The combination of TOPSIS method and Dijkstra’s algorithm in multi-attribute routing

This paper introduces a new method called multi-attribute Dijkstra that is an extension of Dijkstra to determine the shortest path between two points of a graph while arcs between points, in addition to the distance, have other attributes such as time(distance), cost, emissions, risk and etc. Technique for order preferences by similarity to ideal (TOPSIS) method is used for ranking and selection of the routes which is a method for solving multi-attribute decision making problems (MADM). In this regard, we try to choose appropriate weights for the attributes to consider the right decision to create a balance between the effective elements in route selection. In this paper, the algorithm of Dijkstra and TOPSIS will be reviewed and the proposed method obtained by the combination of these two will also be described. Finally, three examples with different conditions are presented to represent the performance of the model. Then these examples are compared with single-attribute Dijkstra to realize effectiveness of the proposed method. Obviously in solving large-scale examples the approach based on coding in appropriate software.