We perform a machine-learning-based network pruning that significantly reduces the complexity of routing and wavelength assignment in large optical networks. A significant computational time reduction is achieved by accepting a minor deterioration of the obtained solution

Andrea Bianco

Cristina Rottondi

Davide Andreoletti

Silvia Giordano

English

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

16 July 2022POLITECNICO DI TORINORepository ISTITUZIONALEA Machine Learning Framework for Scalable Routing and Wavelength Assignment in Large Optical Networks /Andreoletti, Davide; Rottondi, Cristina Emma Margherita; Bianco, Andrea; Giordano, Silvia. - ELETTRONICO. - (2021),pp. 1-3. ((Intervento presentato al convegno 2021 Optical Fiber Communications Conference and Exhibition (OFC)tenutosi a San Francisco, CA, USA nel 6-10 July 2021.OriginalA Machine Learning Framework for Scalable Routing and Wavelength Assignment in Large OpticalNetworksIEEE postprint/Author's Accepted ManuscriptPublisher:PublishedDOI:Terms of use:openAccessPublisher copyright©2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in anycurrent or future media, including reprinting/republishing this material for advertising or promotional purposes, creatingnew collecting works, for resale or lists, or reuse of any copyrighted component of this work in other works.(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2937145 since: 2021-11-11T17:42:13ZIEEE/Optica Publishing GroupA Machine Learning Framework for ScalableRouting and Wavelength Assignment in LargeOptical NetworksDavide Andreoletti1, Cristina Rottondi2, Andrea Bianco2 and Silvia Giordano11Networking Laboratory, University of Applied Sciences of Southern Switzerland, Viganello, Switzerland2 Politecnico di Torino, Italy, 3 Politecnico di Milano, Italy{davide.andreoletti,silvia.giordano}@supsi.ch,{cristina.rottondi,andrea.bianco}@polito.itAbstract: We perform a machine-learning-based network pruning that significantly re-duces the complexity of routing and wavelength assignment in large optical networks. Asignificant computational time reduction is achieved by accepting a minor deterioration ofthe obtained solution. © 2021 The Author(s)1. IntroductionToday’s Internet is a complex ecosystem composed of a large number of interconnected Autonomous Systems(ASs) that transport, mainly over optical networks, massive amounts of traffic generated by bandwidth-hungryand latency-sensitive services. In this scenario, effective network management strategies must be implemented tomeet the increasingly-stringent performance requirements of current and upcoming services. This managementmight require, for instance, the quick resolution of common network planning problems. Unfortunately, exactoptimization methods like the mixed integer linear programming suffer from severe scalability issues, that preventtheir application to large real-world networks, especially when timely decision-making is required. Such issues arecommonly tackled by means of heuristic approaches, which are capable to provide sub-optimal solutions in shortertime [2]. In recent years, Machine Learning (ML) has been used to further reduce these scalability limitations,either by directly replacing exact optimization methods, or by enhancing existing heuristic approaches.In this work, we consider the Routing and Wavelength Assignment (RWA) problem in large optical networks.This problem was proven to be NP-hard, and ML-based approaches have been proposed to reduce its complexity.In [4] a model that maps a given traffic demand to a sequence of links along a specific wavelength is learned bymeans of supervised classification. In [5], a deep neural network is employed to select the best RWA strategy fora given traffic demand, under preliminary calculation of a predefined number of shortest paths. Reinforcementlearning frameworks for routing, modulation format and spectrum assignment have also been devised for networkscenarios with dynamic traffic [6, 7]. Despite these emerging ML-based solutions, the most common approachto tackle the RWA problem is a simple heuristic that first computes the shortest path over which the lightpathis routed and then assigns an optical channel. This strategy makes it possible to solve the RWA in a reasonableamount of time, but still suffers from scalability issues that prevent its real-time application on very large networks.To handle this problem, we develop a ML-based pruning system that, given an input graph and a source/destinationpair, returns a sub-graph formed only by the nodes that most likely belong to the shortest path. In this way, the sizeof the original graph is dramatically reduced, and the computational time of the RWA task significantly lowered(of up to 35%), as observed from extensive simulations performed over a network with tens of thousands of nodesand links. This improvement is achieved with an acceptable increment in the blocking probability, and a negligibleincrease of the average length of the computed shortest paths.2. Machine Learning Framework for Scalable Routing in Large Optical NetworksFirst, let us remark that the complexity of the RWA for a given lightpath can be significantly reduced if thistask is executed on a sub-portion of the original network that contains the shortest path between source anddestination of the considered lightpath. Starting from this observation, we propose a ML algorithm that i) estimatesthe likelihood that each node of the network belongs to the shortest path between a source and a destination andii) prunes the network accordingly, i.e., by selecting the nodes (and the links interconnecting such nodes) whoselikelihood is higher than a pruning threshold. Then, the RWA task is executed on the obtained reduced network,as depicted in Fig.1. As common in the literature, we also assume that the routing phase is performed usingthe Dijkstra algorithm, while the wavelength assignment phase is executed with either the First-Fit (FF) or theRandom Wavelength Selection (RS) strategy. Given a network with |V | nodes, |E| links with |W | optical channelsFig. 