Chapter 4 The traveling salesman problem

Jünger, Michael; Reinelt, Gerhard; Rinaldi, Giovanni

doi:10.1016/s0927-0507(05)80121-5

Cited by 239 publications

(136 citation statements)

References 93 publications

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“…• The 2-node transformation proposed by Jonker and Volgenant [1983] (see also Jünger et al [1995]). A complete undirected graph with 2n vertices is obtained from the original complete directed one by adding a copy, n + i, of each vertex i ∈ V , and by (i) setting to 0 the cost of the edge {i, n + i} for each vertex i ∈ V , (ii) setting the cost of edge {n + i, j} to c ij + M , for each couple of vertices i, j ∈ V , where M is a sufficiently large positive value, and (iii) setting to +∞ the costs of all the remaining edges.…”

Section: Transformation Of Atsp Instances Into Stsp Instancesmentioning

confidence: 99%

Exact algorithms for different classes of vehicle routing problems

Roberti¹

2012

4OR-Q J Oper Res

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Section: Transformation Of Atsp Instances Into Stsp Instancesmentioning

confidence: 99%

Exact algorithms for different classes of vehicle routing problems

Roberti¹

2012

4OR-Q J Oper Res

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“…The core serves as input of an algorithm, and is iteratively updated until no elements outside of the core can improve the solution. Such an approach has, for example, been successfully applied to the travelling salesman problem (Junger et al 1995), a matching problem (see, e.g., Gerards 1997), the linear assignment problem (Volgenant 1996) and the set-covering problem (Caprara et al 1999). We propose a coreoriented approach which enables us to consider a reduced number of arcs and thus work on sparser subproblems of the original problem.…”

Section: Core-oriented Approachmentioning

confidence: 99%

Models and Algorithms for Single-Depot Vehicle Scheduling

Freling

Wagelmans

Paixão

2001

Transportation Science

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V ehicle scheduling is the process of assigning vehicles to a set of predetermined trips with fixed starting and ending times, while minimizing capital and operating costs. This paper considers modeling, algorithmic, and computational aspects of the polynomially solvable case in which there is a single depot and vehicles are identical. A quasiassignment formulation is reviewed and an alternative asymmetric assignment formulation is given. The main contributions of the paper are a new two-phase approach which is valid in the case of a special cost structure, an auction algorithm for the quasiassignment problem, a core-oriented approach, and an extensive computational study. New algorithms are compared with the most successful algorithms for the vehicle-scheduling problem, using both randomly generated and real-life data. The new algorithms show a significant performance improvement with respect to computation time. Such improvement can, for example, be very important when this particular vehicle-scheduling problem appears as a subproblem in more complex vehicle-and crew-scheduling problems.The single-depot vehicle-scheduling problem (SDVSP) is defined as follows: Given a depot and a set of trips with fixed starting and ending times, and given the travelling times between all pairs of locations, find a feasible minimum-cost schedule such that (1) each trip is assigned to a vehicle, and (2) each vehicle performs a feasible sequence of trips. All the vehicles are supposed to be identical. A schedule for a vehicle is composed of vehicle blocks, where each block is a departure from the depot, the service of a feasible sequence of trips, and the return to the depot. The cost function is usually a combination of vehicle capital (fixed) and operational (variable) cost. The SDVSP is well known to be solvable in polynomial time.Overviews of algorithms and applications for the SDVSP and some of its extensions can be found in Daduna and Paixão (1995) and in Desrosiers et al. (1995). Several network-flow-type algorithms have been proposed for the SDVSP in the literature. In particular, the SDVSP has been formulated as a linear assignment problem, a transportation problem, a minimum-cost flow problem, a quasiassignment problem, and a matching problem. We briefly discuss the most relevant algorithms. Let n be the number of trips to be covered by vehicles. Paixão and Branco (1987) propose an O n 3 quasiassignment algorithm which is specially designed for the SDVSP. Computational results indicate that this approach significantly outperforms approaches based on transportation and linear-assignment models. The quasiassignment algorithm is a modified version of the Hungarian algorithm for the linear assignment problem, including the improvements proposed by Jonker and Volgenant (1986). An extension of this algorithm can also deal with a fixed number of vehicles (see Paixão and Branco 1988). Dell'Amico (1989) (see also Dell'Amico et al. 1993) proposes an O n 3 successive shortest-path algorithm for the SDVSP, which uses the initializ...

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“…Besides the distribution system described in the previous section, the problem is of great importance in such areas as X-ray crystallography [6], job scheduling [5], circuit board drilling [7], DNA mapping [8], etc. Although, the problem is quite easy to state, it is extremely difficult to solve (the TSP belongs to the class of NP-hard problems [9]).…”

Section: Genetic Algorithm For Solving the Tspmentioning

confidence: 99%

FPGA-Based Implementation of Genetic Algorithm for the Traveling Salesman Problem and Its Industrial Application

Skliarova

Ferrari

2002

Developments in Applied Artificial Intelligence

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Abstract.In this paper an adaptive distribution system for manufacturing applications is considered and examined. The system receives a set of various components at a source point and supplies these components to destination points. The objective is to minimize the total distance that has to be traveled. At each destination point some control algorithms have to be activated and each segment of motion between destination points has also to be controlled. The paper suggests a model for such a distribution system based on autonomous sub-algorithms that can further be linked hierarchically. The links are set up during execution time (during motion) with the aid of the results obtained from solving the respective traveling salesman problem (TSP) that gives a proper tour of minimal length. The paper proposes an FPGA-based solution, which integrates a specialized virtual controller implementing hierarchical control algorithms and a hardware realization of genetic algorithm for the TSP.

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Chapter 4 The traveling salesman problem

Cited by 239 publications

References 93 publications

Exact algorithms for different classes of vehicle routing problems

Exact algorithms for different classes of vehicle routing problems

Models and Algorithms for Single-Depot Vehicle Scheduling

FPGA-Based Implementation of Genetic Algorithm for the Traveling Salesman Problem and Its Industrial Application

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