Accelerating the Design of Optical Networks using Surrogate Models

Accelerating the Design of Optical Networks using Surrogate Models

IV INTERNATIONAL WORKSHOP ON TRENDS IN OPTICAL TECHNOLOGIES – PROF. CARMELO J. A. BASTOS-FILHO, PHD

Carmelo J. Bastos-Filho (Assoc. Prof. UPE) ,

Danilo R. B. Araújo (Ph.D. Student, UFPE)

Erick A. Barboza (Ph.D. Student, UFPE)

Joaquim F. Martins-fi lho (Assoc. Prof. UFPE)


Major question for this presentation

Is it possible to bring knowledge from other areas to improve the solutions for optical

networks?

In order to answer the general question, we will try to answer more specific questions!How to evaluate the current available methods to assess optical networks?

• An overview about the trade-off between accuracy and performance of the available tools

What is machine learning?• A brief overview on Artificial Neural Networks• What kind of applications we can develop?

What is Network Science?• A brief introduction to network metrics and generative models

How can we develop surrogate models to assess optical networks?• The major challenges related to the use of alternative procedures to assess optical networks• Network sciences + Artificial Neural Nets + Physical layer information Can we develop a suitable

surrogate model to assess optical networks???

What is the impact of using these surrogate models to design optical networks?

• A comparative study between “traditional” approaches and surrogate-based approaches



Designing Optical Networks In order to design optical networks, one must define:

1. The physical topology;

2. The equipments to be deployed (amplifiers, ROADMs, number of TX cards);

3. The deployed modulation format, grooming scheme, etc., ….


Designing Optical Networks In order to design optical networks, one must define:

1. The physical topology;

2. The equipments to be deployed (amplifiers, ROADMs, number of TX cards);

3. The deployed modulation format, grooming scheme, etc., ….

This means that you have a lot of variables!!!!


Designing Optical Networks (Let’s try to simplify)

One has to define:

• Which nodes should be connected [a1,2; a1,3; ... ; an-1,n]? • ai,j=1 if i and j are connected, and ai,j=0 otherwise;

• Which type of amplifier should be deployed in each link [amp1,2; amp1,3; ... ; ampn-1,n]? • ampi,j can assume different labels depending on the availability and suitability;

• How many wavelengths must be available in each link [w1,2; w1,3; ... ; wn-1,n]? • wi,j is the number of wavelengths between node i and j;

• Which equipments should be installed in each node [ROADM1; ROADM2; ... ; ROADMn]? Even if we try to simplify even more by using the same type of amplifier and ROADM in the entire network, and we deploy the same number of wavelengths for all links ◦ We still have (n2-n)/2 + 2 variables◦ [a1,2; a1,3; ... ; an-1,n; ROADM; w]

Examples using this description


For n = 14 |X| = 93

The number of variables grows quickly when larger networks are used

Examples using this description


For n = 14 |X| = 93For n = 34 |X| = 563

The number of variables grows quickly when larger networks are used

How to find the best “configuration”?


OPTIMIZATION METHODS!!!!

EXAMPLES:Integer Linear Programming;Evolutionary Algorithms;Swarm Intelligence;Multi-objective optimization.



The state-of-art optimization algorithms can not garantee the optimum solution for such a high dimensionality!!!!

OPTIMIZATION METHODS!!!!

EXAMPLES:Integer Linear Programming;Evolutionary Algorithms;Swarm Intelligence algorithms;Multi-objective optimization.



Besides, in all cases it is mandatory to have metrics to guide the optimization process! Objective functions:CAPEX;OPEX;Energy consumption;Network performance metrics.



Network performance metrics Examples: Blocking Probability (in dynamic traffic networks)Utilization rate (for static networks)Etc…

How to evaluate the “Objective function”?

Fide

lity

Resource efficiency

Experimental Measures


Fidelity of the analysis in comparison with real dataResource efficiency in terms of financial or computational costs


Fide

lity

Resource efficiency


Simulations Based on Numerical Models




Fide

lity

Resource efficiency


𝑦= 𝑓 (𝑥 )Simulations Based on Numerical Models

Simulations Based on Analytical Models




Fide

lity

Resource efficiency






Is there any other possibility??


Fide

lity

Resource efficiency


Surrogate Models Based on Machine Learning





How to evaluate the current available methods for optical networks analysis?

