| TAOP86 |
Combinatorial Optimization with Environmental Applications, 8 ECTS credits.
/Kombinatorisk optimering med miljötillämpningar/
For:
IT
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Prel. scheduled
hours: 68
Rec. self-study hours: 145
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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 combinatorial optimization problems, often based on
different network and graph structures. Sustainable development and
environmental aspects are prominent aspects in the applications that
are discussed. An important point is the ability to choose and use
the most efficient algorithm for each specific problem structure. 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:
describe important types of combinatorial optimization problems.
formulate combinatorial optimization problems as mathematical models,possibly with graph terminology, and determine the difficulty of the problems with the help of complexity theory.
explain the design of and the principles behind efficient solution methods and choose and use the methods for solving different types of combinatorial optimization problems.
use available software for solving optimization problems.
take part of development of software for optimization problems.
develop heuristics for certain structured combinatorial optimization problems.
explain and use basic concepts, such as local and global optimality, convexity, extreme point, complexity, duality, heuristic, branch-and-bound, cutting planes, and basic graph theory, especially trees and cycles of different kinds.
give examples of how combinatorial 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)
Linear algebra, Discrete structures, Data structures and algorithms
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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Organisation:
The course is given as seminars, computer exercises and work in PBL
groups. The seminars can be seen as a mixture of lectures and
exercises, and treats theory, methods and models. Time is also spend
on exercises in model formulation and problem solving. The computer
exercises contain both implementation of optimization algorithms and
solution of combinatorial optimization problems with the help of
available software.
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Course contents:
Introduction to optimization, problem formulation, graphical solution,
computational complexity, problem complexity. The simplex method, linear duality and sensitivity analysis. Basic graph theory and
overview of different optimization problems in graphs. Models and
methods for finding minimal spanning tree, minimum cost traveling
salesman tour, minimum cost postman tour, shortest path, minimum cost
assignment, minimum cost flow and maximal flow. Methods for integer
programming, especially branch-and-bound, cutting planes and dynamic
programming. Heuristics for hard combinatorial optimization problems.
Examples on applications that concern different aspects within
sustainable development, for instance concerning a scenario that is
common for several courses.
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Course literature:
Kaj Holmberg: Optimering (Liber, 2010).
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Examination: |
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Written examination
Laborations
Work in PBL group.
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4 ECTS
2 ECTS
2 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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