### Optimization and Systems Theory Seminar

Friday, March 15, 2002, 11.00-12.00, Room 3721, Lindstedtsv. 25

**Mikael Prytz**

Division of Optimization and Systems Theory

Department of Mathematics

KTH

E-mail: mikael.prytz@math.kth.se

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On optimization in design of telecommunications networks with
multicast and unicast traffic

This talk gives a survey of my thesis that will be defended on March
21, 2002. The thesis addresses certain optimization problems arising in
telecommunications network design, specifically capacity dimensioning
of telecommunications networks with multicast and unicast traffic, and
a multicast routing location problem.
A brief review of telecommunications networks design and a discussion
of optimization models and solution strategies is given. Next the
specific problems studied in the four appended papers of the thesis
are described including proposed solution schemes and computional
results. The solution strategies include Lagrangian decomposition and
Lagrangian relaxation, specialized branch-and-bound strategies, and
LP-based branch-and-cut together with valid inequalities. The
decomposition methods induce subproblems that are Steiner tree
problems, binary and continuous knapsack problems, and shortest path
problems.

The four specific network design problems considered are: general step
cost capacity dimensioning of a multicast enabled backbone
communications network, capacity dimensioning of a multicast network
with shortest path tree restrictions on achievable routing
distribution tree topologies, Rendezvous Point (RP) placement problem
for shared multicast trees in an existing shortest path routing
network, and finally, unicast network capacity dimensioning problem
with general step costs and single path routing.

Calendar of seminars

*Last update: March 7, 2002 by
Anders Forsgren,
anders.forsgren@math.kth.se.
*