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¨ oping University First Network Meeting for Sida- and ISP-funded PhD Students in Mathematics Stockholm 7–8 March 2017 1 / 6
My Supervisors Torbj¨ orn Larsson Nils-Hassan Quttineh Egbert Mujuni Main supervisor Assistant supervisor Assistant supervisor Link¨ oping University Link¨ oping University University of Dar es Salaam 2 / 6
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. 3 / 6
Research Model We consider the assignment problem � � f = min c ij x ij i j � s.t. a j x ij ≤ b i , ∀ i (1) j � x ij = 1 , ∀ j i x ij = 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. 4 / 6
Application Of the Study This study can be used to solve a real life problems in the areas of routing, scheduling, location and assignment. 5 / 6
Tack s˚ a mycket! Thank you! 6 / 6
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