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

Abstract

This paper introduces a new method called multi-attribute Dijkstra that is an extension of Dijkstra used to determine the shortest path between two points of a graph while arcs between the points, in addition to the distance, have other attributes such as time (distance), cost, emissions, risk, etc. Technique for order preferences by similarity to the ideal (TOPSIS) method is used for ranking and selecting 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 for creating a balance between the effiective 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 the effiectiveness of the proposed method. Obviously, in solving large-scale examples, the approach is based on coding in appropriate software.