Fide

lity

Resource efficiency


Surrogate Models Based on Machine Learning




How to improve the fidelity of surrogate models based

on machine learning?

?


What should we know to develop good machine learning surrogates? Network Science

◦Metrics◦Generative models

Machine learning techniques◦Artificial Neural Networks

What is Network Science?

[1] T. G. LEWIS. NETWORK SCIENCE - THEORY AND APPLICATIONS. JOHN WILEY & SONS, 2009.

Network science is a multidisciplinary research field that can be applied to any problem modeled by graphs, in which the inputs or the topology of the graph can vary along the time

Recent developments in Network Science include:• Proposal of metrics that can explain the structure and the behaviour of

real world networks• Proposal of generative models that can represent the topology structures

of real world networks



Some well known metrics:• Average path length (APL): the average of the minimum path for all pairs of

nodes (source, destination) – mean value of the shortest path routes• Algebraic connectivity (AC): second smaller eigenvalue of the Laplacian

matrix – it is related to the robustness of the network• Density (d): ratio between the number of established links and the maximum

number of possible links• Diameter (D): the longest shortest path• Entropy (I): measures the uncertainty regarding the degree of a given node• Clustering coefficient (CC): it is calculated based on the number of

triangulations between nodes



Some well known generative models:• K-Regular: consists in linking each node i with the following k nodes

• entropy equal to zero and the diameter/APL depend on k• Ring networks are a special case




• entropy equal to zero and the diameter/APL depend on k• Erdos-Renyi (ER): a link between i and j is randomly established, according to the

probability p• High entropy, lower APL/CC• Not applied to real world networks




• entropy equal to zero and the diameter/APL depend on k• Erdos-Renyi (ER): a link between i and j is randomly established, according

to the probability p• High entropy, lower APL/CC

• Watts-Strogatz (WS): starts with k-regular networks and performs rewiring processes with the probability rp• Lower entropy, low APL and high CC• It can be suitable for transport networks!



Some well known generative models:

• K-Regular: consists in linking each node i with the following k nodes• entropy equal to zero and the diameter/APL depend on k

• Erdos-Renyi (ER): a link between i and j is randomly established, according to the probability p• High entropy, lower APL/CC

• Watts-Strogatz (WS): starts with k-regular networks and after that rewires new connections with the probability rp• Lower entropy, low APL and high CC

• Barabási-Albert (BA): starts with 3 nodes fully connected and each new nodes is added by using the preferential attachment concept (hubs attracts new connections)• High entropy and lower APL/diameter• presence of hubs – can be used for access networks


Artificial Neural Networks It is not a “magical” black box tool, instead it is a distributed tool for function approximation ◦ It was demonstrated some decades ago

Each neuron applies a non-linear function over the weighted sum of the inputs

If <the number of inputs forms a complete set regarding the required output> and <there are enough neurons in the hidden layer> and <the number of patterns presented to adjust the weights of the neurons is enough> then ◦ <an ANN can be used to approximate one desired measure, i.e. the output>

◦ *there are some well known algorithms to train the ANN. We used the backpropagation one (widely and most used)


ANN Applications for Optical Networks

•We can use Multi-Layer Perceptron to map the NF and GF as a function of the input and output powers applied to the amplifier. •MLPs may avoid the necessity of a small step to obtain a high resolution characterization.

• One can measure operation points with a gain interval of 3 dB, which results presenting errors as low as of 0.1 dB.


ANN Applications for Optical Cognitive Networks

We have developed an approach to adjust the operating point of a cascade of amplifiers (6 in a row for the results in the figure) based on the delta rule deployed to train the ANN


Let’s get back to Surrogates


How can we define a surrogate model to assess optical networks?

We handle the following problem:• Given: a RWA algorithm, the fiber topology and the

specification of the optical devices• Goal: To estimate the blocking probability (BP);• Subject to: the lack of an available wavelength or

unacceptable QoT due to physical impairments.


Some possible surrogates to estimate BP:• Simulations based on Monte Carlo experiments based on

discrete events• It can be precise, but it needs a lot of time!



Some possible surrogates to estimate BP:• Simulations based on Monte Carlo experiments based on

discrete events• It can be precise, but it needs a lot of time!

• Closed analytical expressions to estimate BP• Fast, but can not represent all practical situations!



Some possible surrogates to estimate BP:• Simulations based on Monte Carlo experiments that evaluate QoT

by using analytical expressions• It can be precise, but needs a lot of time!

