The Multiple Steiner TSP with order constraints: complexity and optimization algorithms

Gabrel, Virginie; Mahjoub, Ali Ridha; Taktak, Raouia; Uchôa, Eduardo

doi:10.1007/s00500-020-05043-y

Cited by 7 publications

(6 citation statements)

References 33 publications

(27 reference statements)

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“…As far as the optimization-based solutions are concerned, as in [46], these consist in pre-assigning the subset of nodes to visit to each robot. In particular, they are based on the following steps: i) partition of the set of vertices to visit V s in m sets, which differ for the two baselines, ii) assignment of each of the m subsets to a robot and iii) solution of a single-Steiner TSP problem for each robot.…”

Section: B Comparative Resultsmentioning

confidence: 99%

“…More specifically, 607 by recalling that the TSP is NP-hard [54] and is a special 608 case of the single Steiner TSP in which all the nodes must 609 be served, i.e., V s ≡ V, the NP-hardness of the single Steiner 610 TSP follows [54]. This NP-hardness is thus inherited also by 611 the multiple robots case addressed in this paper [46]. Notably, 612 heuristics like in [35] and [40] could be designed to cope 613 with the NP-hardness of the problem and make the solution 614 computation more affordable.…”

mentioning

confidence: 90%

“…To summarize, as reported above, existing formulations do not provide a viable solution accounting for both points i) and ii), i.e., the simple TSP requires a single robot to visit all the possible locations, the Steiner TSP requires a single robot to visit a subset of locations, the multi TSP requires multiple robots to visit all possible locations, the vehicle routing requires multiple robots with limited capacity to visit all the locations, while the GMDTSP requires multiple robots to visit all clusters, so that at least one node for each cluster is visited by at least one robot. It is worth mentioning that a multi-Steiner TSP is also addressed in [46]. However, a fundamental difference compared to our contribution is that the work in [46] assumes that the set of nodes to serve is preassigned to each robot.…”

mentioning

confidence: 99%

“…It is worth mentioning that a multi-Steiner TSP is also addressed in [46]. However, a fundamental difference compared to our contribution is that the work in [46] assumes that the set of nodes to serve is preassigned to each robot. In contrast, we here aim to determine the optimal set of nodes to assign to each robot as an output of the optimization problem.…”

mentioning

confidence: 99%

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Route Optimization in Precision Agriculture Settings: A Multi-Steiner TSP Formulation

Furchi

Lippi

Carpio

et al. 2023

IEEE Trans. Automat. Sci. Eng.

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In this work, we propose a route planning strategy 1 for heterogeneous mobile robots in Precision Agriculture (PA) 2 settings. Given a set of agricultural tasks to be performed 3 at specific locations, we formulate a multi-Steiner Traveling 4 Salesman Problem (TSP) to define the optimal assignment of 5 these tasks to the robots as well as the respective optimal paths 6 to be followed. The optimality criterion aims to minimize the total 7 time required to execute all the tasks, as well as the cumulative 8 execution times of the robots. Costs for travelling from one 9 location to another, for maneuvering and for executing the task 10 as well as limited energy capacity of the robots are considered. 11 In addition, we propose a sub-optimal formulation to mitigate the 12 computational complexity by leveraging the fact that generally 13 in PA settings only a few locations require agricultural tasks in a 14 certain period of interest compared to all possible locations in the 15 field. A formal analysis of the optimality gap between the optimal 16 and the sub-optimal formulations is provided. The effectiveness 17 of the approach is validated in a simulated orchard where three 18 heterogeneous aerial vehicles perform inspection tasks. 19 Note to Practitioners-This paper aims at providing an efficient 20 solution to PA needs by deploying a team of robots able 21 to perform agricultural tasks at given locations in large-scale 22 orchards. In particular, a novel general optimization problem is 23 proposed that, given a set of mobile and possibly heterogeneous 24 robots and a set of agricultural tasks to carry out, defines the 25 assignment of these tasks to the robots as well as the routes to 26 follow, while minimizing the total and the cumulative execution 27 times of the robots. Existing approaches for route optimization 28 in PA generally involves complete coverage of the field by one 29 or multiple robots and do not account for maneuvering costs 30 with general layouts of the field. We consider costs for travelling 31 from one location to another, for executing the task and for 32 maneuvering without any restriction on the layout of the plants 33 as well as we take into account the limited energy capacity of the 34 robots. We also provide a sub-optimal formulation which reduces 35 the computational burden by relaxing the optimization of the 36 maneuvering costs at the locations where agricultural tasks are 37 Manuscript

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Section: B Comparative Resultsmentioning

confidence: 99%

mentioning

confidence: 90%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Route Optimization in Precision Agriculture Settings: A Multi-Steiner TSP Formulation

Furchi

Lippi

Carpio

et al. 2023

IEEE Trans. Automat. Sci. Eng.

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“…(i.e., such that the distance between joint pairs is minimized) is NP-hard [56]. However, a feasible nonoptimal solution can be obtained through an iterative greedy approach.…”

Section: Joint Placementmentioning

confidence: 99%

Kinegami: Algorithmic Design of Compliant Kinematic Chains From Tubular Origami

et al. 2023

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Origami processes can generate both rigid and compliant structures from the same homogeneous sheet material. In this article, we advance the origami robotics literature by showing that it is possible to construct an arbitrary rigid kinematic chain with prescribed joint compliance from a single tubular sheet. Our "Kinegami" algorithm converts a Denavit-Hartenberg specification into a single-sheet crease pattern for an equivalent serial robot mechanism by composing origami modules from a catalogue. The algorithm arises from the key observation that tubular origami linkage design reduces to a Dubins path planning problem. The automatically generated structural connections and movable joints that realize the specified design can also be endowed with independent user-specified compliance. We apply the Kinegami algorithm to a number of common robot mechanisms and hand-fold their algorithmically generated single-sheet crease patterns into functioning kinematic chains. We believe this is the first completely automated end-to-end system for converting an abstract manipulator specification into a physically realizable origami design that requires no additional human input.

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