1: Representation of the overall ML-aided RWA strategyand diameter |D| << |E|, the complexity of the Dijkstra algorithm is O(|V | log |V |+ |E|), while the complexityof both FF and RS is O(|WD|). In real-world large networks, the number of optical channels is below 100, but thenumber of nodes and links might easily reach tens of thousands. Therefore, an effective network pruning systemhas the potential to drastically reduce the complexity of the RWA problem.More in detail, the proposed network pruning system is based on a ML inference system that computes thelikelihood pisd that the generic node ni belongs to the shortest path between a source node ns and a destinationnode nd . To train and then query this inference system, a suitable nodes representation strategy is required. Weargue that the nodes belonging to a shortest path likely share some topological properties (e.g., similar positionswith respect to a particular node), and we propose a representation that aims to capture this property. We randomlyselect K anchor nodes, and we represent the generic node ni as a vector vi whose j-th component is the length ofthe shortest path between ni and the j-th anchor, with j ∈ {1, ...,K}. The training process is then performed as aregression to learn how to map the set of representations of nodes ni, ns and nd onto a real value pisd within the range[0,1], which indicates the probability that ni belongs to the shortest path between ns and nd . More specifically, theML algorithm is fed with a vector of size 3K obtained by juxtaposing vi, vs and vd (i.e., the vectors representing ni,ns and nd , respectively). The probabilities are then ”binarized” as a function of a pruning threshold parameter γ: ifpisd ≤ γ , ni is pruned, otherwise ni is kept in the reduced network. The considered ML algorithm is a Decision Treetrained using a dataset formed by shortest paths computed between randomly-selected pair of nodes. The size ofthe training set is equal to the 0.4% of the total number of shortest paths between any pair of nodes in considerednetwork (which are |V | · (|V |− 1)/2). Note that our ML framework is developed having scalability as a primarydesign objective. For this reason, we have chosen a nodes representation strategy and an inference ML algorithmthat only involve low-complexity operations. After the training phase, the ML-based inference system can be usedto implement the network pruning system. As the ML prediction is prone to errors, nodes belonging to the shortestpath might be mistakenly pruned, and this can eventually lead to sub-optimal solutions of the RWA, or even tothe impossibility of finding a path between source and destination. In this latter case, we envision a re-executionof the RWA task either on the original graph, or on a graph pruned considering a lower node selection threshold.This re-execution introduces a time overhead, as further discussed in Sec.3.3. ResultsWe assess the performance of the RWA task executed with the proposed ML-aided network pruning system bycomparison to those obtained without the pruning phase, considering a network of |V |= 50166 nodes and 103252links with |W | = 80 optical channels per link and formed by interconnecting 1000 ASs. Both the intra-ASs andinter-ASs networks are generated according to the model described in Ref. [1].Fig. 2 shows the average time required to compute 3000 shortest paths for γ ∈ [0.45,0.7] . Specifically, wecompare the computational times of the ”Dijkstra” algorithm executed on the original graph with the ”ML-aided” on the pruned graph under three scenarios: (1) if the path is not found, it is re-computed executing Di-0.45 0.5 0.55 0.6 0.65 0.78 ·10−20.10.120.140.16ML threshold, γExecutionTime(s)DijkstraML-aided (1)ML-aided (2)ML-aided (3)(a) k = 3 anchor nodes0.45 0.5 0.55 0.6 0.65 0.70.10.120.140.16ML threshold, γExecutionTime(s)DijkstraML-aided (1)ML-aided (2)ML-aided (3)(b) k = 5 anchor nodes0.45 0.5 0.55 0.6 0.65 0.70.10.120.140.16ML threshold, γExecutionTime(s)DijkstraML-aided (1)ML-aided (2)ML-aided (3)(c) k = 7 anchor nodesFig. 