# Popis předmětu - BE4M35KO

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BE4M35KO Combinatorial Optimization
Role:PS, PV, P Rozsah výuky:3P+2C
Katedra:13135 Jazyk výuky:EN
Garanti:  Zakončení:Z,ZK
Přednášející:Hanzálek Z. Kreditů:6
Cvičící:Osob je mnoho Semestr:L

Webová stránka:

https://cw.fel.cvut.cz/wiki/courses/a4m35ko/start

Anotace:

The goal is to show the problems and algorithms of combinatorial optimization (often called discrete optimization; there is a strong overlap with the term operations research). Following the courses on linear algebra, graph theory, and basics of optimization, we show optimization techniques based on graphs, integer linear programming, heuristics, approximation algorithms and state space search methods. We focus on application of optimization in stores, ground transportation, flight transportation, logistics, planning of human resources, scheduling in production lines, message routing, scheduling in parallel computers.

Osnovy přednášek:

 1 Introduction to Basic Terms of Combinatorial Optimization, Example Applications and a Test of Preliminary Knowledge 2 Integer Linear Programming - Algorithms 3 Problem Formulation by Integer Linear Programming 4 The Shortest Paths. Problem Formulation by Shortest Paths. 5 Problem Formulation by Shortest Paths. 6 Flows and Cuts - Algorithms and Problem Formulation. Test I. 7 Multicommodity network flows 8 Knapsack Problem and Pseudo-polynomial Algorithms 9 Traveling Salesman Problem and Approximation Algorithms 10 Monoprocessor Scheduling 11 Scheduling on Parallel Processors. Test II. 12 Project Scheduling with Time Windows. 13 Constraint Programming. 14 Reserved

Osnovy cvičení:

 1 Policy and Individual Project Market 2 Introduction to the Experimental Environment and Optimization Library 3 Integer Linear Programming 4 Individual Project I - Assignment and Problem Classification 5 Traveling Salesman Problem 6 Individual Project II - Related Work and Solution 7 Applications of Network Flows and Cuts 8 Individual Project III - Consultation 9 Test III 10 Scheduling 11 Advanced Methods for Solving Combinatorial Problems 12 Individual Project IV - evaluation and written report 13 Ungraded Assessment 14 Reserved

Literatura:

 B. H. Korte and J. Vygen, Combinatorial Optimization: Theory and Algorithms.
Springer, sixth ed., 2018. http://dx.doi.org/10.1007/978-3-662-56039-6
 J. Blazevicz, Scheduling Computer and Manufacturing Processes. Springer,
second ed., 2001.
 J. Demel, Grafy a jejich aplikace. Academia, second ed., 2015.
https://kix.fsv.cvut.cz/~demel/grafy/gr.pdf