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 Focusing on the Golden Ball Metaheuristic: An Extended Study on a Wider Set of Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
E. Osaba ◽  
F. Diaz ◽  
R. Carballedo ◽  
E. Onieva ◽  
A. Perallos
Keyword(s):  
Genetic Algorithms ◽  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
Golden Ball ◽  
The One

Nowadays, the development of new metaheuristics for solving optimization problems is a topic of interest in the scientific community. In the literature, a large number of techniques of this kind can be found. Anyway, there are many recently proposed techniques, such as the artificial bee colony and imperialist competitive algorithm. This paper is focused on one recently published technique, the one called Golden Ball (GB). The GB is a multiple-population metaheuristic based on soccer concepts. Although it was designed to solve combinatorial optimization problems, until now, it has only been tested with two simple routing problems: the traveling salesman problem and the capacitated vehicle routing problem. In this paper, the GB is applied to four different combinatorial optimization problems. Two of them are routing problems, which are more complex than the previously used ones: the asymmetric traveling salesman problem and the vehicle routing problem with backhauls. Additionally, one constraint satisfaction problem (the n-queen problem) and one combinatorial design problem (the one-dimensional bin packing problem) have also been used. The outcomes obtained by GB are compared with the ones got by two different genetic algorithms and two distributed genetic algorithms. Additionally, two statistical tests are conducted to compare these results.

scholarly journals Heuristic Algorithms for Solving the Generalized Vehicle Routing Problem

2011 ◽  
Vol 6 (1) ◽  
pp. 158 ◽  
Author(s):  
Petrică Claudiu Pop ◽  
Ioana Zelina ◽  
Vasile Lupşe ◽  
Corina Pop Sitar ◽  
Camelia Chira
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Routing Problem ◽  
Practical Applications ◽  
Combinatorial Optimization Problems ◽  
The Many ◽  
The Given ◽  
Generalized Vehicle Routing Problem

The vehicle routing problem (VRP) is one of the most famous combinatorial optimization problems and has been intensively studied due to the many practical applications in the field of distribution, collection, logistics, etc. We study a generalization of the VRP called the generalized vehicle routing problem (GVRP) where given a partition of the nodes of the graph into node sets we want to find the optimal routes from the given depot to the number of predefined clusters which include exactly one node from each cluster. The purpose of this paper is to present heuristic algorithms to solve this problem approximately. We present constructive algorithms and local search algorithms for solving the generalized vehicle routing problem.

scholarly journals ОГЛЯД ЗАВДАНЬ МАРШРУТИЗАЦІЇ, ЩО ЗВОДЯТЬСЯ ДО ЗАДАЧІ КОМІВОЯЖЕРА

2020 ◽  
pp. 152-159
Author(s):  
Ольга Борисовна Маций
Keyword(s):  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Information Technologies ◽  
Traveling Salesman ◽  
Routing Problems ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
Np Complete ◽  
Modern Information ◽  
The Traveling Salesman Problem

The solution to the problem of improving the management of the transport process depends not only on the level of modernization of vehicles and the degree of use of modern information technologies, but also on the choice of routes that reduce the cost of transporting goods and passengers. Actual working conditions of vehicles in road networks put forward a number of tasks for optimizing closed routes, which are based on the classic routing problem (VRP - Vehicle Routing Problem).VRP is one of the generalizations of the hard-to-solve traveling salesman problem. The traveling salesman task is NP-complete. It refers to the main tasks of combinatorial optimization and, forming a continuously replenished set of applications and generalizations, remains an urgent research topic. An exact solution to the traveling salesman problem can be found only by reducing the enumeration of the type of branches and boundaries, which are not always applicable in operational planning by vehicle traffic. Therefore, the development of new and improvement of currently known methods for solving routing problems, reducible to the traveling salesman problem, and their software implementation is both a theoretical and practically important problem.The article considers the class of routing problems reducible to the traveling salesman problem. It is shown that optimization tasks for closed routes (routing problems), which are an important part of transport logistics, occupy key positions in the management of the processes of moving goods and passengers with the support of modern information technologies. An obvious feature that combines the considered list of routing problems (the symmetric traveling salesman problem, the problem of packing in containers, the school bus problem) is that they are formulated as generalizations or variants of the NP-complete traveling salesman problem with restrictions that narrow the scope of feasible solutions. The strongest restrictions become insufficient solvability conditions, stimulating interest in the study of combinatorial optimization problems associated with the traveling salesman problem.

