Multi-depot Multiple TSP: a polyhedral study and computational results

Benavent, Enrique; Martínez, Antonio

doi:10.1007/s10479-011-1024-y

Cited by 43 publications

(65 citation statements)

References 19 publications

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“…Benavent and Martínez‐Sykora describe one type of an MDRP that is very similar to one of the variants investigated in this article. The authors present the multi‐depot multiple TSP (MDMTSP) and study the related polyhedron, where they show that the path elimination constraints used in their problem are facet‐defining under very mild conditions.…”

Section: Introductionmentioning

confidence: 81%

“…Previous studies describe formulations on undirected graphs using edge variables only, in which the use of binary edge variables automatically excludes two‐node cycles (i.e., cycles with a depot and a client) unless suitable modifications are performed. In particular, use a variable

u_{i j}

, defined as binary for every pair

i, j \in C

to indicate whether the edge

{i, j}

between clients i and j is used in the solution, and defined as {0,1,2} for every pair

d \in D

i \in C

indicating, respectively, whether the edge linking depot d and client i is not used or if it is used once or twice, with the latter case forming a two‐node cycle. The edge variables in can be related with the directed variables

x_{i j}

through the equalities

u_{i j} = x_{i j} + x_{j i}

for every edge

{i, j}

.…”

Section: Routing Problems With Multiple Depotsmentioning

confidence: 99%

See 1 more Smart Citation

New path elimination constraints for multi‐depot routing problems

2017

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Multi‐depot routing problems arise in distribution logistics where a set of vehicles based at several depots are used to serve a number of clients. Most variants of this problem have the basic requirement that the route of each vehicle starts and ends at the same depot. This article describes new inequalities, namely multi‐cut constraints (MCC), which enforce this requirement in mathematical programming formulations of multi‐depot routing problems. The MCCs are exponential in size, and are equivalent to a compact three‐index formulation for the problem in terms of the associated linear programming relaxations. The article describes how a generalization of the MCCs can be obtained, in a similar manner, by using a stronger version of the three‐index formulation. The connection between the compact and the exponential formulations implies a separation procedure based on max‐flow/min‐cut computations, which has reduced complexity in comparison with a previously known set of constraints described for the same purpose. The new inequalities are used in a branch‐and‐cut algorithm. Computational results are presented for instances with up to 300 clients and 60 depots. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(3), 246–261 2017

show abstract

Section: Introductionmentioning

confidence: 81%

u_{i j}

, defined as binary for every pair

i, j \in C

to indicate whether the edge

{i, j}

between clients i and j is used in the solution, and defined as {0,1,2} for every pair

d \in D

i \in C

x_{i j}

through the equalities

u_{i j} = x_{i j} + x_{j i}

for every edge

{i, j}

.…”

Section: Routing Problems With Multiple Depotsmentioning

confidence: 99%

New path elimination constraints for multi‐depot routing problems

2017

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“…The HMDMTSP reduces to the MDMTSP when all the vehicles are homogeneous. Authors in [4] present an exact algorithm to solve the MDMTSP. Another variant of the MDMTSP that has received considerable attention in the literature is the single depot multiple traveling salesman problem, which we abbreviate as MTSP.…”

Section: Related Workmentioning

confidence: 99%

“…The HMDMTSP is a generalization of the multiple depot multiple traveling salesman problem (MDMTSP) which is known to be NP-Hard [4]. We formulate the HMDMTSP as a mixed-integer linear program and develop a branch-andcut algorithm to compute optimal solutions for the same.…”

Section: Introductionmentioning

confidence: 99%

An exact algorithm for a heterogeneous, multiple depot, multiple traveling salesman problem

Sundar

Rathinam

2015

2015 International Conference on Unmanned Aircraft Systems (ICUAS)

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Unmanned aerial vehicles are being used in several monitoring applications to collect data from a set of targets. These vehicles are heterogeneous in the sense that they can differ either in their motion constraints or sensing capabilities. Furthermore, not all vehicles may be able to visit a given target because vehicles may occasionally be equipped with disparate sensors due to the respective payload restrictions. This article addresses a problem where a group of heterogeneous vehicles located at distinct depots visit a set of targets. The targets are partitioned into disjoint subsets: targets to be visited by specific vehicles and targets that any of the vehicles can visit. The objective is to find an optimal tour for each vehicle starting at its respective depot such that each target is visited at least once by some vehicle, the vehicle-target constraints are satisfied and the sum of the costs of the tours for all the vehicles is minimized. We formulate the problem as a mixed-integer linear program and develop a branch-and-cut algorithm to compute an optimal solution to the problem. Computational results show that optimal solutions for problems involving 100 targets and 5 vehicles can be obtained within 300 seconds on average, further corroborating the effectiveness of the proposed approach.

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“…However, in the optimization problem we are dealing with, the objective is to minimize the maximum tour length which makes traditional mTSP a little bit different from our problem. In addition in traditional mTSP, all the salesmen start from the same city and come back to that city, but in our problem the salesmen are allowed to depart from any city (approximately similar to multi-depot mTSP [8]). These differences can be included in any algorithm that may be used to solve mTSP problem.…”

Section: B Multi-channel Scenariomentioning

confidence: 99%

Dynamic multi-channel packet scheduling in an underwater acoustic sensor network

Ramezani

Leus

2013

2013 Asilomar Conference on Signals, Systems and Computers

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Abstract-This article considers the broadcasting task in an underwater acoustic sensor network when a few sensor nodes want to transmit their packets to the nodes within their communication range in a collision-free manner. Here, the information about sensor nodes' position and their maximum communication range has been used to minimize the broadcasting time. We have shown that the concept of dynamic channel splitting (multichannel communications with variable number of channels) has a great impact on the reduction of the broadcasting time. Furthermore, it is shown that in a single hop network, the broadcasting time minimization can be modeled as the multidepot multiple traveling salesman problem which can be solved sub-optimally through many optimization tools such as Genetic algorithm, and other heuristic methods.

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Multi-depot Multiple TSP: a polyhedral study and computational results

Cited by 43 publications

References 19 publications

New path elimination constraints for multi‐depot routing problems

New path elimination constraints for multi‐depot routing problems

An exact algorithm for a heterogeneous, multiple depot, multiple traveling salesman problem

Dynamic multi-channel packet scheduling in an underwater acoustic sensor network

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