An investigation of Decomposition Methods For
Solving Multi-level Optimization Problems
Uledi Ngulo
Department of Mathematics, University of Dar es Salaam
Department of Mathematics, Linköping University
First Network Meeting for Sida- and ISP-funded PhD Students in
Mathematics
Stockholm 7–8 March 2017
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My Supervisors
Torbjörn Larsson
Nils-Hassan Quttineh
Egbert Mujuni
Main supervisor
Linköping University
Assistant supervisor
Linköping University
Assistant supervisor
University of Dar es Salaam
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Introduction
The study aims at research in the field of large scale
multi-level optimization models and methods, that is,
optimization problems and methods that involve two or more
coupled optimization problems. This structure appears
frequently in applications.
A commonly used approach for multi-level optimization is to
decompose the overall problem into a sequence of single-level
problems, that are coordinated through a feedback mechanism
in order to yield overall optimality.
The project includes both basic research on the development
of decomposition techniques and research on multi-level
applications.
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Research Model
We consider the assignment problem
XX
f = min
cij xij
i
s.t.
j
X
aj xij ≤ bi ,
∀i
(1)
j
X
xij = 1,
∀j
i
xij = 0/1, ∀i, j
There are number of decomposition techniques which can be
used to solve the multi-level optimization problem one of
them is Lagrangian relaxation method.
The problem is decomposed using the Lagrangian relaxation
method into a series of knapsack problem which are easier
hard that are solved in a polynomial time.
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Application Of the Study
This study can be used to solve a real life problems in the areas of
routing, scheduling, location and assignment.
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Tack så mycket!
Thank you!
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