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ICTON 2014 Th.B3.6

Simulated Annealing Algorithm for Optimization of Elastic

Optical Networks with Unicast and Anycast Traffic

0LFKDá$LELQ and Krzysztof Walkowiak*, Member, IEEE

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ABSTRACT

The growing number of services like Content Delivery Networks (CDNs) and cloud computing triggers

a sustainable growth of data transfer and consequently leads to an increasing interest in anycasting

that is an efficient way to provision network requests related to Data Centers. On the other hand, Elastic Optical

Network (EON) is an effective and cost-efficient solution for optical networks, which can support bandwidth-

demanding needs ranging beyond 100 Gb/s. This paper focuses on joint optimization of unicast and anycast

traffic in EONs including both Routing and Spectrum Allocation (RSA). We propose a novel heuristic algorithm

to solve the RSA problem. The algorithm – named VSA – is a hybrid method that combines a Simulated

Annealing (SA) approach and a simple greedy algorithm. To evaluate our approach, we run a wide range of

experiments on real network topologies. First, we tune VSA to find the best values of the algorithm’s

parameters. Next, we compare the performance of VSA against CPLEX (optimal results) and other heuristics.

According to our experiments, VSA can improve the solution provided by a greedy algorithm by more than 10%

and on average is about 4% worse in comparison to the optimal results.

Keywords: elastic optical networks, anycast traffic, simulated annealing.

1. INTRODUCTION

In recent years, we can observe a continued growth of data transfer, which triggers the demand to develop an

efficient and scalable optical transport platform for a capacity beyond 100 Gb/s [1]. Moreover, a substantial

increase can be seen in anycast traffic defined as one-to-one-of-many transmission techniques. This increase is

caused by the introduction of new services, such as CDNs, cloud computing, IPTV and Video On Demand

(VOD) [2], [4]. One of the technologies, which enable improved use of flexible optical network, is a scalable and

efficient architecture called SLICE. This approach permits sharing links with a capacity beyond 100 Gb/s into

smaller slices and combines them into larger groups. As a result we can achieve a greater variety of spectrum

selection scenarios [3]. The SLICE approach, also known as Elastic Optical Network (EON), is an evolution of

current optical networks. In contrast to current solutions, EON allows the resources to be assigned accordingly to

the size of the required bandwidth [2].

A new optimization problem, known as Routing and Spectrum Allocation (RSA), occurs with the development

of the EON technology. In this paper, we propose a novel metaheuristic algorithm for an RSA problem with joint

unicast and anycast traffic. The proposed VSA algorithm is a hybrid method that improves a solution yielded by

a simple greedy algorithm by using Simulated Annealing approach. An important part of metaheuristics is tuning

of the algorithm. Therefore, we pay special attention to evaluate selection of algorithm’s parameters. According

to the best of our knowledge, this is the first paper that proposes a SA algorithm in the optimization of EONs

with joint unicast and anycast flows.

The remainder of the paper is organized as follows. In Section 2, we describe a heuristic algorithm – VSA.

In Section 3, we present numerical results for algorithm tuning, followed by our results and lastly we conclude

our findings.

2. HEURISTIC ALGORITHM

In this Section, we present a novel VSA algorithm proposed to solve RSA problems with joint unicast and

anycast traffic. In particular, we solve two ILP models with two different objective functions. The first one –

called MaxSpec – minimizes the maximum spectrum usage and was formulated in [4]. The second model called

AvgSpec focuses on minimization of average spectrum usage and was presented in [7]. The VSA method is

based on the SA approach, which is a generic probabilistic heuristic for the global optimization of a given

function in a large search space.

In VSA, a solution of the optimization problem is represented as a sequence (ordering) of demands. To

calculate the objective function of a particular solution, we allocate the demands in the network one by one

according to the particular sequence using a following procedure. For each demand, we analyze all possible

candidate paths provided in advance (HJ., using N-shortest path algorithm). For each examined path, using the

First Fit approach we calculate the value of the considered objective function, assuming that the demand is

assigned to a particular path. Finally, we select a candidate path that guarantees the best value of the objective

function. In the case of anycast demands, the candidate paths leading to all possible Data Center (DC) nodes are

analyzed. Below, we present a pseudo-code of the algorithm.

978-1-4799-5601-2/14/$31.00 ©2014 IEEE 1

ICTON 2014 Th.B3.6

Algorithm 1 VSA

1:FXUUHQW5

m

FXUUHQW0; EHVW

m

FXUUHQW5,

7

m

EHVWP

2: while (LLPD[ and 7!0.01):

3: G1

m

rand(D), G2

m

rand(D)

4. Swap(G1G2); calculate FXUUHQW5

5. WHPS$

m

countAllTakenSlices();

6. if (WHPS$ < EHVW):

7: EHVW

m

WHPS$;

8: GHOWD

m

WHPS$–FXUUHQW5;

9: if (GHOWD < 0):

10: FXUUHQW5

m

WHPS$;

11: else:

12: [

m

rand();

13: if ([ < exp-GHOWD7)):

14: FXUUHQW5

m

WHPS$;

15: else:

16: Swap(G1G2);

