An integer programming approach for the time-dependent traveling salesman problem with time windows

2017 ◽  
Vol 88 ◽  
pp. 280-289 ◽  
Author(s):  
Agustín Montero ◽  
Isabel Méndez-Díaz ◽  
Juan José Miranda-Bront
Keyword(s):  
Integer Programming ◽  
Traveling Salesman Problem ◽  
Time Windows ◽  
Traveling Salesman ◽  
Time Dependent ◽  
Programming Approach

Dynamic Discretization Discovery for Solving the Time-Dependent Traveling Salesman Problem with Time Windows

2020 ◽  
Vol 54 (3) ◽  
pp. 703-720 ◽  
Author(s):  
Duc Minh Vu ◽  
Mike Hewitt ◽  
Natashia Boland ◽  
Martin Savelsbergh
Keyword(s):  
Integer Programming ◽  
Traveling Salesman Problem ◽  
Time Windows ◽  
Traveling Salesman ◽  
Time Dependent ◽  
Programming Formulation ◽  
Solution Approach ◽  
Integer Programming Formulation ◽  
Time Dependencies ◽  
Time Expanded Network

We present a new solution approach for the time-dependent traveling salesman problem with time windows. This problem considers a salesman who departs from his home, has to visit a number of cities within a predetermined period of time, and then, returns home. The problem allows for travel times that can depend on the time of departure. We consider two objectives for the problem: (1) a makespan objective that seeks to return the salesman to his home as early as possible and (2) a duration objective that seeks to minimize the amount of time that he is away from his home. The solution approach is based on an integer programming formulation of the problem on a time-expanded network, because doing so enables time dependencies to be embedded in the definition of the network. However, because such a time-expanded network (and thus, the integer programming formulation) can rapidly become prohibitively large, the solution approach uses a dynamic discretization discovery framework, which has been effective in other contexts. Our computational results indicate that the solution approach outperforms the best-known methods on benchmark instances and is robust with respect to instance parameters.

Time-dependent asymmetric traveling salesman problem with time windows: Properties and an exact algorithm

2019 ◽  
Vol 261 ◽  
pp. 28-39 ◽  
Author(s):  
Anna Arigliano ◽  
Gianpaolo Ghiani ◽  
Antonio Grieco ◽  
Emanuela Guerriero ◽  
Isaac Plana
Keyword(s):  
Traveling Salesman Problem ◽  
Time Windows ◽  
Exact Algorithm ◽  
Traveling Salesman ◽  
Time Dependent ◽  
Asymmetric Traveling Salesman Problem

scholarly journals An Optimal Algorithm for the Traveling Salesman Problem with Time Windows

1995 ◽  
Vol 43 (2) ◽  
pp. 367-371 ◽  
Author(s):  
Yvan Dumas ◽  
Jacques Desrosiers ◽  
Eric Gelinas ◽  
Marius M. Solomon
Keyword(s):  
Traveling Salesman Problem ◽  
Optimal Algorithm ◽  
Time Windows ◽  
Traveling Salesman ◽  
The Traveling Salesman Problem

scholarly journals Dynamic Shortest Paths Methods for the Time-Dependent TSP

Algorithms ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 21
Author(s):  
Christoph Hansknecht ◽  
Imke Joormann ◽  
Sebastian Stiller
Keyword(s):  
Column Generation ◽  
Traveling Salesman Problem ◽  
Shortest Path ◽  
Valid Inequalities ◽  
Shortest Paths ◽  
Traveling Salesman ◽  
Time Dependent ◽  
Full Generality ◽  
Branching Rule ◽  
The Traveling Salesman Problem

The time-dependent traveling salesman problem (TDTSP) asks for a shortest Hamiltonian tour in a directed graph where (asymmetric) arc-costs depend on the time the arc is entered. With traffic data abundantly available, methods to optimize routes with respect to time-dependent travel times are widely desired. This holds in particular for the traveling salesman problem, which is a corner stone of logistic planning. In this paper, we devise column-generation-based IP methods to solve the TDTSP in full generality, both for arc- and path-based formulations. The algorithmic key is a time-dependent shortest path problem, which arises from the pricing problem of the column generation and is of independent interest—namely, to find paths in a time-expanded graph that are acyclic in the underlying (non-expanded) graph. As this problem is computationally too costly, we price over the set of paths that contain no cycles of length k. In addition, we devise—tailored for the TDTSP—several families of valid inequalities, primal heuristics, a propagation method, and a branching rule. Combining these with the time-dependent shortest path pricing we provide—to our knowledge—the first elaborate method to solve the TDTSP in general and with fully general time-dependence. We also provide for results on complexity and approximability of the TDTSP. In computational experiments on randomly generated instances, we are able to solve the large majority of small instances (20 nodes) to optimality, while closing about two thirds of the remaining gap of the large instances (40 nodes) after one hour of computation.

A Generalized Insertion Heuristic for the Traveling Salesman Problem with Time Windows

1998 ◽  
Vol 46 (3) ◽  
pp. 330-335 ◽  
Author(s):  
Michel Gendreau ◽  
Alain Hertz ◽  
Gilbert Laporte ◽  
Mihnea Stan
Keyword(s):  
Traveling Salesman Problem ◽  
Time Windows ◽  
Traveling Salesman ◽  
The Traveling Salesman Problem ◽  
Insertion Heuristic
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