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.

scholarly journals Traveling-Salesman-Problem Algorithm Based on Simulated Annealing and Gene-Expression Programming

Information ◽  
2018 ◽  
Vol 10 (1) ◽  
pp. 7 ◽  
Author(s):  
Ai-Hua Zhou ◽  
Li-Peng Zhu ◽  
Bin Hu ◽  
Song Deng ◽  
Yan Song ◽  
...  
Keyword(s):  
Gene Expression ◽  
Simulated Annealing ◽  
Traveling Salesman Problem ◽  
Heuristic Algorithms ◽  
Gene Expression Programming ◽  
Optimal Solution ◽  
Traveling Salesman ◽  
Np Hard Problem ◽  
Convergence Performance ◽  
The Traveling Salesman Problem

The traveling-salesman problem can be regarded as an NP-hard problem. To better solve the best solution, many heuristic algorithms, such as simulated annealing, ant-colony optimization, tabu search, and genetic algorithm, were used. However, these algorithms either are easy to fall into local optimization or have low or poor convergence performance. This paper proposes a new algorithm based on simulated annealing and gene-expression programming to better solve the problem. In the algorithm, we use simulated annealing to increase the diversity of the Gene Expression Programming (GEP) population and improve the ability of global search. The comparative experiments results, using six benchmark instances, show that the proposed algorithm outperforms other well-known heuristic algorithms in terms of the best solution, the worst solution, the running time of the algorithm, the rate of difference between the best solution and the known optimal solution, and the convergent speed of algorithms.

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.

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

2012 ◽  
pp. 342-352
Author(s):  
Gilbert Laporte
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Traveling Salesman Problem ◽  
Vehicle Routing Problem ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Exact Algorithms ◽  
Traveling Salesman ◽  
Routing Problem ◽  
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.

scholarly journals Modeling of transportation logistics processes for the urban environment

2019 ◽  
Vol 91 ◽  
pp. 05021
Author(s):  
Petr Romanov ◽  
Irina Romanova
Keyword(s):  
Traveling Salesman Problem ◽  
Minimum Spanning Tree ◽  
Heuristic Algorithms ◽  
Road Transport ◽  
Traveling Salesman ◽  
Ant Colony Optimization Algorithm ◽  
Software Environment ◽  
Greedy Approach ◽  
Trading Network ◽  
The Traveling Salesman Problem

The article deals with the approach to modeling the road transport movement in large cities (with a population of over 100 thousand people) for the delivery of goods from a large warehouse to stores belonging to a trading network company, with the task of optimizing these movements. The main purposes of this optimization task are: to reduce the transportation time; to conduct a rational distribution of vehicles; to reduce the number of required vehicles involved in these transportations; to reduce operating costs for the maintenance of vehicles. The problem statement and its solution on the basis of heuristic algorithms of the Traveling Salesman Problem are given. The article presents a comparative analysis of the most popular methods for solving the Traveling Salesman Problem (Greedy Approach, Modified Greedy Approach, Minimum Spanning Tree, Monte Carlo Simplification Model, Ant Colony Optimization, Algorithm of Little) on the basis of experimental research and simulation. As a result of the analysis, it is proposed to use the Algorithm of Little for optimizing of road transport movement in the delivery of goods. The article provides an example of solving a specific problem using the developed calculation procedure and a computer program “Traveling Salesman Problem” (developed in Pascal in the software environment Delphi 7).

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.

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