Multi-Objective Optimization for Topology Control in Hybrid FSO/RF Networks

Jaime LlorcaDecember 8, 2004

Outline Hybrid FSO/RF Networks Topology Control Problem Statement Optimal solution

Constraint method Weighting method

Heuristics Comparison versus optimal

Conclusions

Hybrid FSO/RF Networks Wireless directional links

FSO: high capacity, low reliability RF: lower capacity, higher reliability

Cost Matrix

0 58 30 38 31 27 60 58 0 27 42 35 33 30 30 27 0 13 27 2 33 38 42 13 0 33 10 25 31 35 27 33 0 22 43 27 33 2 10 22 0 42 60 30 33 25 43 42 0

Topology Control

Dynamic networks Atmospheric obscuration Nodes mobility

Topology Control Dynamic topology reconfiguration in

order to optimize performance

Problem Statement Dynamically select the best

possible topology Objectives:

Maximize total capacity Minimize total power expenditure

Constraints 2 transceivers per node Bi-connectivity

Ring Topologies

Link Parameters Capacity (C)

FSO and RF: C = 1.1 Gbps RF: C = 100 Mbps

Power expenditure (P)

FSO and RF: P = (PTX)FSO + (PTX)RF

RF: P = (PTX)RF

RX TXP P att( , )FSO FSOatt f L

( , )RF RFatt f L

/TX RX FSOFSOP P att

/TX RX RFRFP P att

Formulation Objectives:

Constraints: Bi-connectivity

Degree constraints

Sub-tour constraints

11 1

max Cn n

ij iji j

x c z

21 1

min Pn n

ij iji j

x p z

1

1

1 j

1

n

iji

n

ijj

x

x i

1

i j

1

2 i 1

u -u 1 ( 1)(1 ) i 1, j 1i

ij

u

u n

n x

Optimal Solution Integer Programming problem

No Convexity! Analogous to the traveling salesman

problem NP-Complete!

Solvable in reasonable time for small number of nodes

Case of study: 7 node network Simulation time: 45 min 10 snapshots (every 5 minutes starting at 0)

Constraint Method Constrain power

expenditure: 11 1

max Cn n

ij iji j

x c z

1 1

s.t. Pn n

ij iji j

x p

Start with a high enough value of ε and keep reducing it to get the P.O set of solutions.

Weakly Pareto Optimality guaranteed Pareto Optimality when a unique solution exists

for a given ε

Weighting method

Keep varying w from 0 to 1 to find the P.O set of solutions

Weakly Pareto Optimality guaranteed P.O. when weights strictly positive May miss P.O. as well as W.P.O points

due to lack of convexity

max (1 )wC w P

T = 0 min

T = 10 min

T = 20 min

T = 30 min

T = 40 min

Heuristics Approximation algorithms to solve the

problem in polynomial time Spanning Ring

Adds edges in increasing order of cost hoping to minimize total cost.

Branch Exchange Starts with an arbitrary topology and

iteratively exchanges link pairs to decrease total cost.

A combination of both used

Multi-objective Heuristics methodology is based on

individual link costs What should the cost be?

Weighted link cost

Try for different values of k and see how the solution moves in the objective space related to the P.O set

ijcost (1 )ij ijkc k p

T = 20 min, k = 0

T = 20 min, k = 0.2

T = 20 min, k = 0.4

T = 20 min, k = 0.6

T = 20 min, k = 0.8

T = 20 min, k = 1

T = 40 min, k = 1

Conclusions Computational complexity of optimal

solution increases exponentially with the number of nodes

Not feasible in dynamic environments Heuristics needed to obtain close-to-

optimal solutions in polynomial time. Useful to obtain the P.O set of solutions

offline, in order to analyze the performance of our heuristics