An Evolutionary Algorithm Approach for Dedicated Path Protection Problem in Elastic Optical Networks

Transcription

1 An Evolutionary Algorithm Approach for Dedicated Path Protection Problem in Elastic Optical Networks Mirosław Klinkowski Department of Transmission and Optical Technologies, National Institute of Telecommunications, Warsaw, Poland Elastic Optical Network (EON) architectures are a very promising solution for next generation optical networks. In EON, a basic problem in network design and operation is the problem of Routing and Spectrum Allocation (RSA). In this work, we focus on RSA in a survivable EON with Dedicated Path Protection (DPP) consideration. Since RSA is a difficult problem itself, we develop an evolutionary algorithm (EA) with the aim to support the search for optimal solutions. We investigate the effectiveness of algorithm for a set of survivable network scenarios. Evaluation results show that the proposed algorithm outperforms reference algorithms from the literature. 1 KEYWORDS: elastic optical networks, evolutionary algorithm, network optimization, dedicated path protection, routing and spectrum allocation INTRODUCTION The communication networking is undergoing fundamental changes which are governed by the development and integration of diverse network technologies and applications within a unified Internet Protocol (IP) packet-oriented network infrastructure. The observed trends result in an exponential growth of the traffic generated by network users and in the need for efficient and flexible optical transport networks able to support multi-rate and huge-bandwidth (100+ Gb/s) connections. The currently deployed wavelength division multiplexing (WDM) optical networks operate within a rigid frequency grid and with single-line-rate transponders making use of single carrier modulation 1 This work has been supported by the Polish National Science Centre under grant agreement DEC- 2011/01/D/ST7/05884.

2 M. Klinkowski techniques. The evolution path of optical communication networks leads toward elastic optical networks (EONs) in which advanced single-carrier modulation formats (such as Phase-Shift Keying and Quadrature Amplitude Modulation) and multi-carrier modulation techniques (such as Optical Orthogonal Frequency Division Multiplexing) are applied for mixed-line-rate transmission and where elastic access to spectral resources is achieved within flexible frequency grids (flexgrid) (Gerstel et al. 2012; Wei et al. 2012). Future optical networks will utilize spectrum resources in optical fibres more efficiently, according to the transmission path characteristics and bandwidth requirements. We refer to some recent papers for more details on EON architectures (Jinno et al. 2009; Meloni et al. 2011) and for reports on proof-of-concept EON experiments (Geisler et al. 2011; Cugini et al. 2012). ITU-T has recently revised the G recommendation and included the definition of a flexible WDM grid (ITU-T G.694.1). According to G.694.1, the frequency spectrum in an optical fiber link is divided into narrow frequency segments (we refer to them as slices). The optical path (lightpath) is determined by its routing path and a channel, which consists of a flexibly (adhoc) assigned subset of slices around a nominal central frequency. Elastic spectrum allocation in EONs differs with channel assignment in fixed-grid WDM networks in that the channel width is not rigidly defined but it can be tailored to the actual width of the transmitted signal. Due to this difference, ordinary Routing and Wavelength Assignment (RWA) algorithms are not appropriate for EONs. In EONs, the problem of finding unoccupied spectrum resources so that to establish a lightpath is called the Routing and Spectrum Allocation (RSA) problem. RSA concerns assigning a contiguous fraction of frequency spectrum to a connection request - we refer to it as the spectrum contiguity constraint - subject to the constraint of no frequency overlapping in network links. The RSA optimization problem is NP-hard (Klinkowski and Walkowiak 2011) and it is more challenging than RWA in fixed grid networks due to the existence of the spectrum contiguity constraint. Offline RSA has been addressed with both Integer Linear Programming (ILP) (e.g., see Christodoulopoulos et al. 2011; Klinkowski et al. 2011; Velasco et al. 2012), metaheuristics (Christodoulopoulos et al. 2011, Klinkowski 2012, Gong et al. 2012), and heuristic algorithms, which are based either on ILP problem 2

