| TAOP88 |
Engineering Optimization, 6 ECTS credits.
/Optimering för ingenjörer/
For:
DPU
EM
KeBi
M
MED
TB
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Prel. scheduled
hours: 52
Rec. self-study hours: 108
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): G2
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Aim:
The course deals with mathematical tools for formulating, solving and
analyzing optimization problems that engineers may encounter. Sustainable development and environmental aspects are prominent aspects in the applications that are discussed. Focus lies on the engineering aspect of building a toolbox with different methods for different problems, and choosing the best method for each problem type. The algorithms are intended to be suitable for large scale problems and implementation on computer.
After finishing the course, the student shall be able to:
- identify optimization problems and classify them according to their properties, mainly with respect to possible solution methods
- formulate optimization problems as effective mathematical models
- explain the design of and the principles behind efficient solution methods and choose and use the methods for solving different types of optimization problems
- use available software for solving optimization problems
- explain and use basic concepts, such as local and global optimality, convexity, extreme point, duality, heuristic, branch-and-bound, cutting planes, and basic graph theory, especially trees and cycles of different kinds
- develop heuristics for certain structured optimization problems
- use optimality conditions for certain optimization problem to determine the optimality of a given solution
- give examples of how optimization can be used to promote sustainable development and improve the environment
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Calculus, linear algebra, and Matlab.
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Supplementary courses:
Large Scale Optimization, Supply Chain Optimization.
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Organisation:
The lectures include theory, problem solving and applications. The exercises are intended to give individual training in problem solving. The laboratory course contains solution of combinatorial optimization problems with the help of available software as well as implementation of optimization algorithm.
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Course contents:
Fundamental concepts and tools for solving optimization problems,
such as mathematical modelling, optimality conditions, convexity, sensitivity analysis, duality, and some graph theory. Basic methods for linear, nonlinear, integer and network optimization.
Heuristics for hard combinatorial optimization problems. Examples on
applications that are relevant for engineers and that concern different aspects within sustainable development.
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Course literature:
Kaj Holmberg: Optimering (Liber, 2010).
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Examination: |
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Written examination
Labarotive work
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4,5 ECTS
1,5 ECTS
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Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Ingegerd Skoglund
Examiner: Kaj Holmberg
Link to the course homepage at the department
Course Syllabus in Swedish
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