Course syllabus - Optimization and simulation

Objectives

The aim of the course is to provide basic knowledge of optimization theory and methods of simulations, as well as develop skills in modelling and solving problems in the appropriate field of technology using efficient algorithms and simulations.

Learning outcomes

Upon completion of the course the student is expected to be able to:

1. construct mathematical models for linear optimization problems
2. describe and apply the theory of linear programming, including the concepts of convexity and duality
3. generate continuous and discrete stochastic variables
4. describe and apply the theory of Monte Carlo-modelling and Monte Carlo-simulation
5. analyse problems in the appropriate field of technology and be able to present the results by well-structured reports and oral presentations

Course content

- Background and basic ideas of linear programming
- Linear modelling
- Convexity, in particular with respect to the domain of definition
- Duality
- Solution methods of linear optimization problems, such as the Simplex method
- Estimation of expected values using stochastic processes, generation of discrete and continuous stochastic variables and processes following different distributions
- Ideas and theory of Monte Carlo-methods, speed of convergence independent of dimension
- Modelling and implementation of  problems in the appropriate field of technology

Tuition

Lectures, study groups and computer based laboratory work.

Specific requirements

Probability Theory and Statistical Inference 7.5 credits; at least 3.5 credits must be completed at the beginning of the course and Numerical Methods for Engineers 7.5 credits or equivalent.

Examination

INL1, Written assignments, 3.5 credits, hand in assignments concerning learning outcomes 1-5, grades Fail (U) or Pass (G).
LAB1, Laboratory work, 2 credits, written and oral presentation concerning learning outcomes 1, 2, 5, grades 3, 4 or 5.
LAB2, Laboratory work, 2 credits, written and oral presentation concerning learning outcomes 3, 4, 5, grades 3, 4 or 5.

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Grading scale: 5, 4, 3