Syllabus for |
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| MVE165 - Linear and integer optimization with applications |
| Linjär och heltalsoptimering med tillämpningar |
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| Syllabus adopted 2020-02-06 by Head of Programme (or corresponding) |
| Owner: MPENM |
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7,5 Credits
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| Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail |
| Education cycle: Second-cycle |
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Major subject: Mathematics |
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Department: 11 - MATHEMATICAL SCIENCES
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Teaching language: English
Application code: 20117
Open for exchange students: Yes
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Credit distribution |
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Examination dates |
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Sp1 |
Sp2 |
Sp3 |
Sp4 |
Summer course |
No Sp |
| 0107 |
Examination |
7,5c |
Grading: TH |
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7,5c
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In programs
MPDSC DATA SCIENCE AND AI, MSC PROGR, Year 1 (elective)
TKTEM ENGINEERING MATHEMATICS, Year 2 (elective)
MPCAS COMPLEX ADAPTIVE SYSTEMS, MSC PROGR, Year 1 (compulsory elective)
MPCAS COMPLEX ADAPTIVE SYSTEMS, MSC PROGR, Year 2 (elective)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)
MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR, Year 1 (compulsory elective)
Examiner:
Ann-Brith Strömberg
Eligibility
General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Specific entry requirements
English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.
Course specific prerequisites
Linear algebra, analysis in one and in several variables. Basic knowledge in MATLAB is desirable.
Aim
A main purpose with the course is to give the students an overview of
important areas where optimization problems often are considered in
applications, and an overview of some important practical techniques for
their solution. Another purpose of the course is to provide insights into
such problem areas from both a application and theoretical perspective,
including the the analysis of an optimization model and suitable choices
of
solution approaches. Work with concrete problems during the course enable
the establishment of these insights.
Learning outcomes (after completion of the course the student should be able to)
After completion of the course the student should be able to
- identify the most important principles for describing linear and integer optimization problems as mathematical optimization models;
- distinguish between some important classes of linear and integer optimization problems.
- utilize linear programming duality for sensitivity analysis of optimal solutions to such problems.
Within each problem class the student should, after completion of the course, be able to
- develop mathematical models of relevant problems within the class;
- identify and describe the most important and useful mathematical properties of the developed models;
- select, adapt, or develop convergent and efficient suitable solution techniques and algorithms for problems within the class;
- implement the chosen/developed algorithms in appropriate software;
- interpret and assess the plausibility of the obtained solutions in relation to the original problem setting;
- examine the sensitivity of a resulting optimal solution with respect to changes in the problem data;
- explain the results of the sensitivity analysis in relation to the models at hand.
Content
This course describes with the aid of, e.g., case studies how linear and integer optimization problems are modelled and solved in practice.
Some typical problems and algorithms that are covered are investment, blending, models of energy systems, production and maintenance planning, network models, routing and transport problems, multi-objective optimization and inventory planning; the simplex method for linear programming, heuristics, the branch-and-bound algorithm.
Organisation
A lecture series of mathematical material, exercise sessions, project work, and oral and written presentations of projects.
Literature
See the course home page.
Examination including compulsory elements
Passed project assignments, passed exercises, oral and written presentations, opposition, and a written exam.