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Design An Efficient Method for Solving Integer Programming by Lagrangian Relaxation
, M.Sc. Thesis Sharif University of Technology ; Eshghi, Kourosh (Supervisor)
Abstract
The subgradient method is one of the most favoriate methods to solve discrete optimization problems. The Easy Implementation and flexibility enbles us to solve a vast types of complicated combinatorial optimization problems. However, the algorithm can be improved by adjusting its parameters and steps.In present research, we present a heuristic structure to modify and improve the algorithm. Then, the proposed algorithm has tested on special classes of discrete optimization problems such as Generealized Assignment and Uncapacitated Warehouse location problems. The results show that the proposed algorithm can improve the efficiency of the classic form of subgradient method.The three main...
An effective optimization algorithm for locally nonconvex lipschitz functions based on mollifier subgradients
, Article Bulletin of the Iranian Mathematical Society ; Volume 37, Issue 1 , 2011 , Pages 171-198 ; 10186301 (ISSN) ; Yousefpour, R ; Sharif University of Technology
Abstract
We present an effective algorithm for minimization of locally nonconvex Lipschitz functions based on mollifier functions approximating the Clarke generalized gradient. To this aim, first we approximate the Clarke generalized gradient by mollifier subgradients. To construct this approximation, we use a set of averaged functions gradients. Then, we show that the convex hull of this set serves as a good approximation for the Clarke generalized gradient. Using this approximation of the Clarke generalized gradient, we establish an algorithm for minimization of locally Lipschitz functions. Based on mollifier subgradient approximation, we propose a dynamic algorithm for finding a direction...
On the possibility of network scheduling with polynomial complexity and delay
, Article IEEE/ACM Transactions on Networking ; 2017 ; 10636692 (ISSN) ; Golestani, S. J ; Sharif University of Technology
Abstract
Considering the collection of all networks with independent set interference model, Shah, Tse, and Tsitsiklis showed that there exist scheduling algorithms with polynomial complexity and delay, only if the maximum independent set problem can be solved in polynomial time (equivalently, P=NP). In this paper, we extend this result to arbitrary collections of networks and present a clear-cut criterion for the existence of polynomial complexity and delay scheduling algorithms relative to a given collection of networks with arbitrary interference models, not confined to independent set interference or SINR models, and not necessarily encompassing all network topologies. This amounts to the...
Proposing a Solution Algorithm for Operating Room Scheduling Problem Using Open Scheduling and Elective Patient Strategy
, M.Sc. Thesis Sharif University of Technology ; Rafiee, Majid (Supervisor)
Abstract
Operating rooms have always been the most expensive and also the most profitable section in hospitals which include approximately one third of cost and two third of income. The management always wants to decrease the cost of hospitals. On the other hand, usually this goal stands against other goals such as patient’s satisfaction. So the manager should make a balance between these goals. In this research, we will propose an integer programming model for operating room scheduling problem without uncertainty for elective patients. In order to make the model more realistic, we want to make connection between operating room theatre and intensive care units. Also, we will consider desirable...