A branch-and-cut algorithm for the undirected prize collecting traveling salesman problem

Networks ◽  
2009 ◽  
Vol 54 (1) ◽  
pp. 56-67 ◽  
Author(s):  
Jean-François Bérubé ◽  
Michel Gendreau ◽  
Jean-Yves Potvin
Keyword(s):  
Traveling Salesman Problem ◽  
Branch And Cut ◽  
Traveling Salesman ◽  
Prize Collecting

scholarly journals A branch-and-cut and MIP-based heuristics for the Prize-Collecting Travelling Salesman Problem

2020 ◽  
Author(s):  
Glaubos Climaco ◽  
Luidi Simonetti ◽  
Isabel Rosseti
Keyword(s):  
Traveling Salesman Problem ◽  
Travelling Salesman Problem ◽  
Branch And Cut ◽  
Traveling Salesman ◽  
Minimum Amount ◽  
Travelling Salesman ◽  
Travel Costs ◽  
Prize Collecting

The Prize Collecting Traveling Salesman Problem (PCTSP) represents a generalization of the well-known Traveling Salesman Problem. The PCTSP can be associated with a salesman that collects a prize in each visited city and pays a penalty for each unvisited city, with travel costs among the cities. The objective is to minimize the sum of the costs of the tour and penalties, while collecting a minimum amount of prize. This paper suggests MIP-based heuristics and a branch-and-cut algorithm to solve the PCTSP. Experiments were conducted with instances of the literature, and the results of our methods turned out to be quite satisfactory.

scholarly journals The traveling salesman problem with pickup and delivery: polyhedral results and a branch-and-cut algorithm

2008 ◽  
Vol 121 (2) ◽  
pp. 269-305 ◽  
Author(s):  
Irina Dumitrescu ◽  
Stefan Ropke ◽  
Jean-François Cordeau ◽  
Gilbert Laporte
Keyword(s):  
Traveling Salesman Problem ◽  
Branch And Cut ◽  
Traveling Salesman ◽  
Pickup And Delivery ◽  
The Traveling Salesman Problem

scholarly journals Polyhedral results and a branch-and-cut algorithm for the double traveling Salesman problem with multiple stacks

2016 ◽  
Vol 21 ◽  
pp. 25-41 ◽  
Author(s):  
Michele Barbato ◽  
Roland Grappe ◽  
Mathieu Lacroix ◽  
Roberto Wolfler Calvo
Keyword(s):  
Traveling Salesman Problem ◽  
Branch And Cut ◽  
Traveling Salesman
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