scholarly journals Prize Collecting Traveling Salesman Problem with Ridesharing

2020 ◽  
Vol 27 (2) ◽  
pp. 13-29
Author(s):  
Ygor Alcântara de Medeiros ◽  
Marco Cesar Goldbarg ◽  
Elizabeth Ferreira Gouvêa Goldbarg
Keyword(s):  
Vehicle Routing ◽  
Traveling Salesman Problem ◽  
Mathematical Formulation ◽  
Maximum Amount ◽  
Traveling Salesman ◽  
Heuristic Methods ◽  
Travel Costs ◽  
Prize Collecting ◽  
The Cost ◽  
Capacitated Vehicle

The Prize Collecting Traveling Salesman Problem with Ridesharing is a model that joins elements from the Prize Collecting Traveling Salesman and the collaborative transport. The salesman is the driver of a capacitated vehicle and uses a ridesharing system to minimize travel costs. There are a penalty and a bonus associated with each vertex of a graph, G, that represents the problem. There is also a cost associated with each edge of G. The salesman must choose a subset of vertices to be visited so that the total bonus collection is at least a given a parameter. The length of the tour plus the sum of penalties of all vertices not visited is as small as possible. There is a set of persons demanding rides. The ride request consists of a pickup and a drop off location, a maximum travel duration, and the maximum amount the person agrees to pay. The driver shares the cost associated with each arc in the tour with the passengers in the vehicle. Constraints from ride requests, as well as the capacity of the car, must be satisfied. We present a mathematical formulation for the problem investigated in this study and solve it in an optimization tool. We also present three heuristics that hybridize exact and heuristic methods. These algorithms use a decomposition strategy that other enriched vehicle routing problems can utilize.

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.

An algorithm for the capacitated vehicle routing problem for picking application in manual warehouses

2019 ◽  
Author(s):  
Eleonora Bottani ◽  
Giorgia Casella ◽  
Caterina Caccia ◽  
Roberto Montanari
Keyword(s):  
Vehicle Routing ◽  
Traveling Salesman Problem ◽  
Vehicle Routing Problem ◽  
Order Picking ◽  
Traveling Salesman ◽  
Manhattan Distance ◽  
Routing Problem ◽  
Capacitated Vehicle Routing Problem ◽  
Termination Criteria ◽  
Capacitated Vehicle

Given that warehouses play a central role in modern supply chains, this study proposes the application of an algorithm for the capacitated vehicle routing problem (CVRP) based on the two-index vehicle flow formulation developed by Baldacci, Hadjiconstantinou, and Mingozzi (2004) for picking purposes in manual warehouses. The study of Theys et al. (2010) is first used to represent the warehouse using a Steiner traveling salesman problem (TSP). Then, a calculation of the picking tour’s length is obtained applying the Manhattan distance. Finally, the algorithm for the CVRP is solved through a cutting plane with the addition of termination criteria related to the capacity of picker. The study analyzes four different warehouse configurations, processing five picking list each. The analysis is carried out exploiting the commercial software MATLAB®, to determine the solution that minimize distance of the order picking tour. The results obtained in MATLAB® show the effectiveness of the chosen algorithm applied to the context of manual order picking.

scholarly journals The multi-path Traveling Salesman Problem with stochastic travel costs

2014 ◽  
Vol 6 (1) ◽  
pp. 3-23 ◽  
Author(s):  
Roberto Tadei ◽  
Guido Perboli ◽  
Francesca Perfetti
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Travel Costs

scholarly journals Heuristics for Two Depot Heterogeneous Unmanned Vehicle Path Planning to Minimize Maximum Travel Cost

Sensors ◽  
2019 ◽  
Vol 19 (11) ◽  
pp. 2461 ◽  
Author(s):  
Jungyun Bae ◽  
Woojin Chung
Keyword(s):  
Path Planning ◽  
Traveling Salesman Problem ◽  
Target Location ◽  
Travel Cost ◽  
Unmanned Vehicles ◽  
Traveling Salesman ◽  
Planning Problem ◽  
Travel Costs ◽  
Primal Dual ◽  
Multiple Depot

A solution to the multiple depot heterogeneous traveling salesman problem with a min-max objective is in great demand with many potential applications of unmanned vehicles, as it is highly related to a reduction in the job completion time. As an initial idea for solving the min-max multiple depot heterogeneous traveling salesman problem, new heuristics for path planning problem of two heterogeneous unmanned vehicles are proposed in this article. Specifically, a task allocation and routing problem of two (structurally) heterogeneous unmanned vehicles that are located in distinctive depots and a set of targets to visit is considered. The unmanned vehicles, being heterogeneous, have different travel costs that are determined by their motion constraints. The objective is to find a tour for each vehicle such that each target location is visited at least once by one of the vehicles while the maximum travel cost is minimized. Two heuristics based on a primal-dual technique are proposed to solve the cases where the travel costs are symmetric and asymmetric. The computational results of the implementation have shown that the proposed algorithms produce feasible solutions of good quality within relatively short computation times.

The Traveling Salesman Problem, the Vehicle Routing Problem, and Their Impact on Combinatorial Optimization

2010 ◽  
Vol 1 (2) ◽  
pp. 82-92 ◽  
Author(s):  
Gilbert Laporte
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Traveling Salesman Problem ◽  
Vehicle Routing Problem ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem

The Traveling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP) are two of the most popular problems in the field of combinatorial optimization. Due to the study of these two problems, there has been a significant growth in families of exact and heuristic algorithms being used today. The purpose of this paper is to show how their study has fostered developments of the most popular algorithms now applied to the solution of combinatorial optimization problems. These include exact algorithms, classical heuristics and metaheuristics.

Sign in / Sign up

Export Citation Format

Share Document