An investigation of Decomposition Methods For Solving Multi-level - - PowerPoint PPT Presentation

An investigation of Decomposition Methods For Solving Multi-level Optimization Problems Uledi Ngulo

Department of Mathematics, University of Dar es Salaam Department of Mathematics, Link¨

• ping University

First Network Meeting for Sida- and ISP-funded PhD Students in Mathematics Stockholm 7–8 March 2017

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My Supervisors

Torbj¨

• rn Larsson

Nils-Hassan Quttineh Egbert Mujuni

Main supervisor Assistant supervisor Assistant supervisor Link¨

• ping University

Link¨

• ping University

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,

• ptimization 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

• f decomposition techniques and research on multi-level

applications.

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Research Model

We consider the assignment problem f = min

• i
• j

cijxij s.t.

• j

ajxij ≤ bi, ∀i

• i

xij = 1, ∀j xij = 0/1, ∀i, j (1) 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 s˚ a mycket! Thank you!

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