# Course Details

#### Name:

**Network Optimization / Network Optimization**

### Basic information

##### Credits:

*Master Degree in Computer Science:* 6 Ects (c)

##### Degree(s):

Compulsory 1^{st} year Master Degree in Computer Science curriculum SEAS

##### Language:

English

### 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.

### Course Content

- 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.
Local Search
Tabu search and Simulated Annealing
MIP based heuristics
- Heuristics for network problems: local search, tabu search, simulated annealing, MIP based heuristics.

### Learning Outcomes (Dublin Descriptors)

On successful completion of this course, the student should

### Prerequisites and Learning Activities

Basic knowledge of:
Discrete Mathematics, Linear Programming, Algorithms and Data Structures, Computational complexity.
Knowledge of at least one programming language.

### Teaching Methods

**Language**: English

Lectures and software training

### Assessment Methods and Criteria

Written text exam and assignment

### Textbooks

- L.A. Wolsey,
**Integer Programming**. Wiley. 1998. * *

### Online Teaching Resources

### Course page updates

This course page is available (with possible updates) also for the following academic years:

*Course information last updated on: 10 settembre 2015, 10:40*