Network Design 2015-2016


Network Design (Progetto di Reti) is a 12 CFU integrated course made of two modules: Network Flows (formerly Progetto e Ottimizzazione di Reti) and Network Optimization (formerly Ottimizzazione Combinatoria 2)

Schedule

Network Flows

  • Tuesday 14.00-16.00 Room A.1.2 (Alan Turing Building)
  • Thursday 11.00-13.00 Room A.1.3 (Alan Turing Building)

Network Optimization

  • Tuesday 11.00-13.00 Room A.1.3 (Alan Turing Building)
  • Wednesday 9.00-13.00 Room A.1.3 (Alan Turing Building)

Office Hours

Wednesday 11:00 - 13:00

From February, 23th

Course Contents

Module Network Flows

  • Network Flows Problem: introduction and definitions
  • Maximum Flows and the path packing problem. Flows and cuts: Max-Flow/Min-Cut theorem. Augmenting path algorithms: Ford and Fulkerson algorithm, Edmonds and Karp algorithm. Generic Preflow-Push algorithm. Flows with lower bounds.
  • Maximum Flows: additional topics and applications. Flows in Unit Capacity Networks. Flows in Bipartite Networks. Network Connectivity.
  • Minimum Cuts. Global Minimum Cuts. Node Identification Algorithm. Random Contraction. Applications.
  • Minimum-Cost Flow Problems. Definition and applications. Optimality Conditions. The Ford-Bellman algorithm for the shortest path problem. Primal algorithms: Augmenting Circuit Algorithm for the Min Cost Flow Problem.
  • Network Simplex Algorithms. Applications of Min Cost Flows.

Module Network Optimization

  • Formulations of Integer and Binary Programs: The Assignment Problem; The Stable Set Problem; Set Covering, Packing and Partitioning; Minimum Spanning Tree; Traveling Salesperson Problem (TSP); Formulations of logical conditions.
  • Mixed Integer Formulations: Modeling Fixed Costs; Uncapacitated Facility Location; Uncapacitated Lot Sizing; Discrete Alternatives; Disjunctive Formulations.
  • Optimality, Relaxation and Bounds. Geometry of R^n: Linear and affine spaces; Polyhedra: dimension, representations, valid inequalities, faces, vertices and facets; Alternative (extended) formulations; Good and Ideal formulations.
  • LP based branch-and-bound algorithm: Preprocessing, Branching strategies, Node and variable selection strategies, Primal heuristics.
  • Cutting Planes algorithms. Valid inequalities. Automatic Reformulation: Gomory's Fractional Cutting Plane Algorithm. Strong valid inequalities: Cover inequalities, lifted cover inequalities; Clique inequalities; Subtour inequalities. Branch-and-cut algorithm.
  • Software tools for Mixed Integer Programming.
  • Lagrangian Duality: Lagrangian relaxation; Lagrangian heuristics.
  • Network Problems: formulations and algorithms. Constrained Spanning Tree Problems; Constrained Shortest Path Problem; Multicommodity Flows; Symmetric and Asymmetric Traveling Salesman Problem; Vehicle Routing Problem; Steiner Tree Problem; Network Design.
  • Heuristics for network problems: local search, tabu search, simulated annealing, MIP based heuristics.

Textbooks

Reference books

  • L.A. Wolsey, Integer Programming, Wiley, 1998.
  • Cook, Cunningham, Pulleyblank, Schrijver , Combinatorial Optimization, Wiley,1998.
  • Ahuja, Magnanti, Orlin, Network Flows, Prentice Hall, 1993.

Further readings

Slides and Notebooks

Slides are in Italian. English slides and Network Optimization slides are available on request Notebooks

Software

Setting up the working environment

After a fresh install of Xubuntu 14.04.4, you can setup the working environment by installing the following packages: