Integer Programming Formulation of Traveling Salesman Problems

1960 ◽  
Vol 7 (4) ◽  
pp. 326-329 ◽  
Author(s):  
C. E. Miller ◽  
A. W. Tucker ◽  
R. A. Zemlin
Keyword(s):  
Integer Programming ◽  
Traveling Salesman ◽  
Programming Formulation ◽  
Traveling Salesman Problems ◽  
Integer Programming Formulation

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.

Mixed Integer Programming Formulation for the Energy-Efficient Train Timetables Problem

2017 ◽  
pp. 65-86
Author(s):  
Rodrigo Alexander Castro Campos ◽  
Sergio Luis Pérez Pérez ◽  
Gualberto Vazquez Casas ◽  
Francisco Javier Zaragoza Martínez
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Energy Efficient ◽  
Mixed Integer ◽  
Programming Formulation ◽  
Integer Programming Formulation
Sign in / Sign up

Export Citation Format

Share Document