3 Evolutionary Algorithm for DPP in EON relaxations (Christodoulopoulos et al. 2011) or on greedy, sequential processing of demands (Christodoulopoulos et al. 2011; Klinkowski et al. 2011). So far, there have been proposed several solutions for survivable EONs in the literature. Regarding offline network design, survivable RSA algorithms for dedicated path protection (DPP) and shared backup path protection (SBPP) in a ring network have been studied in Takagi et al DPP in a network with generalized connectivity has been addressed with both ILP formulation (Klinkowski and Walkowiak 2012) and heuristic algorithms (Patel et al. 2011; Klinkowski and Walkowiak 2012). Concurrently, an ILP formulation (Eira et al. 2012), a metaheuristic algorithm (Castro et al. 2012), and heuristic algorithms (Eira et al. 2012; Liu et al. 2012) have been proposed for SBPP. Eventually, in Assis et al. 2012, a MILP formulation and an heuristic algorithm have been presented for the so-called squeezed protection scheme in which the protection of a lightpath may not cover its entire bandwidth but it is allowed to be partial. All these solutions assure single-link failure survivability. Evolutionary algorithms (EA) are an effective population-based mataheuristic approach for providing near-optimal solutions for large-scale optimization problems (Talbi 2009). In this paper, we employ EA in the search for optimal RSA solutions in an EON with dedicated path protection (DPP) consideration and static traffic demands. In particular, we develop an efficient EA-based algorithm which, as numerical results show, outperforms other reference algorithms for the offline RSA/DPP problem in EON. This paper extends our recent work presented in a conference paper (Klinkowski 2012). Initially, we have focused on a DPP scenario in which a pair of working and backup lightpaths has allocated the Same Channel (SC), i.e., the same segment of spectrum. Here, we contribute with an extension and evaluation of the EA algorithm adapted to an alternative DPP scenario, namely, with Different Channel (DC) allocation. It should be mentioned that, however, an evolutionary approach for optimizing RSA has been recently presented in Gong et al. 2012, still, to the best of our knowledge, the application of EA in survivable EON scenarios has not been studied in the literature prior to Klinkowski 2012 and this work. Besides, Gong et al propose a twopopulation based algorithm which differs with our one-population based EA approach. 3

4 M. Klinkowski The article is organized as follows. In the following section, we discuss the details of both SC and DC survivable network scenarios and formulate the RSA/DPP problem. In the next section, we describe our EA-based approach to solve RSA/DPP. Then we present numerical results. Finally, we conclude the work. PROBLEM FORMULATION In this section, we formulate an offline problem of Routing and Spectrum Allocation with Dedicated Path Protection in an EON with static traffic demands and subject to single-link failures. Among network survivability schemes, connection recovery through path protection, in which back up network resources (i.e., lightpaths) are provisioned in advance for each connection, is preferred due to its quick recovery time. In DPP, each connection has its own backup resources, on the contrary to SBPP, in which backup resources can be shared between the demands whose primary paths are not likely to fail at the same time. Similarly as in Patel et al and Klinkowski and Walkowiak 2012, we distinguish two DPP scenarios, namely: a) with Same Channel (SC) allocation and b) with Different Channel (DC) allocation; we denote the resulting problems as RSA/DPP/SC and RSA/DPP/DC, respectively. Case SC is a cost-effective scenario in which the transponders are shared between primary (working) and backup connections and a traffic demand has allocated the same segment of optical frequency spectrum (i.e., channel) on its primary and backup path. Such a solution reduces the network cost and alleviates the connection switching time, as discussed in Patel et al In the DC case, the SC constraint of having the same operating channel in both primary and backup connections is relaxed, by these means, reducing spectrum requirements in the network (Patel et al. 2011; Klinkowski and Walkowiak 2012). One way to implement this scenario is to install dedicated (for both working and backup lightpaths) transponders. However, this is an expensive approach since it doubles the cost of transponders installed in the network. An alternative solution is to use laser-tunable transponders which are able to modify the central frequency of the transmitted optical signal (Buus 2006). Since such technology is commercially available and adopted in WDM 4

