Vahid Baradaran; Armaghan Azarikhah
Abstract
The development of a variety of public transportation systems that cover different areas, has made it difficult for passengers and users to choose the type of transportation system and appropriate route between two specified departures. In large cities such as Tehran, a network of public transportation ...
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The development of a variety of public transportation systems that cover different areas, has made it difficult for passengers and users to choose the type of transportation system and appropriate route between two specified departures. In large cities such as Tehran, a network of public transportation systems, called multi-modal systems, are consist of stations as nodes and public transport vehicles intermediate between the two consecutive stations as arcs. Travelers are looking continuously for a way to find the optimal route in complex multi-modal transportation networks to reach their desired destination with minimal cost and confusion. In this paper, a multi-objective programming model with three objective functions has been developed for routing in multi-modal transport systems. The objectives of the proposed model are to minimize the cost, travel time and the number of vehicle types. By examining the validation of models by test issues, two exact and meta-heuristic algorithms (ant colony algorithm) have been developed to solve the proposed model. The results show that problem solving by exact method for networks with more than 15 nodes are non-operating, while the meta-heuristic algorithm provides the same problems with same precision in the exact method but with logical time.
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.
