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Graduate courses

Departments' graduate courses for PhD-students.

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Syllabus for

Academic year
MVE165 - Linear and integer optimization with applications
Linjär och heltalsoptimering med tillämpningar
 
Syllabus adopted 2017-02-10 by Head of Programme (or corresponding)
Owner: MPENM
7,5 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: Second-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English
Open for exchange students: Yes

Course elements   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0107 Examination 7,5c Grading: TH   7,5c    

In programs

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


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Eligibility:


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

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.
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 cases how linear and integer optimization problems are modelled and solved in practice. In addition to a lecture series given by teachers at MV there is a series of guest lectures, given mainly by researchers at other departments of Chalmers and University of Gothenburg. The contents of the course may therefore vary in terms of topics between the years, but a common basis is the practical solution of optimization problems. Some of the guest lectures are connected to project assignments, which also constitute the main basis for the examination.


Some typical problems, algorithm techniques, and software that will be covered and utilized often over the years are investment, blending, models of energy systems, production and maintenance planning, network models, routing and transport, multi-objective optimization and inventory planning; simplex and interior point methods for linear programming, heuristics, dynamic programming; AMPL, Cplex, and Matlab.

Organisation

A lecture series of mathematical material and a guest series of lecture  with practical material, project work, as well as oral and written student presentations of projects.

Literature

Optimization. J. Lundgren, M. Rönnqvist, and P. Värbrand. Studentlitteratur, 2010.

Optimization Exercises. M. Henningsson, J. Lundgren, M. Rönnqvist, and P. Värbrand. Studentlitteratur, 2010.

Examination including compulsory elements

Passed project assignments, passed exercises, oral and written presentations, opposition, and an oral exam.


Published: Fri 18 Dec 2009. Modified: Wed 04 Apr 2018