5 Evolutionary Algorithm for DPP in EON core network applications (Blum 2010), we believe that it is also a viable solution for elastic optical networks. The considered RSA/DPP problem can be formally stated as: Given: 1. an EON represented by a graph G=(V,E), where V denotes the set of nodes, and E denotes the set of fiber links connecting two nodes in V; 2. a frequency spectrum, the same for each link in E (without loss of generality), with the flexgrid represented by an ordered set of frequency slices S={s 1,s 2,...,s S }; 3. a set D of static traffic demands to be transported with path protection guarantees; each demand d is represented by a tuple (o d, t d, n d ), where o d and t d are source and destination nodes respectively, and n d is the requested number of slices. Find a primary lightpath and a backup lightpath over the EON for every transported demand subject to the following constraints: 1. spectrum contiguity: for each demand, the slices should be allocated each next to the other (i.e., adjacent) in the frequency spectrum, 2. spectrum continuity: for each demand, the subset of allocated slices should be the same for each link on the selected routing path, 3. slice capacity: a slice in a link can be allocated to one demand at most, 4. same channel (applies only for RSA/DPP/SC): for each demand, the primary and backup lightpath should have allocated the same subset of slices, and with the objective to minimize the width of spectrum (denoted as Φ) required in the network. Here, we assume the same optimization objective as in Takagi et al. 2010, Patel et al. 2011, and Eira et al

6 M. Klinkowski The requested number of slices n d is a function of the requested bandwidth, the modulation technique applied, the slice width in the flexgrid, and the guard band introduced to separate two spectrum adjacent connections, among others. For a given network scenario, where both the transmission parameters and flexgrid definitions are given, there is a relation between n d and the requested bandwidth (e.g., see Sec. II in Christodoulopoulos et al. 2011). Therefore, without loss of generality, we express the demand volume by means of the number of slices. Assuming the flexgrid definition proposed in G and its requirement to have the spectrum allocated symmetrically around a central frequency, n d is considered to be an even number, i.e., n d {2i: i Z + }. For more details, we refer to the G recommendation. In this paper, we consider that a set of candidate routing paths is given. Let P denote the set of all candidate paths. Each path p P is identified with a subset p E. Let Q denote the set of pairs of paths (p,q), where p P is a primary path and q P is a backup path. Let Q d denote the set of path pairs for demand d D; each set Q d comprises only paths that have the origin in o d and the termination in t d. In this work, we assume each Q d has the same number of candidate path pairs, which is denoted as k (i.e., Q d =k). Apart from that, we assure the network is resilient to single link failures by assuming that Q is a set of link disjoint path pairs. Let N be the set of the numbers of requested slices, i.e., N={n: d D,n d =n}, and n max =max{n N} and n min =min{n N} be, respectively, the largest and the smallest number in this set. In the remainder of this paper, we consider that the set of demands D={d 1,...,d i,d i+1,...,d D } is an ordered set and, in particular, the demands are sorted in decreasing order of n d, i.e., i we have n di n d(i+1). Eventually, let D n be the set including all demands with n requested slices, i.e., D n ={d:d D,n d =n}, n N. EVOLUTIONARY ALGORITHM FOR RSA/DPP In this section, we present a EA metaheuristic-based algorithm for the off-line RSA/DPP problem in EON. In the following, we describe our approach to solve the problem and then we focus on EA implementation details. 6

