A modified active set algorithm for transportation discrete network design bi-level problem
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Transportation discrete network design problem (DNDP) is about how to modify an existing network of roads and highways in order to improve its total system travel time, and the candidate road building or expansion plan can only be added as a whole. DNDP can be formulated into a bi-level problem with binary variables. An active set algorithm has been proposed to solve the bi-level discrete network design problem, while it made an assumption that the capacity increase and construction cost of each road are based on the number of lanes. This paper considers a more general case when the capacity increase and construction cost are specified for each candidate plan. This paper also uses numerical methods instead of solvers to solve each step, so it provides a more direct understanding and control of the algorithm and running procedure. By analyzing the differences and getting corresponding solving methods, a modified active set algorithm is proposed in the paper. In the implementation of the algorithm and the validation, we use binary numeral system and ternary numeral system to avoid too many layers of loop and save storage space. Numerical experiments show the correctness and efficiency of the proposed modified active set algorithm.
KeywordsDiscrete network design Bi-level problem Binary variable Modified active set algorithm Binary and ternary numeral system
We are grateful to Yafeng Yin for providing the problem and the original active set algorithm, and also the valuable discussions with him. P. M. Pardalos was partially supported by LATNA Laboratory, NRU HSE, RF government grant, ag. 11.G34.31.0057, National Research University Higher School of Economics, Nizhny Novgorod, Russia.
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