Abstract
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.
Highlights
E step is to plan the rolling stock and the crews. e final component of the planning process is the dispatching strategy
Well-known benchmark instances for this problem have been available for decades, the state of the art lacks optimal solutions for these instances. e 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
E main contribution of this paper is that, for the first time, all these benchmark instances for the uncapacitated line planning problem with integrated passenger routing are solved to optimality. e amount of lines necessary to offer each passenger a direct connection along his/her shortest path between origin and destination is determined for the first time
Summary
E step is to plan the rolling stock and the crews. e final component of the planning process is the dispatching strategy. E main contribution of this paper is that, for the first time, all these benchmark instances for the uncapacitated line planning problem with integrated passenger routing are solved to optimality. 4. Methodology is section starts with a detailed discussion of a number of essential concepts and components implemented in our algorithm to optimally solve the uncapacitated line planning problem with integrated passenger routing.
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