Solving the Multi-Commodity Flow Problem using a Multi-Objective - - PowerPoint PPT Presentation

Solving the Multi-Commodity Flow Problem using a Multi-Objective Genetic Algorithm

Noel Farrugia, Johann A. Briffa, Victor Buttigieg

Department of Communications and Computer Engineering University Of Malta

Introduction

• Compared to 2015, generated Internet traffic will triple by

2020.

• Single path routing algorithms, such as Open Shortest Path

First (OSPF), are unable handle this traffic efficiently.

• Developed a Multi-Objective Genetic Algorithm (MOGA) that

solves the Multi-Commodity Flow Problem.

• The developed MOGA increases the total network flow by 6%

compared to an OSPF-like setup without using multipath.

1

The Multi-Commodity Flow Problem

• The MCFP deals with routing a set of flows/commodities

from a source to a destination over a network, without exceeding any link capacity.

• In this work we deal with a variant of the MCFP, the

Multi-Commodity Maximum-Flow Minimum-Cost (MCMFMC).

• The MCMFMC maximises the total network flow passing

through the network at the lowest possible cost.

• The cost of a link is equivalent to its delay value.

2

Linear Programming – Limitations

• Optimal solution for MCMFMC problem can be found using

Linear Programming (LP).

• LP cannot be used for multi-objective problems.
• LP handles objectives sequentially.
• Flow maximisation always takes priority over cost

minimisation.

• May lead to a routing solution that splits a flow over multiple

paths.

• Transmission Control Protocol (TCP) - the most commonly

used transport protocol - suffers severe performance degradation when a flow is split over multiple paths.

3

Multi-Objective Genetic Algorithm – MOGA

• To overcome the limitations of LP, a MOGA has been

developed.

• The MOGA generates valid routing solutions for a given flow

set with constraints similar to the MCFP.

• The quality of a routing solution is assessed using three
• bjectives:
• Total Network Flow.
• Proportion of Flows with Minimum Delay.
• Flow Splits.

4

MOGA – Objectives – Total Network Flow

• Fundamental routing algorithm aim is total network flow

maximisation.

• The total network data rate impacts:
• The network efficiency.
• The flow satisfaction rate.

5

MOGA – Objectives – Proportion of Flows with Minimum Delay

• Routing algorithm must favour transmission on paths with

lower delays.

• The objective reflects the proportion of data transmitted on

the low delay paths compared to the rest.

• The more data allocated to the lower cost paths, the higher

the metric value will be.

6

MOGA – Objectives – Flow Splits

Minimisation of the number of flow splits is beneficial because it:

• Reduces the negative impact multipath has on TCP.
• Reduces the number of entries stored in the routers’ network

table.

7

MOGA – Chromosome Representation

• Each flow is allowed to transmit on a fixed set of paths.
• The paths are found using the K-Shortest Path (KSP)

Algorithm.

• Chromosome is defined as the sequence C = (G1, G2, ..., Gn).
• Gi = (gi,1, gi,2, ..., gi,ki) is the sequence of genes related to

flow fi.

• Each element gi,j ∈ R≥0 represents the data rate flow fi can

transmit on path pi,j.

8

MOGA – Chromosome Representation – Example

1 9 8 3 2 6 7 4 5

30/1 30/1 5Mbps/1ms 30/1 30/5 30/1 10/1 30/5 30/5 30/1 30/1 Flow 1 Path 1: 5 Mbps Flow 1 Path 2: 5 Mbps Flow 2 Path 1: 5 Mbps Flow 2 Path 2: 15 Mbps

Flow 1 transmitting @10 Mbps Flow 2 transmitting @20 Mbps C = ((5, 5), (5, 15))

9

MOGA – Crossover

• Generates new routing solutions by combining two

chromosomes together.

• A mixing ratio z ∈ U(0, 1) is chosen for every crossover.
• Each gene sequence is swapped with probability z.

Ca Cb (Ga1, Ga2, Ga3) (Gb1, Gb2, Gb3) ((2, 10), (1, 5), (2, 3)) ((1, 3), (7, 1), (3, 2))

?

((2, 10), (7, 1), (2, 3)) (1, 3), (1, 5), (3, 2))

Crossover Example 10

MOGA – Mutation

• Works on a single chromosome.
• Modifies the data rate assignment of a fraction µ of the flows.
• Three mutation operators are used:
• Flow Maximisation.
• Cost Minimisation.
• Path usage minimisation.

11

Results – Setup

• The MOGA uses the NSGA-II algorithm and is developed

using the DEAP framework.

• Network simulations are carried out using ns3.26.
• The KSP algorithm is set with k = 5.
• The following flow network loads are used:

Network Load Data Rate (Mbps) Mean

• Std. Deviation

Low 5 0.25 High 25 2.5 The Medium load setup has an equal number of flows having a Low and High load profile.

12

Results – Setup

The 2017 G´ EANT network topology is used with the following modifications:

• Red Links: 30Mbps.
• Light Blue: 60Mbps.
• Dark Blue: 120Mbps.
• The link delay attribute is

proportional to the geographical distance between the cities. 2017 G´ EANT Network Topology 13

Results – Comparison with Previous Work

The presented MOGA (MOGA-II) is compared with:

• Our previous MOGA (MOGA-I).
• Multi-Commodity Max-Flow Min-Cost (KSP-LP) with k = 5.
• Multi-Commodity Max-Flow Min-Cost with k = 1 to represent

OSPF (KSP-LP-1).

14

Results – Maximum Allocated Total Network Flow

50 100 150 200 250 300 Number of Flows 500 1000 1500 2000 2500 3000 Total Network Flow (Mbps)

MOGA-I MOGA-II KSP-LP KSP-LP-1 Low Medium High Requested

15

Results – Projection of Pareto Front

10 20 30 40 Flow Splits 1800 1900 2000 2100 2200 2300 2400 Total Network Flow (Mbps)

MOGA-I MOGA-II KSP-LP KSP-LP-1

• Solution with the maximum Total Network Flow at zero Flow Splits.

16

Results – Projection of Pareto Front

80 90 100 110 120 130 140 150 Proportion of Flows with Minimum Delay 1800 1900 2000 2100 2200 2300 2400 Total Network Flow (Mbps)

MOGA-I MOGA-II KSP-LP KSP-LP-1

• Solution with the maximum Total Network Flow at zero Flow Splits.

17

Results – Network Simulation – Throughput

5 10 15 20 25 30 35 Flow Throughput (Mbps) 0.0 0.2 0.4 0.6 0.8 1.0 Probability

MOGA-I (1623.9 Mbps) MOGA-II (1969.3 Mbps) KSP-LP (1803.5 Mbps) KSP-LP-1 (1826.7 Mbps)

18

Results – Network Simulation – Delay

20 40 60 80 100 Delay (ms) 0.0 0.2 0.4 0.6 0.8 1.0 Probability

MOGA-I MOGA-II KSP-LP KSP-LP-1

19

Conclusion

• Present a MOGA used to find a routing solution capable of

increasing network efficiency.

• Improves on our previous work by presenting new orthogonal
• bjectives that better represent the solutions we are after.
• The presented MOGA performs:
• 6% better than an OSPF-like setup when using TCP in terms
• f Total Network Flow.
• 25% better than our previous algorithm in terms of Total

Network Flow.

20