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Engineering Optimization, 6 credits
Optimering för ingenjörer, 6 hp
TAOP88
Main field of study
Mathematics Applied MathematicsCourse level
First cycleCourse type
Programme courseExaminer
Kaj HolmbergDirector of studies or equivalent
Ingegerd SkoglundEducation components
Preliminary scheduled hours: 52 hRecommended self-study hours: 108 h
ECV = Elective / Compulsory / Voluntary
Main field of study
Mathematics, Applied MathematicsCourse level
First cycleAdvancement level
G2XCourse offered for
- Energy-Environment-Management M Sc in Engineering
- Design and Product Development
- Chemical Biology, M Sc in Engineering
- Biomedical Engineering, M Sc in Engineering
- Mechanical Engineering, M Sc in Engineering
- Engineering Biology, 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
Calculus, linear algebra, and Matlab.Intended learning outcomes
The course deals with mathematical tools for formulating, solving and analyzing optimization problems that engineers may encounter. Sustainable development and environmental aspects are prominent aspects in the applications that are discussed. Focus lies on the engineering aspect of building a toolbox with different methods for different problems, and choosing the best method for each problem type. The algorithms are intended to be suitable for large scale problems and implementation on computer. After finishing the course, the student shall be able to:
- identify optimization problems and classify them according to their properties, mainly with respect to possible solution methods
- formulate optimization problems as effective mathematical models
- explain the design of and the principles behind efficient solution methods and choose and use the methods for solving different types of optimization problems
- use available software for solving optimization problems
- explain and use basic concepts, such as local and global optimality, convexity, extreme point, duality, heuristic, branch-and-bound, cutting planes, and basic graph theory, especially trees and cycles of different kinds
- develop heuristics for certain structured optimization problems
- use optimality conditions for certain optimization problem to determine the optimality of a given solution
- give examples of how optimization can be used to promote sustainable development and improve the environment
Course content
Fundamental concepts and tools for solving optimization problems,
such as mathematical modelling, optimality conditions, convexity, sensitivity analysis, duality, and some graph theory. Basic methods for linear, nonlinear, integer and network optimization.
Heuristics for hard combinatorial optimization problems. Examples on
applications that are relevant for engineers and that concern different aspects within sustainable development.
Teaching and working methods
The lectures include theory, problem solving and applications. The exercises are intended to give individual training in problem solving. The laboratory course contains solution of combinatorial optimization problems with the help of available software as well as implementation of optimization algorithm.
Examination
| LAB1 | Laboratory work | 1.5 credits | U, G |
| TEN1 | Written examination | 4.5 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Other information
Supplementary courses: Large Scale Optimization, Supply Chain Optimization.
Department
Matematiska institutionenDirector of Studies or equivalent
Ingegerd SkoglundExaminer
Kaj HolmbergCourse website and other links
http://courses.mai.liu.se/GU/TAOP88Education components
Preliminary scheduled hours: 52 hRecommended self-study hours: 108 h
Course literature
Kaj Holmberg: Optimering (Liber, 2010).| Code | Name | Scope | Grading scale |
|---|---|---|---|
| LAB1 | Laboratory work | 1.5 credits | U, G |
| TEN1 | Written examination | 4.5 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.
Course literature is preliminary.
Kaj Holmberg: Optimering (Liber, 2010).
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 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
|
|||
| 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
|
LAB1
TEN1
|
||
| 2.2 Experimentation, investigation, and knowledge discovery |
|
|
X
|
LAB1
|
||
| 2.3 System thinking |
X
|
|
X
|
LAB1
TEN1
|
||
| 2.4 Attitudes, thought, and learning |
X
|
X
|
X
|
LAB1
TEN1
|
||
| 2.5 Ethics, equity, and other responsibilities |
X
|
X
|
X
|
LAB1
TEN1
|
||
| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
|
|
X
|
LAB1
|
||
| 3.2 Communications |
|
|
X
|
LAB1
|
||
| 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
|
TEN1
|
||
| 4.2 Enterprise and business context |
|
|
X
|
|||
| 4.3 Conceiving, system engineering and management |
|
X
|
X
|
LAB1
TEN1
|
||
| 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 |
|
|
X
|
|||
| 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
|
LAB1
|
||
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