7 Evolutionary Algorithm for DPP in EON Algorithm Approach To solve RSA/DPP, we propose a hybrid approach in which we combine EA with a greedy RSA algorithm. The role of EA is to look for a sequence of demands which, when processed by the RSA algorithm, minimizes the occupied spectrum width (Φ). In details, the RSA subroutine serves the demands, one-by-one, in an order determined in the EA phase. Then, having performed RSA, we calculate Φ by counting the number of slices s S that are occupied in network links:, (1) where x s =1 if slice s S is occupied in any link e E, and equal to 0 otherwise. The value of Φ indicates the quality of solution and, by this means, it supports EA in the search for better sequences of demands (the details are discussed in following subsections). RSA Subroutine As the greedy RSA algorithm we use the MSF (Most Subcarriers/Slices First) algorithm presented in Christodoulopoulos et al. 2011, which we adapt to the DPP context. MSF performs RSA for a set of demands that are arranged and processed in decreasing order of the number of requested slices. If we assume that s dp denotes the largest slice index among the slices allocated to demand d on routing path p, then MSF looks for such path p * (among all candidate paths) and such unallocated spectrum segment on this path (consisting of n d slices) that minimizes s dp. Then, demand d is allocated on path p * within spectrum segment [s dp -n d +1, s dp ], and the procedure is repeated for the rest of demands. As shown in Christodoulopoulos et al. 2011, MSF is an effective heuristic for minimizing Φ, which is our optimization objective. The application of MSF is straightforward in the SC scenario since the allocated spectrum segment is the same on both primary path p and backup path q, i.e., s dp =s dq. Therefore, in SC a criteria for selecting a pair of primary-backup paths minimization of s dp, i.e., from set Q d for demand d is the. In the DC scenario, the choice of a criteria function for selecting a path pair (p,q) from set Q d is more complicated since s dp and s dq may differ 7

8 M. Klinkowski and the optimization according to one of them does not necessarily lead to the minimization of the objective function (Φ). Therefore, we consider several alternative criteria functions for selecting a path pair in DC, namely: 1), 2), 3), 4), where path pair is selected as. In the Algorithm Tuning section, we show that, among these criteria, option 4) leads to best results. EA Details Figure 1. EA components: a) chromosome, b) crossover operator, c) mutation operator. In our EA, each individual in the population represents a sequence (permutation) of demands. The objective of EA is to find such a permutation of demands which, when processed by the RSA subroutine, minimizes the occupied spectrum width. The EA algorithm starts with creating the initial population. Better permutations are found over a number of generations. Operators such as crossover and mutation explore further possible permutations. In our approach, all the individuals are feasible solutions therefore no additional constraint handling procedures are necessary. When the stopping criterion is satisfied, a near-optimal sequence of demands is found. Below we describe in details the relevant building blocks of our EA. Representation: The encoded solution (chromosome) is a vector of numbers, coded as π=[π 1,,π D ], which represents a sequence of demands (to be processed by the RSA algorithm). In order to assure that the demands are sorted in decreasing order of n d, which is required by our MSF-based RSA algorithm, vector π of each chromosome is formed and maintained by EA as a concatenation of smaller vector segments π n, where π n represents a permutation vector of demands belonging to D n for 8

9 Evolutionary Algorithm for DPP in EON each n N. As a result, starting with segment π nmax, which is a permutation vector of demands belonging to D nmax, we form π=[π nmax,,π n,,π nmin ]. In Figure 1a) we present two exemplary chromosomes p1 and p2 formed for the case of D =9 demands among which there are 3 demands requesting 6 slices (segment π 6, in position 1-3), 2 demands requesting 4 slices (segment π 4, in position 4-5), and 4 demands requesting 2 slices (segment π 2, in position 6-9). The order of demands is ( ) and ( ), respectively, for p1 and p2. Population Initialization: The EA starts with an initial population of chromosomes. Permutation vectors π n, n N, of each chromosome are generated randomly. As discussed in Talbi 2009, the larger the population the better the convergence toward good results, however, at the cost of time complexity. Therefore, in this work, a population of M=60 chromosomes is maintained, which is a practical value as stated in Talbi Fitness Function: The objective function to be minimized is the spectrum width, which is an output of our greedy RSA algorithm (described in the RSA Subroutine section). Therefore, in order to drive the search toward better solutions, we use a fitness value (f) that corresponds to the objective value (Φ), in particular, f = -Φ. Selection of Chromosomes for the Next Generation: We use the stochastic universal sampling method (Talbi 2009) for selecting two parents to produce new individuals for the next generation. Crossover: We use the uniform crossover operator (Talbi 2009) by which a single offspring is created from two parents by coping randomly segments π n from either parent for each n N. In Figure 1b), segments π 6 and π 2 are selected from parent p1 and segment π 4 is selected from parent p2 to create offspring o. Mutation: The mutation procedure is applied after the crossover on each offspring independently. Specifically, for randomly selected segment π n, n N, we exchange the position of two randomly 9

