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 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.
Learning Outcomes (Dublin Descriptors)
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
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