17: 7

m

7M;

18: return EHVW;

In line 1, we calculate an initial solution (sequence of demands and value of the objective function) denoted as

FXUUHQW0 using the MSF algorithm introduced in [5]. This solution is selected as the best solution – EHVW and

current solution – FXUUHQW5. Also, in line 1, we calculate initial temperature 7. We present an innovative

approach for the calculation of this parameter that is fully automated. We take the result (number of slices)

generated by MSF in line 1 and multiply it by Pparameter, which is an input tuning parameter of VSA. The

simulation is being processed until we fulfill conditions from line 2 (number of iterations Lis smaller than the

maximum number LPD[and the temperature 7 has not reached absolute temperature, which is equal to 0.01). In

line 3, we randomly select two demands, swap them in the sequence of demands and calculate a new result. We

save the number of the current solution (number of slices) (countAllTakenSlices()) into WHPS$ variable and then

process it by using the SA algorithm. If condition in line 6 is fulfilled, we assign a temporary result to best result

and calculate GHOWD – difference between FXUUHQW5DQGWHPS$. Next, in line 9 we review if the current solution is

better than the best by checking the value of GHOWD and accordingly we assign FXUUHQW as WHPS$. If it is not

fulfilled, we randomly pick a value of [ (line 12) and check if it is smaller than Boltzmann function of

probability distribution (line 13). If it is fulfilled, we repeat the same operation as in line 10. Alternatively, (LH., [

is larger or equal then Boltzmann function), we swap the demands to restore the previous state without saving

the result. Finally, we reduce the temperature 7 with the M parameter, named as a cooling rate parameter. When

we fulfill conditions from the loop in line 2, we return best result as a result of an algorithm. For better

understanding of the algorithm refer to [6].

3. NUMERICAL RESULTS

In this Section, we discuss the results of computational experiments. The goal of the experiments is threefold.

First, we evaluate the performance of the VSA by tuning the three input parameters – jump parameter, number of

iterations and the initial temperature. Second, we focus on the trade-off between the execution time and the

effectiveness of the algorithm. Finally, we compare two objective functions considered in optimization.

3.1 Experiments design

The experiments were performed using four network topologies - Euro28, Euro16, UBN24 and NSF15 (Fig. 1).

In the experiments, we apply an anycast ratio ($5) parameter that is related to a ratio between anycast and

unicast traffic in the network. In detail, we assume that K$Q\ and K8QL denote the overall volume of all anycast and

unicast demands, respectively. Next, let K$OO = K$Q\ + K8QL denote the overall demand in the network. The $5

parameter is defined as the volume (capacity) of all anycast demands divided by the volume of all demands in

the network, LH., $5 = K$Q\ / K$OO.

We run various simulation scenarios. Parameters that we changed in each scenario are as follows: ratio of

anycast to unicast traffic – 0%, 20%, 40%, 60%, 80%, 100% ($5); number of DC (replica) nodes – 1, 2, 3, (4 –

for UBN24 and Euro28) and candidate paths – 2, 3, 5, 10, 30. For each value of $5we generate 5 demand sets,

which were tested for 12 (16 for bigger topologies) different scenarios of location and number of DCs. This gave

us the overall number of 360 (480 for bigger topologies) separate experiments. Since CPLEX can find optimal

results of considered ILP models only for relatively small instances, to obtain optimal results we use only

smaller topologies (NSF15 and Euro16), with overall demand K$OO equal to 2.5 Tbps, and the number of candidate

paths is N = 2. Afterwards we compare the optimal results given by CPLEX 11.0 solver [8] to the following

reference algorithms: FF [3], MSF [5] and LSF [5]. However, for experiments presenting the relationship

between both maximum spectrum and average spectrum, we use all larger topologies with overall demand K$OO

ranging from 40 Tbps to 50 Tbps. Concerning EONs assumptions, we use the half distance law, as in [4], [5] and

[9], for selecting modulation levels for lightpath connections.

3.2 Tuning of the VSA Algorithm

To tune VSA, we examine Euro16 topology for 15 separate cases different in terms of DC nodes numbers,

amount of anycast and unicast traffic and number of candidate paths. We conduct simulations to tune the

following three parameters of VSA algorithm: number of iterations, initial temperature 7calculated according to

2

ICTON 2014 Th.B3.6

the m parameter and the cooling rate parameter – M Firstly, we tune cooling rate (M) and define initial temperature

using m parameter. We consider all combinations of three cases of M and three cases of m resulting in 9 scenarios

summarized in Table 1.

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Each individual result is averaged over 15 cases and 10 repetitions of the algorithm for each case. The number

of iterations is limited to 15,000. As we can see in Table 1, the best combination of tuning parameters is obtained

in scenario S5 – the average optimality gap of VSA for this scenario is 2.12%. According to additional

simulations carried out to determine the number of iterations, we set this parameter to 10,000, since this value

provided the best trade-off between quality of results and execution time. As a result of the tuning process, we

select the following values for further experiments: number of iterations – 10,000,m = 5%,M=0.99. The results

of the tuning process presented above refer to the MaxSpec function, however in the case of the second AvgSpec

function, the results of tuning process were comparable.

