A note on the prize collecting traveling salesman problem

1993 ◽  
Vol 59 (1-3) ◽  
pp. 413-420 ◽  
Author(s):  
Daniel Bienstock ◽  
Michel X. Goemans ◽  
David Simchi-Levi ◽  
David Williamson
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Prize Collecting

scholarly journals The online Prize-Collecting Traveling Salesman Problem

2008 ◽  
Vol 107 (6) ◽  
pp. 199-204 ◽  
Author(s):  
Giorgio Ausiello ◽  
Vincenzo Bonifaci ◽  
Luigi Laura
Keyword(s):  
Traveling Salesman Problem ◽  
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 Traveling Salesman Problem with Optional Bonus Collection, Pickup Time and Passengers

2020 ◽  
Vol 27 (1) ◽  
pp. 62-82
Author(s):  
José Gomes Lopes Filho ◽  
Marco Cesar Goldbarg ◽  
Elizabeth Ferreira Gouvêa Goldbarg ◽  
Vinícius Araújo Petch
Keyword(s):  
Traveling Salesman Problem ◽  
Heuristic Algorithms ◽  
Economic Effect ◽  
Mathematical Formulation ◽  
Traveling Salesman ◽  
Hybrid Routing ◽  
Maximum Value ◽  
Prize Collecting ◽  
The Traveling Salesman Problem ◽  
Specific Amount

This study introduces a variant of the Traveling Salesman Problem, named Traveling Salesman Problem with Optional Bonus Collection, Pickup Time and Passengers (PCVP-BoTc). It is a variant that incorporates elements of the Prize Collecting Traveling Salesman Problem and Ridesharing into the PCV. The objective is to optimize the revenue of the driver, which selectively defines which delivery or collection tasks to perform along the route. The economic effect of the collection is modeled by a bonus. The model can be applied to the solution of hybrid routing systems with route tasks and solidary transport. The driver, while performing the selected tasks, can give rides to persons who share route costs with him. Passengers are protected by restrictions concerning the maximum value they agree to pay for a ride and maximum travel duration. The activity of collecting the bonus in each locality demands a specific amount of time, affects the route duration, and is interconnected with the embarkment of passengers. Two mathematical formulations are presented for the problem and validated by a computational experiment using a solver. We propose four heuristic algorithms; three of them are hybrid metaheuristics. We tested the mathematical formulation implementations for 24 instances and the heuristic algorithms for 48.

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
Sign in / Sign up

Export Citation Format

Share Document