TSP with Multiple Time-Windows and Selective Cities

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8197)


We address a special TSP in which the set of cities is partitioned into two subsets: mandatory cities and selective cities. All mandatory cities should be visited once within one of the corresponding predefined multiple time windows. A subset of the selective cities, whose cardinality depends on the tour completion time, should be visited within one of the associated multiple time windows. The objective is to plan a tour, not exceeding a predefined number of days, that minimizes a linear combination of the total traveled distance as well as the total waiting time. We present a mixed integer linear programming (MILP) model for the problem and propose a heuristic approach to solve it. Computational experiments address two real world problems that arise in different practical contexts.


Traveling salesman problem multiple time windows mixed integer linear programming branch-and-bound heuristics 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.CIO and ISAUTLLisboaPortugal
  2. 2.IPMA, Portuguese Institute of the Sea and AtmosphereLisboaPortugal
  3. 3.CIO and DEIO, Faculdade de CiênciasUniversidade de LisboaLisboaPortugal

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