Programme of Course "Network Optimization"
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1. Course Objectives
Ability to recognize and model network optimization problems as Integer Linear Programming problems. Knowledge of fundamental algorithmic techniques for solving large scale Integer Linear Programming problems. Knowledge of commercial and open source Integer Linear Programming solvers.
2. Course Contents and learning outcomes (Dublin Descriptors)
Topics of the course include:
 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 branchandbound 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. Branchandcut 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. Local Search Tabu search and Simulated Annealing MIP based heuristics
 Heuristics for network problems: local search, tabu search, simulated annealing, MIP based heuristics.
On successful completion of this course, the student should

Know and define single objective network optimization problems

Use and design exact or heuristic algorithms to solve single objective network optimization problems

Ability to judge models and methods to tackle network optimization problems

Ability to explain the models, the algorithms and the computational complexity needed to solve network optimization problems

Ability to learn stateofart algorithms for network optimization problems
3. Course Prerequisites
Basic knowledge of: Discrete Mathematics, Linear Programming, Algorithms and Data Structures, Computational complexity. Knowledge of at least one programming language.
4. Teaching methods and language
Lectures and software training
Language:English
Reference textbooks
 L.A. Wolsey, Integer Programming. Wiley. 1998.
5. Assessment Methods
Written text exam and assignment
Course information last updated on: 10 settembre 2015, 10:40