10 M. Klinkowski selected elements in this segment. In Figure 1c), segment π 2 is selected and, within this segment, the position of demands 9 and 6 is exchanged. Replacement: New individuals replace old individuals if their fitness values are better than those of the old ones. Apart from that, in this work we consider that: a) at least E best individuals survive to the next generation, and b) X percent of the population at the next generation, not including the survivals from the old population, are created by the crossover function. In the Algorithm Tuning section we evaluate the impact of E and X on the algorithm performance. The population size at each generation is maintained fixed and equal to M. In the Numerical Result section we evaluate different values of M. Stopping Criteria: Our EA terminates after G generations. In this work, we perform the algorithm evaluation for G {1,10,50,100,200}. Algorithm Complexity The algorithm complexity is polynomial in time. In particular, the computation complexity of MSF is bounded by O( D k S E ), where D is the number of demands to be processed, k is the number of candidate path pairs per demand, and S E corresponds to the (worst-case) complexity of the search of unoccupied slices. MSF is called once for each chromosome. The number of chromosomes is limited by the product of the population size (M) and the number of generations (G) in EA. NUMERICAL RESULTS In this section, we evaluate the performance of our EA-MSF algorithm, presented in the previous section, and compare it with other reference algorithms. We focus on the occupied spectrum width (Φ), in terms of the number of slices, and computation time (T; in seconds). As the reference algorithms we use: AG - an Auxiliary Graph-based algorithm proposed in Patel et al for dedicated path protection, and a pure MSF algorithm. Note that MSF was originally developed in the context of the RSA problem without additional survivability constraints. Therefore, we have adapted it in order to address the SC and DC constraints which are present in the DPP scenario (see the RSA 10

11 Evolutionary Algorithm for DPP in EON Subroutine section for implementation details). Moreover, for small network scenarios, we provide optimal results obtained with an ILP formulation of the RSA/DPP problem (we refer to Klinkowski and Walkowiak 2012 for the formulation). Also, we provide a lower bound (LB) on Φ, obtained by solving a multicommodity routing problem with the spectrum continuity and channel assignment constraints relaxed (see Sec. III-A in Christodoulopoulos et al. 2011). Figure 2. Network topologies. The evaluation is performed for SIMPLE6 (6 nodes, 16 links), INT9 (9 nodes, 26 links), NSF15 (15 nodes, 46 links), and UBN24 (24 nodes, 86 links) network topologies (see Figure 2). We set S =1500, which is large enough to accommodate all demands without their blocking in the most demanding scenario; in other words, we assure that Φ S. Candidate pairs of primary-backup paths are link disjoint paths and they are calculated as the shortest paths, taking into account the overall length of both paths. We consider k {2,3, 10,30}. The requested spectrum n d is an even number generated with a uniform distribution and for randomly selected demand pair (o d, t d ), where o d,t d V and o d t d. In particular, n d N={2,4,..., n max }, where n max {8,16}. For fair evaluation, we consider all algorithms operate on an ordered set of demands D (as defined in the previous section). Both the EA procedure of EA-MSF and the AG algorithm are implemented in MATLAB. In order to speed up the processing of the MSF subroutine, we implement it in C++ and call as an external function from MATLAB. We use IBM ILOG CPLEX v.12.4 to solve ILP. The evaluation is performed 11

