solving the static manycast rwa problem in optical networks using evolutionary programming

Solving the Static Manycast RWA Problem in OpticalNetworks Using Evolutionary Programming

Amiyne Zakouni1, Jiawei Luo1(✉), and Fouad Kharroubi2(✉)

1 School of Computer Science and Electronic Engineering, Hunan University,Changsha, 410082, China

[email protected], [email protected] School of Mathematics and Computer Science, Yichun University, Yichun, 336000, China

[email protected]

Abstract. The Static RWA (Routing and Wavelength Assignment) problem inOptical Networks is a combinatorial optimization problem fit to iterative searchmethods. In this article we further investigate the static manycast RWA problemin optical networks and solve it using an evolutionary programming (EP) strategysuch that the number of the manycast requests established for a given number ofwavelengths is maximized. The proposed algorithm solves, approximately, thewavelength assignment problem while a backtracking approach is used to solvethe routing issue. We present the details of our proposed algorithm and compareit to another metaheuristic named genetic algorithm (GA). EP shows a 24 %improvement over GA.

Keywords: Backtracking · Evolutionary programming · Genetic algorithm ·Manycast · Max-RWA · Metaheuristics · Optical networks

1 Introduction

The future of many technologies such as video conferencing, grid computing, e-Scienceand peer-to-peer (P2P) will employ a massive amount of data and support for point tomultipoint communication. To fortify these accommodations, the next-generationInternet will be predicated on optical networks that can provide immense amounts ofbandwidth. Manycast [1–3], is a new type of communication that can fortify the pointto multipoint nature of future services, in addition to fortifying generally used commu‐nication types. The manycast is a generalization of the multicast communication para‐digm [4]. Indeed, multicast differs from manycast in that the destinations are determined,though in manycast the destinations must be picked. Manycast is especially useful ingrid/cloud computing and e-Science. In the majority of the above cases, we are regularlydealing with a prodigious amount of data.

In these cases, a service provider might have various servers that give an identicalservice. In particular, consider parallel substance conveyance in an e-Science context.e-Science regularly creates a lot of data [1] that may then be stored in different areas foreither backup purposes or so that numerous exploration labs can then process it locally.We can utilize manycast to pick some subset of these locations (e.g., the reduced cost

© Springer International Publishing Switzerland 2016D.-S. Huang and K.-H. Jo (Eds.): ICIC 2016, Part II, LNCS 9772, pp. 147–157, 2016.DOI: 10.1007/978-3-319-42294-7_12

storage clusters) to send this data in parallel along a light-tree set up by the networksystem. This issue can likewise be solved utilizing multicast rather than manycast, yetthere are a few disadvantages. Rather than utilizing manycast, where the system wouldpick the subset of destinations for us, we can utilize multicast by picking k destinationsat the source. The primary disadvantage stems from the client point of view. The nodeschosen at the source may be heavily loaded or may provide a slower transfer rate thandifferent nodes in the candidate set. Furthermore, manycast grants the freedom to choosedifferent nodes depending on the state of the network, prompting better execution forclient applications and more efficient usage of WDM networks. WDM can provideunprecedented bandwidth, reduce processing costs, and enable efficient failure handling[5, 6]. An end-to-end lightpath has to be established prior to the communication betweenany two nodes in an optical network. A sequence of lightpath requests arrive over timewith each lightpath assigned a random holding time.

These lightpaths should be set up dynamically by deciding a route across the networkconnecting the source to the destination and allocating a free wavelength along the path.Actual lightpaths cannot be rerouted to accommodate new lightpath requests until theyare free, so some of the lightpath requests may be blocked if there are no free wavelengthsalong the path [7]. Therefore, finding a physical route for each lightpath demand andallocating to each route a wavelength, subject to the constraints, is known as the Routingand Wavelength Assignment (RWA) problem [8–10]. The concept of a lightpath isgeneralized into that of a light-tree [11], which unlike a lightpath, a light-tree hasmultiple destination nodes. Thus, a light-tree forms a tree rooted at the source nodeinstead of the typical path created in the physical topology.

The solution to the manycast RWA problem can be either, given a fixed number ofwavelengths and a set of manycast requests, to maximize the total number of manycastrequests admitted (Max-RWA), or to minimize the number of wavelengths used (Min-RWA), provided that wavelength availability is sufficient to route all of the requests [12].Given the hard computations of the linear integer program [13], we analyze the problemusing metaheuristics. Our objective, given a fixed number of wavelengths, is to maximizethe number of manycast requests to be established in a given session or traffic matrix.