2: Execution time of the routing algorithms for several values of the pruning threshold γ when shortest pathsare computed on the original graph (Dijkstra), the pruned graph (ML-aided (1)), the pruned graph only when apath is found (ML-aided (2)) and the pruned graph with optimized threshold selection (ML-aided(3))jkstra on the original graph; (2) only when a path is found and (3) if the path is not found, the shortest pathis re-computed over a graph pruned setting a lower node selection threshold γ and, if also this re-computationfails, Dijkstra is executed on the original graph. As for scheme (3), at the second iteration γ is chosen bymeans of an optimization strategy that we omit due to space limitations. Fig.2(a), 2(b) and 2(c) report the ex-ecution time considering K = 3,5,7 anchors nodes, respectively. Results show that network pruning leads to asignificant gain in terms of computational time, and this gain increases with increasing K (e.g., from 29% to35% when K goes from 3 to 7). Augmenting K also increases the robustness with respect to a variation of γ .0.45 0.5 0.55 0.6 0.65 0.70.40.60.8ML threshold, γPercentageofpathsfoundbytheML(%)K = 3K = 5K = 7Fig. 3: Percentage of paths found on thepruned graph for several values of the nodeselection thresholdFurthermore, increasing γ reduces the computational time on thepruned graph when the path is found but, conversely, this timeincreases if path re-computation is also considered (where a re-computation done through a second optimized threshold selectionoutperforms the selection directly on the original graph).From now on, we focus on ML-aided (1) option. We mea-sure the percentage of extra-length of the paths found on thepruned network with respect to the length of the shortest pathsand the percentage of paths directly found on the pruned net-work. As for the former, we observe a negligible extra-length thatranges from a minimum of 0.7% (with K = 3 and γ = 0.7) toa maximum of 1.6% (with K = 7 and γ = 0.6). As for the lat-ter, Fig.3 shows that the percentage of times a path is found di-rectly on the pruned network decreases with increasing γ (as thegraph might be more easily disconnected after network pruning).A higher robustness to the variation of γ is achieved by setting K to higher values. For instance, this percentageexperiences a significant drop - from 96% to 39% - when K = 3, but only from 96% to 74% when K = 5.·10−4 ·10−3 ·10−2OG/FF 6.71±0.95 5.87±0.19 1.700±0.024OG/RS 8.15±0.81 5.92±0.19 1.710±0.023PG/FF 9.90±0.98 6.80±0.21 1.900±0.024PG/RS 11.70±1.01 6.90±0.20 1.900±0.023Table 1: Average Blocking ProbabilityWe then evaluate the performance of the entire RWAprocess when the ML-aided (1) pruning system is em-ployed. To this end, we simulate a dynamic traffic sce-nario where the arrival times of 104 requests are char-acterized by a Poisson distribution and their duration bya negative exponential distribution. Requests are routedon the shortest path between their sources and destina-tions using the Dijkstra algorithm and an optical channelis assigned using either the FF or the RS strategy. If no available spectrum slot is found, the request is blocked.This experiment is repeated in three different load scenarios characterized by blocking probabilities in the order of10−4, 10−3 and 10−2. Each experiment is independently repeated 20 times and the average blocking probabilitiesand 95% confidence intervals are shown in Tab.1, where OG and PG stand for original and pruned graph, respec-tively. We observe a minimal increase of the blocking probability when the RWA task is executed on the graphpruned considering γ = 0.5. Finally, note also that the time required to pre-compute the shortest path between eachnode pair in the considered network takes around 100 minutes, while the ML algorithm can be trained in a muchshorter time, which grows linearly with the training set. As an example, 6 seconds are sufficient to train a modelachieving a prediction accuracy of 93% on unseen nodes, while a training of 60 seconds increases the accuracyto about 96% (note that prediction accuracy is the fraction of nodes correctly labelled as belonging/not belongingto the shortest path between a node pair). Moreover, though the path pre-computation strategy exploiting Dijkstracan be applied to static topologies, it is not suitable for topologies that change over time. Dynamic topologies willbe considered in a future work.In summary, the proposed ML-based network pruning strategy significantly reduces the computational com-plexity of the RWA task with a minor blocking probability deterioration.References1. A. Elmokashfi et al., “On the scalability of BGP: The role oftopology growth. IEEE Journal on Selected Areas in Com-munications, vol. 28, no. 8, pp. 1250-1261, 2010.2. B. Jaumard et al., “Efficient spectrum utilization in large scaleRWA problems. IEEE/ACM TON, vol. 25, no. 2, pp. 1263-1278, 2017.3. C. L. Gutterman et al., “Neural network based wavelengthassignment in optical switching”, Workshop on Big Data An-alytics and Machine Learning for Data Communication Net-works, 2017.4. I. Martı́n et al., “Machine learning-based routing and wave-length assignment in software-defined optical networks,”IEEE TNSM, vol. 16, no. 3, pp. 871-883,5. J. Yu et al., “A deep learning based RSA strategy for elasticoptical networks” IEEE ICOCN, 2019.6. X. Chen et al., “DeepRMSA:A deep reinforcement learningframework for routing, modulation and spectrum assignmentin elastic optical networks,” IEEE/OSA JLT, vol. 37, no. 16,pp. 4155–4163, 2019.7. X. Luo et al., “Leveraging double-agent-based deep rein-forcement learning to global optimization of elastic opticalnetworks with enhanced survivability,” Optics express, vol.27, no. 6, pp. 7896–7911, 2019.

A Machine Learning Framework for Scalable Routing and Wavelength Assignment in Large Optical Networks

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A Machine Learning Framework for Scalable Routing and Wavelength Assignment in Large Optical Networks

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