12 M. Klinkowski on an Intel i5 3.3GHz 16GB computer. If not mentioned otherwise, the results are averaged over 100 randomly generated demand sets. Algorithm Tuning We begin with comparing different criteria functions to be used for selecting routes in the MSF algorithm in the DC scenario (see the discussion in the RSA Subroutine section). In Table 1, we present the corresponding evaluation results obtained in the NSF15 and UBN24 networks under, respectively, D =210 and D =552, and n max =16 for both networks. As we can see, the minimization of the sum of slice indexes on both primary and backup paths (i.e., min{s dp +s dq }) leads to best results. Therefore, in the remainder of the paper we consider that this criteria is applied in the DC scenario in both the MSF algorithm and the RSA subroutine of EA-MSF. TABLE 1 Performance of MSF with different route selection criteria functions in DC. Scenario min{s dp } min{s dq } min{max{s dp,s dq }} min{s dp + s dq } k Φ NSF ,98 463,66 464,94 462, ,50 416,34 400,26 393, ,46 393,34 381,40 377,12 UBN , , ,24 999, ,24 812,28 794,72 739, ,46 738,38 731,02 705,76 Next, we evaluate the impact of two EA parameters, namely, E and X, on the performance of EA-MSF algorithm. The evaluation if performed in the NSF15 network with D =210, n max =16, k=10 and under the SC constraint. We consider E {2,4,6,12}, and X {20%,30%,50%,80%}. In Table 2, we present relative results of Φ with respect to the minimum value of Φ obtained for E=2 and X=50%. In the remainder of the paper, we evaluate EA-MSF with E=2 and X=50%. TABLE 2 Performance of EA-MSF under different values of E and X. E \ X 20% 30% 50% 80% Average 2 0,11% 0,17% 0,00% 0,70% 0,24% 4 0,16% 0,45% 0,16% 0,55% 0,33% 6 0,10% 0,30% 0,41% 0,78% 0,40% 12 0,41% 0,47% 0,17% 1,09% 0,53% 12

13 Evolutionary Algorithm for DPP in EON Average 0,19% 0,35% 0,19% 0,78% Optimality of EA-MSF In Table 3 we compare performance results of heuristic algorithms with the optimal ones (ILP) in small network scenarios. We consider D =10 and D =15, respectively, for SIMPLE6 and INT9, and n max =8 for both networks. EA-MSF runs G=50 generations. Due to the complexity of ILP, which does not reach optimality for about 62 out of 150 cases (39%) in a 2h period, the results for INT9 are averaged over the remaining 88 demand sets. Note that LB is the same for both SC and DC scenarios since in the multicommodity routing problem, which is solved to achieve the lower bound, the channel assignment constraints responsible for the difference between SC and DC are relaxed. We can see that EA-MSF outperforms other heuristics and its performance gap to optimal results is between 0,80-3,60%. Also, we can see that MSF and, consequently, EA-MSF perform better in the SC scenario than in the DC scenario. It comes from the fact that RSA decisions in the original version of MSF concern single route selections, while in DPP a pair of paths has to be selected. Now, since the selection of a disjoint pair of paths (p,q) with a minimum slice index in SC can be considered as a selection of super-path P=p q with the minimum slice index (see the RSA Subroutine section), therefore adapted MSF performs well in the SC scenario. However, the case of DC is not trivial. Here, both p and q may occupy different channels and, therefore, the adapted version of MSF requires route selection strategies that incorporate the slice indexes of both paths. As we show in the Algorithm Tuning section, a good strategy leading to minimal Φ results is to minimize the sum of the slice indexes. Eventually, the development of more sophisticated RSA algorithms for DC will be required so that to find solutions closer to optimal ones and such investigation is left for future work. TABLE 3 Optimality gap. Scenario LB ILP AG MSF EA-MSF k Channel Φ Φ T Optimality gap SIMPLE6 2 SC 25,02 27, ,78% 3,96% 0,81% 13

