An ant colony algorithm for solving Bi-criteria network flow problems in dynamic networks

Multi-objective shortest path problem is one of the most important problems in network optimization that seeks for the efficient paths satisfying several conflicting objectives between two nodes of a network. The present study tries to focus on the problem of finding the maximum flow along with the shortest path in a dynamic network that this type of the network is presented in. For solving bi-criteria network problems, a two-phased exact algorithm and an ant colony (ACO) algorithm based on bi-criteria are used, where the two-phased exact algorithm is presented by Abbsi et al. and the bi-criteria ant colony algorithm is presented by Ghoseiri et al. First, the two-phased complete enumeration algorithm was used to generate the non-dominated paths. Then, the efficiency and validation of the solutions generated by both the algorithms are compared. The computational results for 33 random instances showed that, the CPU time of the ACO algorithm has exponential growth comparing to the two-phased complete enumeration algorithm.