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Multi-Objective Optimization for Topology Control in Hybrid FSO/RF Networks
Jaime LlorcaDecember 8, 2004
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Outline Hybrid FSO/RF Networks Topology Control Problem Statement Optimal solution
Constraint method Weighting method
Heuristics Comparison versus optimal
Conclusions
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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
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Topology Control
Dynamic networks Atmospheric obscuration Nodes mobility
Topology Control Dynamic topology reconfiguration in
order to optimize performance
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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
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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
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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
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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)
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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
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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
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T = 0 min
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T = 10 min
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T = 20 min
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T = 30 min
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T = 40 min
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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
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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
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T = 20 min, k = 0
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T = 20 min, k = 0.2
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T = 20 min, k = 0.4
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T = 20 min, k = 0.6
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T = 20 min, k = 0.8
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T = 20 min, k = 1
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T = 40 min, k = 1
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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