14 M. Klinkowski 2 DC 25,02 25, ,28% 3,56% 3 SC 24,88 27, ,85% 3,45% 0,91% 3 DC 24,88 25, ,92% 3,60% INT9 2 SC 33,61 34,79 22,6 10,89% 3,80% 1,34% 2 DC 33,61 33,61 9,4-4,08% 2,04% Performance Comparison In Table 4 we present performance results obtained with heuristic algorithms in larger networks. In the evaluation, D =210 and D =552, respectively, for NSF15 and UBN24, and n max =16 for both networks. EA-MSF runs G=200 generations. Since AG is designed for the SC scenario and it calculates routing paths online, i.e., without using candidate paths, we present its results in a dedicated row. In the comparison AG vs. EA-MSF we consider k=30 for EA-MSF. Similarly as in small networks, EA-MSF achieves better performance (in terms of Φ) than the reference algorithms. In details, the performance gap, defined as a relative performance improvement, is of about 20%-35% and 4%-11%, respectively, when comparing EA-MSF with AG and MSF. We can see that Φ can be improved considerably (about 15-19% for NSF15 and 20%-30% for UBN24) if there are more path pairs available in the set of candidate paths (k=2 vs. k=30). For MSF, the average computation times are below 0,5 seconds in the most demanding scenario. The computation times for EA-MSF are presented in the next section. TABLE 4 Comparison of heuristic algorithms. Scenario LB AG MSF EA-MSF EA-MSF vs. AG EA-MSF vs. MSF k Channel Φ Performance gap NSF15 2 SC 428,5-537,8 492,1-9,30% 2 DC 428,5-462,8 434,61-6,49% 10 SC 333,2-485,4 436,7-11,16% 10 DC 333,2-393,6 364,0-8,10% 30 SC 321,3-461,96 417,2-10,71% 30 DC 321,3-377,1 352,5-6,98% - SC - 566, ,79% - UBN24 2 SC 955,7-1083,3 1026,9-5,49% 2 DC 955,7-999,1 963,5-3,70% 10 SC 665,6-923,5 856,6-7,81% 10 DC 665,6-739,5 703,9-5,06% 14

15 Evolutionary Algorithm for DPP in EON 30 SC 665,3-836,6 785,5-6,50% 30 DC 665,3-705,8 681,0-3,56% - SC - 942, ,96% - EA-MSF Performance In Table 5 we present the EA-MSF performance results in a function of the number of generations (G). The improvement between G=1 and G=200 is of about 1%-5%, however, at the cost of extended computation time, which grows almost linearly with G. The impact of k on computation times is much smaller. Therefore, it is worth to have a large set of candidate paths since it has a great impact on the value of Φ (as shown in the previous section). We can see that above certain G the objective function (Φ) does not improve significantly. In particular, we find that G=50 is a reasonable trade-off between solution quality and computation time for EA-MSF in the studied scenarios. In order to evaluate the effectiveness of the evolutionary-base technique applied in EA-MSF, we have compared it with a random-based algorithm (RND). RND runs MSF for a number (denoted as K) of randomly generated permutations of the demand set and selects the solution with the best objective function. For the sake of comparability, we have assumed K=G*M iterations, which is roughly the total number of individuals generated during the EA-MSF algorithm runtime; in the evaluation, M=50 and, therefore, K=3000. In the analyzed large network scenarios with k {2,10,30}, in average, EA-MSF always provide better results than RND. We report that the performance gap of EA-MSF vs. RND is of about 1,90%-2,40% in NSF15 and 1,00%-1,50% in UBN24. TABLE 5 Performance of EA-MSF in a function of the number of generations (G); T in seconds. Scenario G = 1 G = 10 G = 50 G = 100 G = 200 G = 1 vs. G = 200 k Channel Φ T Φ T Φ T Φ T Φ T Improvement in Φ NSF15 2 SC 513 1, , ,33% 2 DC 443 1, , ,95% 10 SC 459 1, , ,16% 10 DC 376 2, ,36% 30 SC 436 2, ,61% 30 DC 363 3, ,98% UBN24 15

