Ali Khatami Firoozabadi; Hossein Mohebbi; Mohammad Zarei Mahmoodabadi
Volume 8, Issue 21 , June 2011, , Pages 39-61
Abstract
Shortest-path problem is one of the well-known optimization problems that has been studied by many scientists in recent years. Applications of this problem such as transportation and communication are generally solved by Dijkstra's Algorithm (Labeling). In this paper, two separate scientific fields, ...
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Shortest-path problem is one of the well-known optimization problems that has been studied by many scientists in recent years. Applications of this problem such as transportation and communication are generally solved by Dijkstra's Algorithm (Labeling). In this paper, two separate scientific fields, electronics and operation research have been linked to each other and a new algorithm has been created for to find the optimization solution of a shortest- path problem by using electric networks and rules. The proposed algorithm can solve the shortest-path problem in directed graphs and no order ones, and also can solve the longest path problems in directed graphs.
In this algorithm, electrical network are used in a way that the resistance value of each branch is equal to each edge weights in the shortest-path problems. Then with using Ohm Law and Kirchhaffs Voltage Law (KVL), the current in each circuit cycle is calculated. Then the branches that contain the most passing current are specified, and according to Ohm’s Law, has the lowest resistance or weight. Thus, the shortest path in the network is achieved. Advantage of this algorithm is faster convergence to the answer and less computing time than the conventional method, especially in networks with more nods. The mentioned algorithm has been described for three examples.
S.M. Ali Khatami Fivouzabadi; Mohsen Rahimi; Ali Mohtashami
Volume 5, Issue 14 , December 2006, , Pages 29-54
Abstract
In this paper, we will consider the problem of courses timetabling in a small educational institute. We will present the mathematical model considering six hard constraints (compelling constraints) and five soft constraints (constraints that are lot compelling, but regarding them results increasing the ...
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In this paper, we will consider the problem of courses timetabling in a small educational institute. We will present the mathematical model considering six hard constraints (compelling constraints) and five soft constraints (constraints that are lot compelling, but regarding them results increasing the utility of timetable). To formulating the model we will use a type of goal programming. In this paper we will try to define decision variables, hard constraints, soft constraints and objective function in a step by step direction. Afterward we will test the model on a mathematical example.