Course syllabus for Linear and integer optimization with applications

Course syllabus adopted 2023-02-14 by Head of Programme (or corresponding).

Overview

  • Swedish nameLinjär och heltalsoptimering med tillämpningar
  • CodeMVE166
  • Credits7.5 Credits
  • OwnerMPENM
  • Education cycleSecond-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language English
  • Application code 20141
  • Open for exchange studentsYes

Credit distribution

0122 Examination, part A 6 c
Grading: TH		0 c0 c0 c6 c0 c0 c
0222 Project, part B 1.5 c
Grading: UG		0 c0 c0 c1.5 c0 c0 c

In programmes

Examiner

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 and model problems from 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; advisement sessions. Additionally, there might be voluntary elements that could give bonus points for the written exam.

Literature

See the course home page.

Examination including compulsory elements

Passed project assignments; a written opposition; a written exam.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.