Urban transportation, especially bus transportation, is an important sign of development in every city in the world. The average waiting time for passengers at correspondence stations of buses is one of the most important measures of effectiveness of bus transportation. To the best of our knowledge, the studies in the literature are about maximizing the number of synchronizations in those correspondence stations whose objective is to minimize the waiting time in the network. The classical definition of synchronization used in the literature related to a time window. In this work, we introduce a new definition of synchronization of two buses in network zones. Within this context, we present a mathematical formulation of the synchronization bus timetabling problem as a multi-objective program, where we use the new meaning for synchronization of two buses in the network zones. Since the problem is NP-hard, we adapt a multi-agent approach to solve it. Numerical experiments show that after adapting the multi-agent approach using our proposed definition, we obtain high-quality solutions compared to the classical definition.
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