VRoptBees

2018 ◽  
Vol 7 (1) ◽  
pp. 32-56
Author(s):  
Thiago A.S. Masutti ◽  
Leandro Nunes de Castro
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Optimization Problems ◽  
The Other ◽  
Vehicle Routing Problems ◽  
Routing Problems ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
Biological Phenomena ◽  
The Traveling Salesman Problem

Combinatorial optimization problems are broadly studied in the literature. On the one hand, their challenging characteristics, such as the constraints and number of potential solutions, inspires their use to test new solution techniques. On the other hand, the practical application of these problems provides support of daily tasks of people and companies. Vehicle routing problems constitute a well-known class of combinatorial optimization problems, from which the Traveling Salesman Problem (TSP) is one of the most elementary ones. TSP corresponds to finding the shortest route that visits all cities within a path returning to the start city. Despite its simplicity, the difficulty in finding its exact solution and its direct application in practical problems in multiple areas make it one of the most studied problems in the literature. Algorithms inspired by biological phenomena are being successfully applied to solve optimization tasks, mainly combinatorial optimization problems. Those inspired by the collective behavior of insects produce good results for solving such problems. This article proposes the VRoptBees, a framework inspired by honeybee behavior to tackle vehicle routing problems. The framework provides a flexible and modular tool to easily build solutions to vehicle routing problems. Together with the framework, two examples of implementation are described, one to solve the TSP and the other to solve the Capacitated Vehicle Routing Problem (CVRP). Tests were conducted with benchmark instances from the literature, showing competitive results.

scholarly journals Sensitive Ants in Solving the Generalized Vehicle Routing Problem

2011 ◽  
Vol 6 (4) ◽  
pp. 731 ◽  
Author(s):  
Camelia-M. Pintea ◽  
Camelia Chira ◽  
Dan Dumitrescu
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Optimization Problems ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
Potential Benefits ◽  
Ant Colony Systems ◽  
Pheromone Trail ◽  
Generalized Vehicle Routing Problem

The idea of sensitivity in ant colony systems has been exploited in hybrid ant-based models with promising results for many combinatorial optimization problems. Heterogeneity is induced in the ant population by endowing individual ants with a certain level of sensitivity to the pheromone trail. The variable pheromone sensitivity within the same population of ants can potentially intensify the search while in the same time inducing diversity for the exploration of the environment. The performance of sensitive ant models is investigated for solving the generalized vehicle routing problem. Numerical results and comparisons are discussed and analysed with a focus on emphasizing any particular aspects and potential benefits related to hybrid ant-based models.

scholarly journals A new efficient transformation of the generalized vehicle routing problem into the classical vehicle routing problem

2011 ◽  
Vol 21 (2) ◽  
pp. 187-198 ◽  
Author(s):  
Petrica Pop ◽  
Corina Pop-Sitar
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Optimization Problems ◽  
Steiner Tree Problem ◽  
Great Effort ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
Generalized Traveling Salesman Problem ◽  
Generalized Vehicle Routing Problem

Classical combinatorial optimization problems can be generalized in a natural way by considering a related problem relative to a given partition of the nodes of the graph into node sets. In the literature one can find generalized problems such as: generalized minimum spanning tree, generalized traveling salesman problem, generalized Steiner tree problem, generalized vehicle routing problem, etc. These generalized problems typically belong to the class of NP-complete problems; they are harder than the classical ones, and nowadays are intensively studied due to their interesting properties and applications in the real world. Because of the complexity of finding the optimal or near-optimal solution in case of the generalized combinatorial optimization problems, great effort has been made, by many researchers, to develop efficient ways of their transformation into classical corresponding variants. We present in this paper an efficient way of transforming the generalized vehicle routing problem into the vehicle routing problem, and a new integer programming formulation of the problem.

scholarly journals Branch and Bound Algorithm for the Traveling Salesman Problem is not a Direct Type Algorithm

2020 ◽  
Vol 27 (1) ◽  
pp. 72-85
Author(s):  
Aleksandr N. Maksimenko
Keyword(s):  
Combinatorial Optimization ◽  
Traveling Salesman Problem ◽  
Branch And Bound ◽  
Optimization Problems ◽  
Clique Number ◽  
Traveling Salesman ◽  
Branch And Bound Algorithm ◽  
Combinatorial Optimization Problems ◽  
Type Algorithm ◽  
The Traveling Salesman Problem

In this paper, we consider the notion of a direct type algorithm introduced by V. A. Bondarenko in 1983. A direct type algorithm is a linear decision tree with some special properties. the concept of a direct type algorithm is determined using the graph of solutions of a combinatorial optimization problem. ‘e vertices of this graph are all feasible solutions of a problem. Two solutions are called adjacent if there are input data for which these and only these solutions are optimal. A key feature of direct type algorithms is that their complexity is bounded from below by the clique number of the solutions graph. In 2015-2018, there were five papers published, the main results of which are estimates of the clique numbers of polyhedron graphs associated with various combinatorial optimization problems. the main motivation in these works is the thesis that the class of direct type algorithms is wide and includes many classical combinatorial algorithms, including the branch and bound algorithm for the traveling salesman problem, proposed by J. D. C. Little, K. G. Murty, D. W. Sweeney, C. Karel in 1963. We show that this algorithm is not a direct type algorithm. Earlier, in 2014, the author of this paper showed that the Hungarian algorithm for the assignment problem is not a direct type algorithm. ‘us, the class of direct type algorithms is not so wide as previously assumed.

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