WS Network Design Problem with Nonlinear Pricing Solved by Hybrid Algorithm

  • Dušan HrabecEmail author
  • Pavel Popela
  • Jan Roupec
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9921)


The aim of the paper is to introduce a wait-and-see (WS) reformulation of the transportation network design problem with stochastic price-dependent demand. The demand is defined by hyperbolic dependency and its parameters are modeled by random variables. Then, a WS reformulation of the mixed integer nonlinear program (MINLP) is proposed. The obtained separable scenario-based model can be repeatedly solved as a finite set of MINLPs by means of integer programming techniques or some heuristics. However, the authors combine a traditional optimization algorithm and a suitable genetic algorithm to obtain a hybrid algorithm that is modified for the WS case. The implementation of this hybrid algorithm and test results, illustrated with figures, are also discussed in the paper.


Stochastic transportation model Network-design problem Nonlinear pricing Wait-and-see approach Genetic algorithm Hybrid algorithm 



This work was supported by the EEA Programme and Norway Grants, within the institutional cooperation project Nr. NF-CZ07-ICP-4-345-2016.


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© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Faculty of Applied InformaticsTomas Bata UniversityZlínCzech Republic
  2. 2.Faculty of Mechanical EngineeringBrno University of TechnologyBrnoCzech Republic

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