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The bus line planning problem or transit network design problem with integrated passenger routing is a challenging combinatorial problem. Although well-known benchmark instances for this problem have been available for decades, the state of the art lacks optimal solutions for these instances. The branch and bound algorithm, presented in this paper, introduces three novel concepts to determine these optimal solutions: (1) a new line pool generation method based on dominance, (2) the introduction of essential links, i.e., links which can be determined beforehand and must be present in the optimal solution, and (3) a new network representation based on adding only extra edges. Next to presenting the newly obtained optimal solutions, each of the abovementioned concepts is examined in isolation in the experiments, and it is shown that they contribute significantly to the success of the algorithm.

An Exact Solution Approach for the Bus Line Planning Problem with Integrated Passenger Routing