The next section reviews the previous work completed on this topic. In Sect. 3, aproblem definition and formulation is given. Section 4 proposes our assignment algo‐rithm EP. In Sect. 5, experimental results and a comparison between the proposedapproaches is presented. Section 6 discusses the empirical results obtained for thesuggested metaheuristics. Finally, conclusions and future work of this paper are drawnin Sect. 7.

2 Previous Work

The RWA problem can be divided into two sub-problems, the path from source to desti‐nation - this is the routing part - and the wavelength along the path, which is the wave‐length assignment part. Both of these sub-problems are NP complete [14] and tightlylinked together. The manycast RWA issue is, therefore, NP complete since it containsthe RWA issue as a special case.

148 A. Zakouni et al.

Manycast is a special type of multicast communication, in which, from a singlesource, we must reach a set of destination nodes. These destination nodes are to beselected instead of being given. In fact, there are many previous works that investigatethe multicast dilemma. This static multicast RWA is studied in numerous pieces ofresearch [15, 16] targeting the objective of minimizing the blocking probability. Many‐cast is also a generalization of unicast where the message needs to be delivered to anyone of the group. Indeed, there is a wealth of recent work [8, 10, 17–19] that proposesa genetic algorithm and an evolutionary programming to solve RWA problem in theunicast case. While in the manycast case, in numerous previous works, the manycastproblem is first presented as quorumcast [2, 20, 21]. In quorumcast, messages are sentto a subset of destinations (quorum pool), which are selected from a set. Charbonneauand Vokkarane [1, 12] propose three heuristics to solve the manycast problem. Theobjective was to minimize the number of wavelengths required to satisfy all of themanycast requests. In our previous work [3], we propose and compare two metaheur‐istics, tabu search algorithm and genetic algorithm to solve the static manycast RWAproblem by maximizing the number of manycast request established for a given numberof wavelengths. In the work [22], an ILP and several heuristics are introduced for solvingmulti-resource manycast in mesh networks. Few studies, however, tackle the manycastservice over optical burst-switched (OBS) networks [23–25].

3 Problem Definition and Formulation

3.1 Problem Definition

Let a network be represented as a graph G(V, E), where V denotes the set of networknodes and E represents the set of unidirectional fibers. Assume that lightpath requestsare unidirectional, each carrying W wavelengths. A manycast request is represented asMR{s, Dc, k} where s, Dc, k denote the source, the set of candidate destination nodes,and k ≤ |Dc| = m is the number of destination nodes needed to reach out of m. If wechange the parameters to k = m = 1 in the manycast request, we can also perform unicast[1]. Therefore, any algorithm that solves the static manycast RWA problem, in general,should adhere to these following constraints:

1. Wavelength Continuity Constraint: The wavelength continuity constraint indicatesthat a specific request for a source-destination pair should follow a single light‐path [26].

2. Wavelength Conflict Constraint: The wavelength conflict constraint affirms that awavelength might be utilized just once per fiber. In this manner no two signals cancross along the same wavelength in a specific fiber [7].

3.2 Problem Formulation

Let be the number of all lightpaths in G. Let be the vector that containsthe request number to which a lightpath belongs. Let be the number of all requestsin G. Let be the number of connection requests desired to be set up forone request. Let be the sum of all utilized traffic by all requests, as follow:

Solving the Static Manycast RWA Problem in Optical Networks 149

. Let matrix

i.e., dij = 1 if lightpaths i and j share a physical link, otherwise dij = 0. Let T = (Ti) bethe Ti = , if the wavelength is assigned to thelightpath-tree i, otherwise Ti = 0. Let vector, i.e., Pi = ,

if the wavelength is allocated to the lightpath i, otherwise Pi = 0.Let , otherwise . Our problem can be math‐ematically formulated as follows:

In constraint (1), wavelengths assigned must be such that no two lightpaths that sharea physical link, belonging to different requests, or use the same wavelength on that link.

In constraint (2), the sum of the elements of P that are different from zero, cannot,

under any circumstance, surpass the number β.

4 Our Proposed Metaheuristics

Previous research offers a variety of solutions, from simple to complex metaheuristicalgorithms for solving the RWA complication. Here, we extend the same EvolutionaryProgramming (EP) presented in [8, 10, 19] based on a backtracking approach but thistime we utilize it to solve the Static Manycast RWA problem.

