Combinatorial Optimization, Introductory Course, 4 credits

Kombinatorisk optimering gk, 4 hp

TAOP33

Course starting semester

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Kaj Holmberg

Director of studies or equivalent

Ingegerd Skoglund

Education components

Preliminary scheduled hours: 42 h
Recommended self-study hours: 65 h

Possible deviation from course syllabus/programme syllabus

ECV = Elective / Compulsory / Voluntary

Course offered for		Semester	Period	Timetable module	Language	Campus	ECV
6CDDD	Computer Science and Engineering, M Sc in Engineering	5 (Autumn 2017)	1	2	Swedish	Linköping, Valla	C
6CMJU	Computer Science and Software Engineering, M Sc in Engineering	7 (Autumn 2017)	1	2	Swedish	Linköping, Valla	C/E

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G2X

Course offered for

Computer Science and Engineering, M Sc in Engineering
Computer Science and Software Engineering, M Sc in Engineering

Specific information

The course is not allowed in the diploma together with TAOP07.

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Linear Algebra

Intended learning outcomes

The course deals with mathematical tools for solving and analyzing combinatorial optimization problems. Focus lies on choosing and using the most efficient algorithm for each specific problem structure. The algorithms are suitable for implementation on computer. After finished course, the student shall be able to:

describe important types of combinatorial optimization problems
formulate combinatorial optimization problems as mathematical models and determine the difficulty of the problems with the help of complexity theory
explain the design of and the principles behind efficient solution methods and use the methods for solving combinatorial optimization problems
use available software for solving optimization problems
take part of development of software for optimization problems
develop a simple heuristic for a structured combinatorial optimization problem
explain and use basic concepts, such as local and global optimality, convexity, extreme point, complexity, duality, basic graph theory and branch-and-bound

Course content

Introduction to optimization, problem formulation, graphical solution,
computational complexity. The simplex method, linear duality and
sensitivity analysis. Basic graph theory, models and methods
for finding minimal spanning tree, traveling salesman tour, postman tour, shortest path, minimum cost flow and maximal flow. Methods for integer programming, such as branch-and-bound. Problem complexity, heuristics.

Teaching and working methods

The lectures and lessons treat theory, methods and models, as well as exercises in model formulation and problem solving. The computer exercises contain both implementation of optimization algorithms and solution of combinatorial optimization problems with the help of available software.

Examination

LAB2	Laboratory work	1 credits	U, G
TEN2	Written examination	3 credits	U, 3, 4, 5

Grades

Department

Director of Studies or equivalent

Examiner

Course website and other links

http://courses.mai.liu.se/GU/TAOP33

Education components

Course literature

Code	Name	Scope	Grading scale
LAB2	Laboratory work	1 credits	U, G
TEN2	Written examination	3 credits	U, 3, 4, 5

Regulations (apply to LiU in its entirety)

The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.

Student rights and obligations (login required)
Linköping University common rules and regulations (in Swedish)

Course literature is preliminary.

Kaj Holmberg: Optimering (Liber, 2010).

Download

Download course literature list as PDF

Note: The course matrix might contain more information in Swedish.

I = Introduce, U = Teach, A = Utilize

		I	U	A	Modules
1. DISCIPLINARY KNOWLEDGE AND REASONING
	1.1 Knowledge of underlying mathematics and science (G1X level)	X	X	X	TEN2
	1.2 Fundamental engineering knowledge (G1X level)			X
	1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)	X	X	X	TEN2
	1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)
	1.5 Insight into current research and development work
2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
	2.1 Analytical reasoning and problem solving	X	X	X	LAB2 TEN2
	2.2 Experimentation, investigation, and knowledge discovery			X	LAB2
	2.3 System thinking	X		X
	2.4 Attitudes, thought, and learning	X	X	X	LAB2 TEN2
	2.5 Ethics, equity, and other responsibilities	X	X	X	LAB2 TEN2
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
	3.1 Teamwork			X	LAB2
	3.2 Communications			X	LAB2
	3.3 Communication in foreign languages
4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
	4.1 External, societal, and environmental context
	4.2 Enterprise and business context			X
	4.3 Conceiving, system engineering and management		X	X	LAB2 TEN2
	4.4 Designing			X
	4.5 Implementing			X
	4.6 Operating
5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS
	5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development
	5.2 Economic conditions for knowledge development			X
	5.3 Identification of needs, structuring and planning of research or development projects
	5.4 Execution of research or development projects
	5.5 Presentation and evaluation of research or development projects			X	LAB2

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