Course Details
Name:
Network design / Network Design
Basic information
Credits:
Master Degree in Computer Science: 12 Ects (c)
Term:
Module Network Flows: 2° semester
Module Network Optimization: 2° semester
Degree(s):
Compulsory 1^{st} year Master Degree in Computer Science curriculum NEDAS
Compulsory 1^{st} year Master Degree in Computer Science curriculum UBIDIS
Elective 1^{st} year Master Degree in Mathematical Engineering curriculum Comune
Language:
English
Course Objectives
Module Network Flows: Ability to recognize and formulate network flow problems
Knowledge of basic and advanced network flow algorithms
Ability to design resolution approaches to solve non standard network flow problems
Module Network Optimization: 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
Module Network Flows
 Network Flows Problem: introduction and definitions
 Maximum Flows and the path packing problem.
Flows and cuts: MaxFlow/MinCut theorem.
Augmenting path algorithms: Ford and Fulkerson algorithm, Edmonds and Karp algorithm.
Generic PreflowPush 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.
 MinimumCost Flow Problems.
Definition and applications.
Optimality Conditions.
The FordBellman 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 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
Module Network Flows
 Know and formulate network flow problems
 Model decision problems as network flow problems
Use base and advanced algorithms to solve network flow problems
 Ability to identify network flow models scope
 Ability to explain network flows models and algorithms
 Ability to learn stateofart algorithms for network flow problems
Module Network Optimization

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
Module Network Flows: Basic knowledge of:
Discrete Mathematics, Linear Programming, Algorithms and Data Structures, Computational complexity
Module Network Optimization: Basic knowledge of:
Discrete Mathematics, Linear Programming, Algorithms and Data Structures, Computational complexity.
Knowledge of at least one programming language.
Teaching Methods
Language: English
Module Network Flows: Lectures
Module Network Optimization: Lectures and software training
Assessment Methods and Criteria
Module Network Flows: Written text exam
Module Network Optimization: Written text exam and assignment
Textbooks
Module Network Flows
 Cunningham, Pulleyblank, Schrijver , Combinatorial Optimization.
 Ahuja, Magnanti, Orlin, Network Flows.
Module Network Optimization
 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, 10:50