Optimization of Realistic Complex Systems, 6 credits

Optimering av realistiska, sammansatta system, 6 hp

TAOP61

Course starting semester

Main field of study

Mathematics Applied Mathematics

Course level

Second cycle

Course type

Programme course

Examiner

Kaj Holmberg

Director of studies or equivalent

Ingegerd Skoglund

Education components

Preliminary scheduled hours: 48 h
Recommended self-study hours: 112 h

Possible deviation from course syllabus/programme syllabus

ECV = Elective / Compulsory / Voluntary

Course offered for		Semester	Period	Timetable module	Language	Campus	ECV
6CKEB	Chemical Biology (Industrial Biotechnology and Production)	9 (Autumn 2017)	2	3	Swedish	Linköping, Valla	E
6CKEB	Chemical Biology (Protein Science and Technology)	9 (Autumn 2017)	2	3	Swedish	Linköping, Valla	E
6CDDD	Computer Science and Engineering, M Sc in Engineering	9 (Autumn 2017)	2	3	Swedish	Linköping, Valla	E
6CMJU	Computer Science and Software Engineering, M Sc in Engineering	9 (Autumn 2017)	2	3	Swedish	Linköping, Valla	E
6CEMM	Energy-Environment-Management	7 (Autumn 2017)	2	3	Swedish	Linköping, Valla	E
6CEMM	Energy-Environment-Management (Sustainable Business Development)	7 (Autumn 2017)	2	3	Swedish	Linköping, Valla	C
6CEMM	Energy-Environment-Management (System Tools for Sustainable Development)	7 (Autumn 2017)	2	3	Swedish	Linköping, Valla	C
6CEMM	Energy-Environment-Management (Technology for Sustainable Development)	7 (Autumn 2017)	2	3	Swedish	Linköping, Valla	C
6CTBI	Engineering Biology, M Sc in Engineering (Industrial Biotechnology and Production)	9 (Autumn 2017)	2	3	Swedish	Linköping, Valla	E
6CITE	Information Technology, M Sc in Engineering	9 (Autumn 2017)	2	3	Swedish	Linköping, Valla	E
6MMAT	Mathematics, Master's programme	3 (Autumn 2017)	2	3	Swedish	Linköping, Valla	E
6MMAT	Mathematics, Master's programme (Modelling and Optimization in Economics)	3 (Autumn 2017)	2	3	Swedish	Linköping, Valla	E

Main field of study

Mathematics, Applied Mathematics

Course level

Second cycle

Advancement level

A1X

Course offered for

Energy-Environment-Management
Computer Science and Engineering, M Sc in Engineering
Chemical Biology
Engineering Biology, M Sc in Engineering
Mathematics, Master's programme
Information Technology, M Sc in Engineering
Computer Science and Software Engineering, M Sc in Engineering

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

Optimization for engineers (or similar basic course in optimization). programming in Matlab.

Intended learning outcomes

The course treats mathematical tools for formulation and solving of optimization problems for realistic complex systems, including environment and energy aspects. Both advanced model formulation and choice of solution method based on the problem structure are included.
Methods used are heuristics and decomposition methods.

After finished course, the student shall be able to:
Formulate complicated optimization problems as mathematical models.
Identify structures in complex model formulations.
Choose suitable solution method based on the problem structure, and motivate the choice.
Explain the principles behind certain heuristic solution methods and decomposition methods, and use them to solve problems.
Plan, develope and realize certain advanced solution techniques for complex optimization problems.
Use general and specialized software for optimization.
Present results orally and in writing.

Course content

Advanced model formulation, metaheuristics, heuristics for combinatorical problems, methods for expensive objective functions, decomposition methods based on Lagrange relaxation. Examples of formulations containing environment and energy aspects.

Teaching and working methods

The course is given as lectures, lessons and project work. The lectures treat theory, solution methods and principles of modeling. The lessons
contain exercises in model formulation and problem solving. The project work contains model formulation, implementation of optimization algorithms, solution of optimization problems with self-made or available software, and presentation of the results.

Examination

PRA1	Project work	3 credits	U, G
TEN1	Written examination	3 credits	U, 3, 4, 5

Grades

Four-grade scale, LiU, U, 3, 4, 5

Department

Matematiska institutionen

Director of Studies or equivalent

Ingegerd Skoglund

Examiner

Kaj Holmberg

Course website and other links

http://courses.mai.liu.se/GU/TAOP61

Education components

Preliminary scheduled hours: 48 h
Recommended self-study hours: 112 h

Course literature

Kaj Holmberg: Optimering (Liber 2010). Kaj Holmberg: Kompletterande material, 2014.

Code	Name	Scope	Grading scale
PRA1	Project work	3 credits	U, G
TEN1	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). Kaj Holmberg: Kompletterande material, 2014.

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	TEN1
	1.2 Fundamental engineering knowledge (G1X level)			X	PRA1
	1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)	X	X	X	TEN1
	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	PRA1 TEN1
	2.2 Experimentation, investigation, and knowledge discovery			X	PRA1
	2.3 System thinking	X		X
	2.4 Attitudes, thought, and learning	X	X	X	PRA1 TEN1
	2.5 Ethics, equity, and other responsibilities	X	X	X	PRA1 TEN1
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
	3.1 Teamwork			X	PRA1
	3.2 Communications			X	PRA1
	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	X	X	X	PRA1
	4.2 Enterprise and business context			X	PRA1
	4.3 Conceiving, system engineering and management		X	X	PRA1
	4.4 Designing			X	PRA1
	4.5 Implementing			X	PRA1
	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			X
	5.2 Economic conditions for knowledge development			X
	5.3 Identification of needs, structuring and planning of research or development projects			X	PRA1
	5.4 Execution of research or development projects			X	PRA1
	5.5 Presentation and evaluation of research or development projects			X	PRA1

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