3.3 Optimality Gap of VSA in MaxSpec and AvgSpec ILP models

In this Section, we present optimality gaps of VSA and other heuristic algorithms. As we can see in Table 2,

VSA is much better than other algorithms, with stable results in terms of confidence intervals. We can easily

notice that the optimality gap of VSA for the AvgSpec model presents similar trends as for the MaxSpec model.

Regarding the execution time, VSA outperforms CPLEX providing optimal results, LH., for Euro16 network

VSA needs about 60 seconds, while CPLEX requires on average 400 seconds. It should be underlined that VSA

can significantly improve the initial solution provided by MSF (about 10% for MaxSpec and about 20% for

AvgSpec).

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3.4 Results LQELJJHUQHWZRUNLQVWDQFHV

Finally, we report additional results to show the difference between average and maximum spectrum usage of

unicast and anycast traffic in EON, evaluated by VSA for bigger networks UBN24 and Euro28. Note that in

Figs. 2 and 3, the number next to the name of function (MaxSpec/AvgSpec) refers to a number of Data Center

nodes in the network. As we can see in Fig. 2, the difference between two examined objective functions grows

with the increase of anycast traffic ratio, however different performance is observed for various number of DC

nodes, In general, with the increase of anycast traffic ratio, the average spectrum usage decreases.

A corresponding trend for maximum spectrum is different, especially for 2 DCs. This follows mostly from the

fact that maximum spectrum denotes the spectrum usage in the most congested link – in the case of 100% of

anycast traffic and with only 2 nodes, the links adjacent to DC nodes are strongly congested and causes high

values of this performance metric. Nevertheless, in the same case, the average utilization of the spectrum is

much smaller, which is the main advantage of anycast traffic. In Fig. 3, we compare two cases in terms of the

number of DC nodes. We can observe that with the increase of anycast traffic ratio, the difference between 1 and

4 DC nodes significantly grows up to factor of five. This is due to the fact that using more DC nodes decrease

Scenario No. M mOptimality

Gap

S1 0.9 10% 2.76%

S2 0.99 10% 2.92%

S3 0.999 10% 3.14%

S4 0.9 5% 2.72%

S5 0.99 5% 2.12%

S6 0.999 5% 2.89%

S7 0.9 2.5% 2.18%

S8 0.99 2.5% 2.21%

S9 0.999 2.5% 2.84%

2SWLPDOLW\JDSIRU0D[6SHF0RGHO

FF MSF LSF VSA

NSF15 45.1% 13.1% 18.1% 3.8%

Euro16 48.6% 11.5% 14.3% 4.3%

/HQJWKVRIFRQILGHQFHLQWHUYDOV

NSF15 2.09% 1.51% 1.78% 0.69%

Euro16 2.15% 1.43% 1.56% 0,92%

2SWLPDOLW\JDSIRU$YJ6SHF0RGHO

FF MSF LSF VSA

NSF15 51.4% 26.7% 22.5% 3.7%

Euro16 50.5% 24.4% 19.0% 4.0%

/HQJWKVRIFRQILGHQFHLQWHUYDOV

NSF15 2.42% 1.59% 1.66% 0.91%

Euro16 2.34% 1.02% 1.26% 0,74%

3

ICTON 2014 Th.B3.6

the lightpaths’ lengths, what is especially visible when there is more anycast traffic, Moreover, this effect is

amplified but possibility to use higher modulation formats which are available to implement as a result of

smaller distance.

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4. CONCLUSIONS

In this paper, we have focused on anycast-oriented EONs. In particular, we have proposed a novel metaheuristic

algorithm named VSA. We have presented detailed results related to tuning for the VSA algorithm. To assess the

algorithm performance, we have compared VSA with other reference algorithms and with optimal results

generated by CPLEX for smaller networks. The numerical experiments have shown that VSA outperforms the

reference heuristics as well as demonstrates significantly lower execution times and brings radically better

scalability than CPLEX. Moreover, we have performed additional experiments to show the difference between

average and maximum spectrum usage in EON. Furthermore, we have shown that increasing the number of DCs

can bring savings in the spectrum usage, especially for large values of the anycast ratio. In future work, we plan

to include in our research on EONs other objective functions such as network CAPEX/OPEX cost and power

consumption, as well as develop a SA algorithm for these new optimization problems. Moreover, we would like

to formulate a SA method for optimization of multicast flows in EONs.

ACKNOWLEDGEMENTS

This work was supported by The Polish National Science Centre (NCN) under Grant DEC-

2012/07/B/ST7/01215 and statutory funds of the Department of Systems and Computer Networks,

Wroclaw University of Technology.

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[3] M. Jinno, H. Takara, B. Kozicki, A. Hirano, Y. Tanaka, Y. Sone, and A. Watanabe, “Distance-adaptive

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[5] K. Christodoulopoulos HWDO., “Elastic bandwidth allocation in flexible OFDM based optical networks”,

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[7] K. Walkowiak, R. *RĞFLHĔand M. Klinkowski, “On minimization of the spectrum usage in elastic optical

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[8] ILOG AMPL/CPLEX software: www.ilog.com/products/cplex/

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