A Hierarchical Market Solution to the Min–Max Multiple Depots Vehicle Routing Problem

Kivelevitch, Elad H.; Sharma, Balaji R.; Ernest, Nicholas; Kumar, Manish; Cohen, Kelly

doi:10.1142/s230138501450006x

Cited by 10 publications

(8 citation statements)

References 21 publications

(48 reference statements)

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“…Three conflicting objectives are considered simultaneously: (i) minimization of the distance traveled; (ii) maximization of satisfaction, which models the necessity of covering the targets within given time windows; and (iii) minimization of the number of UAVs. A vehicle routing problem with multiple depots is the model used in [ 18 ]. In the VRP nomenclature, the depot is the place where the vehicles start and finish their tasks.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multi-UAV Routing for Area Coverage and Remote Sensing with Minimum Time

Avellar

Pereira

Pimenta

et al. 2015

Sensors

238

149

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This paper presents a solution for the problem of minimum time coverage of ground areas using a group of unmanned air vehicles (UAVs) equipped with image sensors. The solution is divided into two parts: (i) the task modeling as a graph whose vertices are geographic coordinates determined in such a way that a single UAV would cover the area in minimum time; and (ii) the solution of a mixed integer linear programming problem, formulated according to the graph variables defined in the first part, to route the team of UAVs over the area. The main contribution of the proposed methodology, when compared with the traditional vehicle routing problem’s (VRP) solutions, is the fact that our method solves some practical problems only encountered during the execution of the task with actual UAVs. In this line, one of the main contributions of the paper is that the number of UAVs used to cover the area is automatically selected by solving the optimization problem. The number of UAVs is influenced by the vehicles’ maximum flight time and by the setup time, which is the time needed to prepare and launch a UAV. To illustrate the methodology, the paper presents experimental results obtained with two hand-launched, fixed-wing UAVs.

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Section: Introductionmentioning

confidence: 99%

“…In the VRP nomenclature, the depot is the place where the vehicles start and finish their tasks. The objective in [ 18 ] is the minimization of the longest tour performed by every UAV, which is equivalent to the minimization of the total mission time.…”

Section: Introductionmentioning

confidence: 99%

Multi-UAV Routing for Area Coverage and Remote Sensing with Minimum Time

Avellar

Pereira

Pimenta

et al. 2015

Sensors

238

149

View full text Add to dashboard Cite

show abstract

“…Thus, this objective is especially useful in the circumstances where the cost (distance or time) caused by any salesman is not allowed to exceed a given limit [9,10]. Nevertheless, there are only a few works in the literatures designed exclusively for the minmax MTSP [10,11,12,13,14,15,16]. Generally speaking, a more common practice is to present a general algorithm for both the objectives, which often lacks a specific mechanism to reduce the maximum distance thoroughly [7,17,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

“…Despite of the important academic and engineering values of the minmax MTSP, the research on it is relatively limited and most of the works are related to its applications. To the best of our knowledge, the largest number of cities on the minmax MTSP by far is 575, while the number of that studied most is still under 200 [7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,25]. Additionally, according to the results of [21], the optimal solution of the minmax MTSP can only be found on the instances with n≤10 within 3600s.…”

Section: Introductionmentioning

confidence: 99%

Memetic algorithm based on sequential variable neighborhood descent for the minmax multiple traveling salesman problem

Wang

Chen

Lin

2017

Computers & Industrial Engineering

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In this paper, we consider the multiple traveling salesman problem (MTSP) with the minmax objective, which includes more than one salesman to serve a set of cities while minimizing the maximum distance traveled by any salesman. For this problem, we have proposed a novel memetic algorithm, which integrates with a sequential variable neighborhood descent that is a powerful local search procedure to exhaustively search the areas near the high-quality solutions. However, there are some inefficient neighborhoods in the existing sequential variable neighborhood descent for the minmax MTSP, which could restrict the search performance. Therefore, we have redefined a new neighborhood sequence where only the neighborhoods that move cities from one tour to another unidirectionally are considered. Computational experiments on a wide range of benchmark problems within an acceptable time limit show that compared with six existing algorithms, the proposed algorithm is better than the other algorithms in terms of three aspects, including the precision, the robustness and the convergence speed. Meanwhile, we have also investigated the total distance traveled by all the salesmen when optimizing the minmax objective, and the results show that in comparison with the six existing algorithms, the proposed algorithm has a better or at least competitive capacity to maintain the total distance as short as possible. Furthermore, two kinds of statistical tests are utilized to examine the significance of the presented results, indicating the superiority of the proposed algorithm over the other algorithms on the minmax objective.

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“…The decentralized problem for multiple robots without dynamics is commonly solved using market-based auctions [21][22][23]. When there are an equal number of robots and tasks, the problem is commonly referred to as the assignment problem, which can be solved efficiently [24,25].…”

Section: Introductionmentioning

confidence: 99%

Heterogeneous Task Allocation and Sequencing via Decentralized Large Neighborhood Search

Sadeghi

Smith

2017

Un. Sys.

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This paper focuses on decentralized task allocation and sequencing for multiple heterogeneous robots. Each task is defined as visiting a point in a subset of the robot configuration space -this definition captures a variety of tasks including inspection and servicing. The robots are heterogeneous in that they may be subject to different differential motion constraints. Our approach is to transform the problem into a multi-vehicle generalized traveling salesman problem (GTSP). To solve the GTSP, we propose a novel decentralized implementation of large-neighborhood search (LNS). Our solution approach leverages the GTSP insertion methods proposed in Fischetti et al. [A branchand-cut algorithm for the symmetric generalized traveling salesman problem, Oper. Res. 45(3) (1997) 378-394]. to repeatedly remove and reinsert tasks from each robot path. Decentralization is achieved using combinatorial-auctions between the robots on tasks removed from robot's path. We provide bounds on the length of the dynamically feasible robot paths produced by the insertion methods. We also show that the number of bids in each combinatorial auction, a crucial factor in the runtime, scales linearly with the number of tasks. Finally, we present extensive benchmarking results to characterize both solution quality and runtime, which show improvements over existing decentralized task allocation methods.

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A Hierarchical Market Solution to the Min–Max Multiple Depots Vehicle Routing Problem

Cited by 10 publications

References 21 publications

Multi-UAV Routing for Area Coverage and Remote Sensing with Minimum Time

Multi-UAV Routing for Area Coverage and Remote Sensing with Minimum Time

Memetic algorithm based on sequential variable neighborhood descent for the minmax multiple traveling salesman problem

Heterogeneous Task Allocation and Sequencing via Decentralized Large Neighborhood Search

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