• Closed analytical expressions to estimate BP• Quick, but not precise!

• Artificial Neural Networks (ANNs) obtained by using a database of previously evaluated optical networks




PROPOSAL:• Artificial Neural Networks as an approximation tool• Networks science metrics to “catch” the network behaviour• General physical layer information to include general information regarding QoT

Output LayerHidden LayerInput Layer

X1

X2

Xp

Z1

Z2

ZM

BP......


Output LayerHidden LayerInput LayerX1

X2

Xp

Z1

Z2

ZM

BP......


First challenge: How to define the input set X?

How can we use surrogates to assess networks?Our proposed methodology is based on combining PCA and best selection

D. R. B. ARAUJO, C. J. A. BASTOS-FILHO, J. F. MARTINS-FILHO, METHODOLOGY TO OBTAIN A FAST AND ACCURATE ESTIMATOR FOR BLOCKING PROBABILITY OF OPTICAL NETWORKS, JOURNAL OF OPTICAL COMMUNICATIONS AND NETWORKING. 7 (5) (2015) 380-391.

Begin

End

1. Select a superset of input variables

2. Create a random dataset of WRONs

3. Evaluate the dataset of WRONs by simulations

5. Define p = 2

8. Use the p variables and the ANN to estimate BP

6. Test all sets of p variables as inputs of the ANN

ΔMSE > 0.05

7. Define p = p + 1

No

Yes

4. Use PCA to remove redundant variables

How can we use surrogates to assess networks?The role of each part of our complete solution [2]

[2] D. R. B. ARAUJO, C. J. A. BASTOS-FILHO, J. F. MARTINS-FILHO, METHODOLOGY TO OBTAIN A FAST AND ACCURATE ESTIMATOR FOR BLOCKING PROBABILITY OF OPTICAL NETWORKS, JOURNAL OF OPTICAL COMMUNICATIONS AND NETWORKING. 7 (5) (2015) 380{391.

Evaluator

Learning Engine

Complex Networks Engine

Start evaluation

Calculate the ANN outcome

Compute inputs

Start training

Discrete event simulator (network

simulator)

Calculate the weights of

ANN

Create a dataset of

WRONs

WRON BP

inputs

dataset

Trained ANN

WRON

WRON

Topological properties

BP

Topological properties

WRON


How can we use surrogates to assess networks?Superset of variables used to build an accurate estimator for BP of WRONs

Index Variable DefinitionX1 W Number of wavelengths

X2 δ OXC isolation factor

X3 CC Clustering coefficient

X4 d Density

X5 Entropy of the DFT of the Laplacian eigenvalues

X6 AC Algebraic connectivity

X7 NC Natural connectivity

X8 Average degree

X9 APL Average path length (hops)

X10 D Diameter (hops)

X11 I(G) Entropy

X12 Dkm Diameter (km)

X13 APLkm Average path length (km)

X14 ρ Spectral radius

X15 CR Concentration of routes

X16 L Traffic load

X17 σPL Standard deviation of the minimum path lengths

X18 d(km) Fiber link density

X19 ∆OSNR Average OSNR margin

X20 σ∆OSNR Standard deviation of the ∆OSNR

An illustrative case study on the performance of our proposal


13

12

14

10

6

4

1

2 9

11

8

7

5

3

26 k

m27

km

42 k

m

76 km

35 km

22 km

100 km

24 km

25 km72 km

55 km

25 km

21 km22 km

35 km

48 km

45 km

48 k

m

28 km

30 km

65 k

m

How can we use surrogates to assess networks?

[2] D. R. B. ARAUJO, C. J. A. BASTOS-FILHO, J. F. MARTINS-FILHO, METHODOLOGY TO OBTAIN A FAST AND ACCURATE ESTIMATOR FOR BLOCKING PROBABILITY OF OPTICAL NETWORKS, JOURNAL OF OPTICAL COMMUNICATIONS AND NETWORKING. 7 (5) (2015) 380{391.

