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

1. Multi-Objective Optimization for Topology Control in Hybrid FSO/RF Networks Jaime Llorca December 8, 2004

2. Outline • Hybrid FSO/RF Networks • Topology Control • Problem Statement • Optimal solution • Constraint method • Weighting method • Heuristics • Comparison versus optimal • Conclusions

3. 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 Hybrid FSO/RF Networks • Wireless directional links • FSO: high capacity, low reliability • RF: lower capacity, higher reliability • Cost Matrix

4. Topology Control • Dynamic networks • Atmospheric obscuration • Nodes mobility • Topology Control • Dynamic topology reconfiguration in order to optimize performance

5. 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

6. 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

7. Formulation • Objectives: • Constraints: • Bi-connectivity • Degree constraints • Sub-tour constraints

8. 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)

15. Constraint Method • Constrain power expenditure: • 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

16. 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

17. T = 0 min

18. T = 10 min

19. T = 20 min

20. T = 30 min

21. T = 40 min

22. 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

23. 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

24. T = 20 min, k = 0

25. T = 20 min, k = 0.2

26. T = 20 min, k = 0.4

27. T = 20 min, k = 0.6

28. T = 20 min, k = 0.8

29. T = 20 min, k = 1

30. T = 40 min, k = 1

31. 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