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The Orienteering Problem with Time Windows Applied to Robotic Melon Harvesting

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Abstract

The goal of a melon harvesting robot is to maximize the number of melons it harvests given a progressive speed. Selecting the sequence of melons that yields this maximum is an example of the orienteering problem with time windows. We present a dynamic programming-based algorithm that yields a strictly optimal solution to this problem. In contrast to similar methods, this algorithm utilizes the unique properties of the robotic harvesting task, such as uniform gain per vertex and time windows, to expand domination criteria and quicken the optimal path selection process. We prove that the complexity of this algorithm is linearithmic in the number of melons and can be implemented online if there is a bound on the density. The results of this algorithm are demonstrated to be significantly better than the standard heuristic solution for a wide range of harvesting robot scenarios.

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Notes

  1. The argument of \(x_{ij}^{*}(t)\) is taken relative to the time it commences the traversal. Thus, \(t=0\) when the manipulator begins at melon i and \(t = T_{ij}\) when it concludes at melon j.

  2. We add the suffix \({\vert }_{t}\) to an array’s symbol whenever the event handler’s time t is necessary for defining the array, or another entity based on the array. Thus, A(v) is \( A(v){\vert }_{t}\), as B(P) is \(B(P){\vert }_{t}\).

  3. The degree of a node is the number of arcs incident to the node.

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Acknowledgments

The authors would like to thank the Israeli Ministry of Agriculture and Rural Development and the Irwin and Joan Jacobs Graduate School of the Technion for their partial support of this research.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Technion, 32000, Haifa, Israel

    Moshe Mann, Dror Rubinstein, Rafi Linker & Itzhak Shmulevich

  2. Agricultural Research Organization - the Volcani Center, 50250, Bet Dagan, Israel

    Boaz Zion

Authors
  1. Moshe Mann
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  2. Boaz Zion
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  3. Dror Rubinstein
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  4. Rafi Linker
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  5. Itzhak Shmulevich
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Correspondence to Moshe Mann.

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Mann, M., Zion, B., Rubinstein, D. et al. The Orienteering Problem with Time Windows Applied to Robotic Melon Harvesting. J Optim Theory Appl 168, 246–267 (2016). https://doi.org/10.1007/s10957-015-0767-z

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  • DOI: https://doi.org/10.1007/s10957-015-0767-z

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