An illustrative case study about the performance of our proposal [2]

p Camada de entrada

2 W, δ 4.02E-3 4.6E-5 -

3 W, δ, d 5.62E-4 2.4E-4 0.86

4 W, δ, d, CR 3.23E-4 1.6E-5 0.43

5 W, δ, d, CR, CC 2.83E-4 1.5E-5 0.12

6 W, δ, d, CR, CC, 2.66E-4 6.8E-6 0.06

7 W, δ, d, CR, CC, , APL (km)

2.57E-4 9.7E-6 0.03

p = 3 p = 4 p = 5 p = 6 p = 7 Results of [8]

SIMTON A

SIMTON B

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

Method to estimation of BP

MS

E

What is the impact of surrogates and network science to design optical networks?

[3] D. R. B. ARA´UJO, C. J. A. BASTOS-FILHO, AND J. F. MARTINS-FILHO. NA EVOLUTIONARY APPROACH WITH SURROGATE MODELS AND NETWORK SCIENCE CONCEPTS TO DESIGN OPTICAL NETWORKS. ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE, 43(08):67–80, 2015.

We have successfully used surrogates and network science concepts to design optical networks

The two main fields under investigation are:• Proposal of generative procedures to create good fiber topologies• Proposal of schemes to combine surrogates and discrete event simulatior to accelerate the

convergence of EA-based approaches

We studied the impact of our proposal to design the 14-node network [3]• Our goal is to find network configurations that presents good trade-off in terms of CAPEX

and blocking probability• We compared our proposal with traditional EA-based approaches

• Previous approaches used random generators and used only network simulations to assess the quality of network configurations


Watt-Strogatz model driven by traffic for seed generation

What is the impact of surrogates and network science to design optical networks?

0.0001 0.001 0.01 0.1 10

2000

4000

6000

8000

10000

12000

CHAVES [7]ARAUJO [8]WS-T

Blocking Probability

Cost

[7] D. A. R. CHAVES, C. J. A. BASTOS-FILHO, J. F. MARTINS-FILHO, MULTIOBJECTIVE PHYSICAL TOPOLOGY DESIGN OF ALL-OPTICAL NETWORKS CONSIDERING QOS AND CAPEX, OPTICAL FIBER COMMUNICATION. OFC 2010, 1{3.[8] D. R. B. ARAUJO, C. J. A. BASTOS-FILHO, E. A. BARBOZA, D. A. R. CHAVES, J. F. MARTINS-FILHO, AN ECIENT MULTI-OBJECTIVE EVOLUTIONARY OPTIMIZER TO DESIGN ALL-OPTICAL NETWORKS CONSIDERING PHYSICAL IMPAIRMENTS AND CAPEX, IN:

INTELLIGENT SYSTEMS DESIGN AND APPLICATIONS (ISDA), 2011 11TH INTERNATIONAL CONFERENCE ON, 2011, PP. 76{81.


Cascade of Surrogate Models (CSM)

0.00001 0.0001 0.001 0.01 0.1 10

2000

4000

6000

8000

10000

12000

PrefEA-NSEA-CSM


Cost

(m.u

.)


Not using surrogates

A reference Pareto front and two fronts obtained after 15 minutes of execution for EA-NS and for our

new proposal. Pareto fronts are for the non-uniform traffic scenario. The cost is given in generic

monetary units (m.u.).

0.00001 0.0001 0.001 0.01 0.1 10

2000

4000

6000

8000

10000

12000

PrefEA-NSEA-CSM


Cost

(m.u

.)

C

B

D

A





0.00001 0.0001 0.001 0.01 0.1 10

2000

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12000

PrefEA-NSEA-CSM


Cost

(m.u

.)

C

B

D

A


Not using surrogates




EXECUTION TIME

Conclusions


Current solutions for analysis and design of optical networks present a trade-off in terms of fidelity and resource efficiency

Network science is a promising research field that can contribute to the development of new network analysis tools

Global performance metrics for optical networks such as blocking probability can be assessed by surrogate models based on machine learning techniques

Topological metrics from network science that summarize the fiber topology are natural candidates to offer reduction of dimensionality for networks assessment

ANNs can be used to forecast the blocking probability of optical networks when the right set of inputs is chosen

Surrogates and generative models can be used together to assist the design of optical networks


Thanks for your attention!

Accelerating the Design of Optical Networks using Surrogate Models


Carmelo J. Bastos-FILHO (Assoc. Prof. UPE) ,

Danilo R. B. Araújo (Ph.D. Student, UFPE)

Erick A. Barboza (Ph.D. Student, UFPE)

Joaquim F. Martins-fi lho (Assoc. Prof. UFPE)

Accelerating the Design of Optical Networks using Surrogate Models

Technology

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