Simulated Annealing algorithm for optimization of elastic optical networks with unicast and anycast traffic

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.

Full text

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 (HJ., 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
EHVWP
2: while (LLPD[ and 7!0.01):
3: G1
m
rand(D), G2
m
rand(D)
4. Swap(G1G2); 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$;
11: else:
12: [
m
rand();
13: if ([ < exp-GHOWD7)):
14: FXUUHQW5
m
WHPS$;
15: else:
16: Swap(G1G2);
17: 7
m
7M;
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 Pparameter, which is an input tuning parameter of VSA. The
simulation is being processed until we fulfill conditions from line 2 (number of iterations Lis 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 FXUUHQW5DQGWHPS$. Next, in line 9 we review if the current solution is
better than the best by checking the value of GHOWD and accordingly we assign FXUUHQW as WHPS$. 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, (LH., [
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, LH., $5 = K$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 $5we generate 5 demand sets,
which were tested for 12 (16 for bigger topologies) different scenarios of location and number of DCs. This gave
us the overall number of 360 (480 for bigger topologies) separate experiments. Since CPLEX can find optimal
results of considered ILP models only for relatively small instances, to obtain optimal results we use only
smaller topologies (NSF15 and Euro16), with overall demand K$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 7calculated 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, LH., 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 LQELJJHUQHWZRUNLQVWDQFHV
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 mOptimality
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\JDSIRU0D[6SHF0RGHO
FF MSF LSF VSA
NSF15 45.1% 13.1% 18.1% 3.8%
Euro16 48.6% 11.5% 14.3% 4.3%
/HQJWKVRIFRQILGHQFHLQWHUYDOV
NSF15 2.09% 1.51% 1.78% 0.69%
Euro16 2.15% 1.43% 1.56% 0,92%
2SWLPDOLW\JDSIRU$YJ6SHF0RGHO
FF MSF LSF VSA
NSF15 51.4% 26.7% 22.5% 3.7%
Euro16 50.5% 24.4% 19.0% 4.0%
/HQJWKVRIFRQILGHQFHLQWHUYDOV
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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