.28 1.49 16.45 5.93 1.76 1.59 8.22 1.75 1.83 31.29 13.46 11.18Avg Link Utilization 35% 37% 37% 37% 43% 44% 43% 37% 38% 38% 37% 50% 51%. 49%Max. Link Utilization 75% 121% 115% 76% 144% 117% 90% 94% 130% 100% 101% 155% 132% 121%Table 2: P-values Optimization - - Scenario B: Two previously known trac matricesMeasureRand302 Rand502D0,1 D0,2 D1 D2 D0,1 D0,2 D1 D2Opt. Before Aer Opt Before Aer Opt. Opt. Before Aer Opt Before Aer Opt.Congestion 1.46 1.39 18.91 2.43 1.73 34.12 16.29 4.07 1.23 1.28 17.76 1.99 1.59 28.30 8.06 5.32Avg Link Utilization 34% 33% 43% 44% 42% 54% 55% 55% 25% 28% 37% 38% 37% 45% 46% 45%Max. Link Utilization 77% 77% 155% 101% 90% 140% 135% 109% 89% 82% 132% 104% 94% 136% 118% 116%3 CONFIGURATION SETTINGSe SOEA and NSGAII have a similar conguration. e individualsthat populate the initial populations are randomly generated. Whilefor link weights optimization the solutions are integer vectors thattake values in the range [1; 20] (each gene encodes a link weight),solutions for parameters p optimization are vectors of real values,one for each node, in the range [0.1 ; 10]. When p = 0.1, no tracis forwarded on non shortest path links, and when p = 10 the nonshortest path links are used nearly as if they were on shortest paths.In the integer representation, the reproduction operators (allwith the same probability) were: Random mutation, Incremen-tal/decrementalmutation, Uniform crossover and Two point crossover,while for real representations, the reproduction operators were:Gaussian Perturbation mutation, Linear Genome Random muta-tion, Uniform crossover and Real Value Arithmetical crossover. Forthe optimization of DEFT weights, a p value of 1 was applied toall nodes. e experiments were run for two synthetic networksRand302 (30 nodes, 110 edges) and Rand502 (50 nodes, 196 edges).4 RESULTSIn the experiments, we consider that a DEFT link weight congura-tion is already installed and optimized for a previously known tracmatrix D0 (Scenario A), or for two trac matrices D0,1 and D0,2(Scenario B). ese experiments analyze scenarios where heavytrac needs to be forwarded, where demands are in the order of 30,40 and 50% of the network capacity. Due to trac changes, wherethe new trac conditions are represented as two trac demandmatrices D1 and D2, which need to be accommodated, the networkstarts to experience congestion problems. Tables 1 and 2 includethe congestion values, average link utilization and maximal linkutilization for the distinct moments in time: the initial optimizedconguration (Opt.); when the new demands are imposed whilepreserving the installed weights conguration and default p values(Before); and aer p value optimization (Aer). For comparison,we also include the results for the link weights optimization of thenew trac demands. e results are the average of 10 runs with atermination criteria of 1000 iterations for link weights optimizationand 200 iterations for the p values optimization.e results show that, by optimizing p values to address newtrac requirements, the congestion levels on the network can bereduced, while preserving the installed weights. In some cases, thenetwork continues to perform eciently, with a congestion mea-sure under 10.6, and therefore it was possible to accommodate thechanges on trac without any disruption on the forwarding paths.Although there are some links that continue to be over-utilizedaer the p values optimization, this became almost negligible. It isimportant to note that this solution aims to keep the forwardingpaths conguration, while temporary trac changes are imposed.5 CONCLUSIONSis work presented two applications of EAs to link state routingprotocols optimization. Single objective and multi-objective EAswere used to obtain near optimal solutions to link weight seingproblems, for DEFT routing protocols. Taking advantage of a pa-rameter used by the routing algorithm, we experimentally analyzeda possible approach to respond to trac changes responsible forcongestion in networks. By optimizing the values of p assignedto each node on the network it was possible, in most cases, to re-duce the overall network congestion for DEFT enabled networks,without resorting to a re-optimization of link weights.Acknowledgments. We thank the Portuguese FCT under the scopeof the strategic funding of UID/BIO/04469/2013 unit and COMPETE2020 (POCI-01-0145-FEDER-006684) and BioTecNorte (NORTE-01-0145-FEDER-000004) funded by European Regional DevelopmentFund (Norte2020 - Programa Operacional Regional do Norte).REFERENCES[1] D. Xu, M. Chiang, and J. Rexford. DEFT: Distributed exponentially-weightedow spliing. Proc. IEEE Conf. Comput. Commun., pp. 71–79, 2007.[2] V. Pereira, M. Rocha and P. Sousa. Optimizing Load Balancing Routing Mech-anisms with Evolutionary Computation. In Proc. of Intelligent Environments2016 (FI&SN), pp. 298-307, 2016.[3] B. Fortz. Internet trac engineering by optimizing ospf weights. In Proceedingsof IEEE INFOCOM, pp. 519–528, 2000.[4] C. Hopps, Analysis of an Equal-Cost Multi-Path Algorithm, Internet EngineeringTask Force , IETF , RFC 2992 (Informational).[5] K. Deb, S. Agrawal, A. Pratap, and T. Meyarivan. A fast and elitist multiobjectivegenetic algorithm: NSGA-II. IEEE Trans. Evolutionary Computation, 6(2): pp.182–197, 2002.300

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