4.1 Evolutionary Programming (EP)

The EP is a stochastic optimization procedure that can be applied to a range of difficultcombinatorial problems. It’s relatively similar to Genetic Algorithm since both thememulate the procedure of natural evolution in order to solve combinatorial optimizationproblems. For this purpose, EP exploits a myriad of techniques inspired by naturalevolution such as selection, mutation, and replacement so that it can create the best near-solutions to optimization issues. Compared with GA, EP has no crossover operator eventhough it also has the mutation function. The key concepts of the EP explained below:

P[8]P[7]P[6]P[5]P[4]P[3]P[2]P[1]P[0] P[8]P[7]P[6]P[5]P[4]P[3]P[2]P[1]P[0]

P[8]P[7]P[6]P[5]P[4]P[3]P[2]P[1]P[0] P[8]P[7]P[6]P[5]P[4]P[3]P[2]P[1]P[0]

P:

P: 201010200 201010200

202010210 202010210

Fig. 1. Mutation phase.


Initial Population: In this phase, each gene in a chromosome solution represents oneof the paths generated through a backtracking algorithm so that we can investigate allthe possible candidate paths between the source and the destination pairs. These candi‐date solutions are called chromosomes which take, in our case, the form of bit strings.Each bit position in the chromosome has W possible values. During this step, we initi‐alize the variables that will be used namely: k, Dc, n, P, Pmax and Fmax.

Selection: In this step, the chromosomes of the next generation are selected from thecurrent population by evaluating all the chromosomes using a fitness function choosingthe best individual.

Mutation: In this stage, the operator randomly inverts some of the bits in a chromo‐some, which is considered as a random mutation of the new pool. Thus, some randomlychosen elements of the vector P (P contains the best-found solution in terms of theallocated wavelength to the chosen paths for a manycast request) containing the valueλ, which represents the wavelength that the lightpath will use, will be randomly changedby a different value of the wavelength λ. In this step, the generated chromosome replaces

Start

Backtracking

Initial Solution

Moreiterations?

Mutation

Constraint (1) is met & New best

solution? is found?

Update the fitness function

Return best solutionNo

No

Yes

Yes

Fig. 2. Evolutionary Programming flow chart.


itself regardless of the fitness function. This concept is shown in Fig. 1. More detailsabout EP can be found in [4, 6, 17–19, 27, 28]. The main working steps of our proposedEP are shown in the general flow (Fig. 2).

4.2 Genetic Algorithm (GA)

The GA is a search technique originally invented by [29] and used in computing to findtrue or approximate solutions to optimization and search problems. Indeed, this meta‐heuristic belongs to the larger class of evolutionary algorithms, which is inspired onprocess of natural selection and is routinely used to generate useful solutions. Geneticalgorithms use biologically-derived techniques such as inheritance, mutation, naturalselection, and crossover (or recombination). More details about GA can be found in

Start

Backtracking

Initial Solution

Moreiterations?

Crossover

Mutation

Constraint (1) is met & New best

solution? is found?

Update the fitness function

Return best solutionNo

No

Yes

Yes

Fig. 3. Genetic Algorithm flow chart.


[3, 4, 6, 17–19, 27–30]. The main working steps of the proposed GA done in our previouswork [3] are shown in this following general flow (Fig. 3):

4.3 Backtracking Algorithm

In the work [8, 10, 19] the authors propose a backtracking algorithm for routing unicastdemands. This algorithm can extend to the manycast case if a path search is done forevery destination one-by-one. Using this method, we have the capacity to investigateall of the possible candidate paths between the source and the destination pairs of thetrees. All research in this paper focuses on the extension of the work done on staticunicast RWA problems by utilizing the backtracking algorithm. Previous studies focuson k-shortest path [5, 31], which is widely used in the literature to find alternative paths.Hence, by using the backtracking approach, our initial search space will contain not onlythe k-shortest paths between each source-destination pair, but also all of the possiblecandidate lightpaths. More details about backtracking can be found in [3, 8, 10, 19].

5 Numerical Results

The hardware we’re using for our experiments is an Intel(R) Core(TM) i7- 4790 k CPU4 GHZ processor with 8 GB RAM, running under Ubuntu 14.04.2. All algorithms werecompiled by GCC compiler of Qt Creator 3.4 (based on Qt 5.4 “64Bit”). Our experimentconsists of 90 extensive tests. The experiment is executed for 5 manycast groupsconsisting of 10, 20, 30, 40 and 50 requests, running each test on two different algorithmswith the same initial population and parameters. The number of wavelengths, W, chosenfor network simulation, is 64, 160, and 320, which are practical values today [32].Moreover, we use three different destination set sizes (4, 6 and 8). For each request MR,we use 3 different sizes of Dc, and k = Dc/2. The maximum number of iterations is fixedat 5000. We run all these simulations on the 14-node NSF network. We assume thatsplitting capabilities and wavelength converters [33] are not adopted in our case.

