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Applied Optimization I, 6 credits
Tillämpad optimering I, 6 hp
TNK104
Main field of study
Mathematics Applied Mathematics Transportation Systems EngineeringCourse level
Second cycleCourse type
Programme courseExaminer
Nikolaos PappasDirector of studies or equivalent
Erik BergfeldtEducation components
Preliminary scheduled hours: 30 hRecommended self-study hours: 130 h
Available for exchange students
YesECV = Elective / Compulsory / Voluntary
| Course offered for | Semester | Period | Timetable module | Language | Campus | ECV | |
|---|---|---|---|---|---|---|---|
| 6CKTS | Communication and Transportation Engineering, M Sc in Engineering | 7 (Autumn 2017) | 1 | 4 | English | Norrköping, Norrköping | E |
| 6CKTS | Communication and Transportation Engineering, M Sc in Engineering | 9 (Autumn 2017) | 1 | 4 | English | Norrköping, Norrköping | E |
| 6CKTS | Communication and Transportation Engineering, M Sc in Engineering (Master Profile Quantitative Logistics) | 7 (Autumn 2017) | 1 | 4 | English | Norrköping, Norrköping | C |
| 6MTSL | Intelligent Transport Systems and Logistics, Master's programme | 3 (Autumn 2017) | 1 | 4 | English | Norrköping, Norrköping | E |
Main field of study
Mathematics, Applied Mathematics, Transportation Systems EngineeringCourse level
Second cycleAdvancement level
A1XCourse offered for
- Intelligent Transport Systems and Logistics, Master's programme
- Communication and Transportation 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
Basic knowledge in linear programming and integer programmingIntended learning outcomes
The course is aimed at providing the participants with knowledge in applied optimization, with focus on the application of theory and methods in combinatorial optimization for modeling and solving optimization problems originating from the area of transport and communication. The course also aims at letting the participants gain insights and practical skills in setting up mathematical models and using optimization methods. After completing the course, the participants shall be able to
- connect the subjects of the course to their study program
- describe fundamental theory and methods in combinatorial optimization and integer programming
- describe classical optimization problems in the area of transport and communications
- explain concepts related to problem complexity and the impact of complexity on large scale optimization
- use a modeling system for setting up optimization models and problem solving
- describe and apply modern heuristics for solving large scale optimization
Course content
Basics of combinatorial optimization; integer programming models; relations between combinatorial optimization, linear programming, and integer programming; branch and bound, and cutting plane for solving integer models; classical combinatorial optimization problems: shortest path, maximum flow, minimum spanning tree, matching, facility location, traveling salesman, and graph coloring; problem complexity: complexity classes, theoretical and practical impact of complexity on large scale optimization; the impact of the choice of integer model in large scale optimization; basic column generation; problem relaxation and relaxation methods; application of heuristics and relaxation methods. heuristics: greedy heuristic, local search, tabu search, simulated annealing.
Teaching and working methods
The course consists of lectures, seminars and computer labs.
Examination
| LAB1 | Laboratory work | 3 credits | U, G |
| PRA1 | Project work | 3 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Department
Institutionen för teknik och naturvetenskapDirector of Studies or equivalent
Erik BergfeldtExaminer
Nikolaos PappasEducation components
Preliminary scheduled hours: 30 hRecommended self-study hours: 130 h
Course literature
Föreläsningsmaterial och hänvisningar till referensartiklar för specifika modeller och metoder.| Code | Name | Scope | Grading scale |
|---|---|---|---|
| LAB1 | Laboratory work | 3 credits | U, G |
| PRA1 | Project work | 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.
Course literature is preliminary.
Föreläsningsmaterial och hänvisningar till referensartiklar för specifika modeller och metoder.
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) |
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X
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X
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LAB1
PRA1
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| 1.2 Fundamental engineering knowledge (G1X level) |
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
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X
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LAB1
PRA1
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
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X
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X
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LAB1
PRA1
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| 2.2 Experimentation, investigation, and knowledge discovery |
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X
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X
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LAB1
PRA1
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| 2.3 System thinking |
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X
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PRA1
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| 2.4 Attitudes, thought, and learning |
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| 2.5 Ethics, equity, and other responsibilities |
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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X
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LAB1
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| 3.2 Communications |
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| 3.3 Communication in foreign languages |
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 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 |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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