A Comparison of Extended Dijkstra and ACO Algorithm for Shortest Path Problem in Dynamic Networks with Delay Times

Shortest path problem is a typical routing optimization problem that is generally involved with a multi-criteria decision-making process. Therefore, the main objective of this paper is to find the shortest path in discrete-time dynamic networks based on bi-criteria of time and reliability by considering the effect of delay times that varies according to different departure time scenarios. Firstly, the well-known single-criterion Dijkstra’s algorithm is extended to fit the conditions of a bi-criteria problem. The solutions obtained from the extended Dijkstra was then compared with a proposed ant colony optimization (ACO) algorithm via a set of multi-objective performance metrics including CPU time, error ratio, spacing and diversity metrics. The analysis was made based on three network scales ranged from small (20-100 nodes), to medium (500-1900 nodes) and large (2000-10000 nodes). The computational results obtained from the analysis suggested that the extended Dijkstra’s algorithm has a higher efficiency in medium and large scaled networks. Furthermore, the comparison of the proposed ACO versus Dijkstra’s algorithm proved the preference of ACO for networks with larger-scaled (nodes over 5000), while, for smaller and medium-scaled networks (nodes 20-2000), the extended Dijkstra’s algorithm has a dominantly better performance in CPU time as compared to proposed ACO.