As it can be seen from the performance results (Fig. 4), we notice that the numberof established sets of manycast sessions increases with the increase of W and decreasewhen the set of destination is larger:

• When D = 4, the proposed EP gives better results up to 24 % compared to GA tech‐nique. However, for other W = 160 and 320, EP and GA algorithms produce thesame results.

• When D = 6, we notice that GA outperform EP, specifically when the manycast groupsizes is less than 20, this out-performance goes up to 5 %.

• When D = 8, GA shows a decent performance that is close to the EP method whenW = 64. Otherwise we observe that GA has a better improvement over EP.

• The time spent by GA or EP to solve the manycast problem increases rapidlydepending on the number of manycasts groups as well as the number of the wave‐lengths. However, the time spent using the EP is three times higher than GA. In fact,since we are dealing with the static case, computations are done offline.

• We should remark that EP shows sufficient performance to solve the manycast RWAproblem in many cases. Nevertheless, it takes a while to reach its end. Thus we


consider the time and minimum number of iterations of the best found solution forthe future work.

Performance Analysis D=4, k=2

0

10

20

30

40

50

10 20 30 40 50 10 20 30 40 50 10 20 30 40 50

Number of Manycasts

Satis

fied

Man

ycas

ts R

eque

sts

GA EP


0

10

20

30

40

10 20 30 40 50 10 20 30 40 50 10 20 30 40 50

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0

10

20

30

40

10 20 30 40 50 10 20 30 40 50 10 20 30 40 50

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Satis

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ycas

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GA EP

w = 64w = 160

w = 320

w = 64w = 160

w = 320

w = 64w = 160

w = 320

Fig. 4. Satisfied manycast requests for D = 4, 6 and 8.


6 Discussion

In small destination sets EP largely performs better than GA. This out-performance goesup to 24 % improvement over GA, in terms of a solution. However, GA run times arevery low compared to the EP approach. GA has shown it can perform better than EP byup to 5 %, especially for large destination sets. This can be related to the crossover siteutilized by GA which maintains diversity in the resolution space. Related to the wave‐length variation, the results are somewhat predictable, since it is easier for small sizemanycast requests to be nearly accepted, most notably when the wavelength number islarge. In contrast, large size requests often require much of the network resources, inturn many requests could not be satisfied.

Regarding the fairness issue, we observe that GA achieves better fairness among themanycast groups in terms of satisfying all the groups of connections whereas the EPhave shown low fairness, specifically when the manycast group increases. For the wave‐length reuse issue, we notice that the probability of the re-use of existing wavelength ishigher only if the frequency of occurrence of a common physical link is very low, seeingthat lately the number of wavelengths increases, so this wavelength reuse problem willbe nonexistent.

Our proposed Genetic Algorithm and Evolutionary Programming approaches asatisfactory solution. Our performance evaluation of 90 tests confirms that, althoughmuch research attempts to solve the multicast RWA problem, only a few studies try todeal with the manycast RWA issue. It is, therefore, important to develop more, newmetaheuristics for solving the manycast RWA problem.

7 Conclusion and Future Work

In this paper we implement and compare two metaheuristic strategies to solve the staticmanycast RWA problem, with a special focus on maximizing the number of manycastrequests established for a given number of wavelengths. The problem was studied forthe static case only. We propose two metaheuristics to compute the approximated solu‐tions, in which GA works better when the destination set are larger. This is when weincrease the destination set. EP has shown good performances for small destination sets.The routing sub-problem is solved using a backtracking algorithm. The proposed GAand EP in this paper are applicable to a real NSF network. A relevant comparison,counting the performance and the time included, is made between the two metaheuris‐tics, making a total of 90 experiments. The time spent by EP, on average, is three timeshigher than GA.

This work can be extended by using both splitting capabilities and wavelengthconverters as we have only considered networks without them. The dynamic manycastproblem can be considered for future work for the manycast issue over wavelength-routed networks. The dynamic manycast complication is especially important for serv‐ices that are related to cloud computing and grid networks, where multiple resources arerequired. Our work concentrates on NSF networks only. Further research on more meta‐heuristics in more irregular and more realistic topologies should be conducted. Further


study can be conducted with broadcasting communications where many-to-manysessions run simultaneously.

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solving the static manycast rwa problem in optical networks using evolutionary programming

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