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Syllabus for

Academic year
TMA521 - Project course in optimization
 
Owner: TM
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: C
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0197 Examination 5,0 c Grading: TH   5,0 c   Contact examiner,  Contact examiner

In programs

TDATA COMPUTER SCIENCE AND ENGINEERING - Algorithms, Year 4 (elective)
TTFYA ENGINEERING PHYSICS, Year 4 (elective)
TITEA SOFTWARE ENGINEERING, Year 3 (elective)
EMMAS MSc PROGR IN ENGINEERING MATHEMATICS, Year 1 (elective)
TM Teknisk matematik, Year 2 (elective)

Examiner:

Professor  Michael Patriksson



Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

Basic knowledge of linear and discrete optimiza-tion.

Aim

The purpose of the course is to give the students insight into some of the most important principles for the efficient solution of practical, large-scale optimization problems, ranging from the modelling to the construction of solution methods. The main activity in the course is the project work, in which the students utilize these principles for the efficient solution of some relevant optimization problem.

Content

A series of lectures capture important concepts in modelling and solution of optimization problems. The purpose is to give insight in how inherent difficulties and problem structures can be identified. Utilizing this knowledge, the student can formulate an appropriate model and identify one or a number of alternative solution principles. In the second part of the course, these principles are applied to project work, where the student from a given problem description identifies a relevant modelling of the problem, structures and sound solution appro-aches, to complete with the numerical solution of some pratical problem using relevant software.
Outline of content: a selection of : I (Optimization problems): Review of linear programming, unimo-dularity and convexity, minimal spanning tree, knapsack problem, location problem, generalized assignment, travelling salesman problem, network design, route planning. II (Principles for algorithms): Decomposition/coordination, restriction, projection, variable fixing, neighbourhood, relaxations (Lag-range, SDP), linearization, line search, coordinating master problem. III (Algorithms): Cutting planes, Lagrangean heuristics, column generation, Dant-zig-Wolfe decomposition, Benders decomposition, derivative free methods, local search, meta heuristics, modern tree search methods.

Literature

S.G. Nash and A. Sofer, Linear and Nonlinear Programming, McGraw-Hill, 1996 (selection).
L.A. Wolsey, Integer Programming, Wiley, 1998 (selection).
Journal articles.

Examination

A written report and oral presentation of the project, opposition; an oral examinatin for a grade higher than pass.


Page manager Published: Thu 03 Nov 2022.