16 M. Klinkowski 2 SC , ,27% 2 SC 976 7, ,26% 10 SC ,60% 10 DC ,23% 30 SC ,14% 30 DC ,45% Comparison of DPP scenarios Eventually, we discuss a trade-off between having less spectrum resources occupied in the network at the cost of applying a more complex DC scenario. To support the discussion, in Table 6 we present comparative results of the spectrum usage in both SC and DC survivable network scenarios. The results are obtained with both MSF and EA-MSF algorithms. We can see that in all reported cases the SC scenario requires at least 15% more spectrum resources than the DC scenario. It is a consequence of the constraint to have both primary and backup lightpaths allocated within the same subset of slices in SC. Since higher spectrum requirements can be translated to higher network costs, as discussed in Palkopoulou et al. 2012, there is a rationale to consider the DC scenario as a valid scenario for EON. However, further analysis, taking into account the cost of re-configurable and tunable transponders, will be required in order to evaluate the cost impact of applying the DC scenario in EON. TABLE 6 Comparison of DPP scenarios; k=30. Network Algorithm Φ in SC Φ in DC Difference in Spectrum Usage NSF15 MSF EA-MSF ,5% 18,4% UBN24 MSF EA-MSF ,5% 15,3% CONCLUSIONS In this paper, we have focused on the problem of off-line routing and spectrum allocation in survivable elastic optical networks with dedicated path protection. To solve the problem, we have proposed a novel EA-MSF algorithm which is based on the evolutionary algorithm metaheuristic combined with a greedy RSA algorithm - as the RSA algorithm we use the MSF algorithm. The aim of EA is to help in the search of RSA solutions which minimize the occupied spectrum width. 16

17 Evolutionary Algorithm for DPP in EON To assess the algorithm performance, we have compared it with reference RSA/DPP algorithms. The performed numerical experiments show that EA-MSF outperforms other reference heuristics. Although the joint application of EA with the MSF algorithm leads to near-optimal results in the same channel allocation scenario, still, in the different channel allocation scenario in which the MSF algorithm has some difficulties, more sophisticated methods are required. Moreover, we have shown that the DC approach allows to save at least 13% of the overall spectrum width than when allocating identical channels to primary and backup lightpaths. This gain is at the expense of tunable transponders that have to be used in the DC scenario instead of shared and simple ones in the SC scenario. In future research, we plan to investigate the application of large-scale optimization methods, such as decomposition methods, for solving the RSA-DPP problem as well as to consider other survivability scenarios in EON including the use of shared protection. REFERENCES Assis, K. D. R., Almeida, R. C., and Waldman, H MILP formulation for squeezed protection in spectrum-sliced elastic optical path networks. Proceedings of the International Symposium on Performance Evaluation of Computer and Telecommunication Systems (SPECTS 2012). Blum, R Evolving Tunable Technologies in Transponder and Transceiver Modules. Technologies-small.pdf. Buus, J. and Murphy, E. J Tunable Lasers in Optical Networks. IEEE Journal of Lightwave Technology 24(1): Castro, A., Ruiz, M., Velasco, L., Junyent, G., and Comellas, J. Path-based recovery in flexgrid optical networks. Proceedings of International Conference on Transparent Optical Networks (ICTON 2012). Christodoulopoulos, K., Tomkos, I., and Varvarigos, E Elastic bandwidth allocation in flexible OFDM based optical networks. IEEE Journal of Lightwave Technology 29(9):

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