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An ACO-based heuristic approach for a route and speed optimization problem in home health care with synchronized visits and carbon emissions

Abstract

The growing concern about the influences of anthropogenic pollutions has forced researchers and scholars to study the environmental concerns. This paper addresses a joint daily route and speed optimization problem in home health care (HHC) with the constraints of synchronized visits and carbon emissions. In this work, the aim is to design a reasonable logistics route with the objective of minimizing the carbon emissions, which has a linear relationship with fuel consumption. This goal can reduce environmental pollution while optimizing operating costs for the HHC company. This paper formulated the problem as a mixed-integer programming (MIP) model and used the Gurobi solver to solve the MIP model with a time limit of 1 h. However, the method based on the MIP model is difficult to solve large-scale instances. Therefore, this paper proposed an ant colony optimization (ACO)-based heuristic approach improved by local search for this problem with large-scale instances. The minimal carbon emissions of each route is calculated by a dynamic programming (DM) algorithm. We designed three kinds of experiments to test the proposed approach, including the basic vehicle routing problem with time window (VRPTW), the studied problem with one speed and the studied problem with two speeds. The experimental results highlight the effectiveness and efficiency of the proposed approach.

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Acknowledgements

The first author would thank the China Scholarship Council for the financial support gratefully. (contract No. 201801810122). The current paper is an extension of the work which had been presented at EA 2019 held in Mulhouse, France, October 29–30, 2019, and the same content used in this paper is the comparison benchmark ACO algorithm in Table 7.

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Hongyuan Luo contributed to idea, conceptualization, methodology, software and writing. Mahjoub Dridi contributed to conceptualization, review and editing. Olivier Grunder contributed to conceptualization, validation, review and editing.

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Correspondence to Olivier Grunder.

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Appendices

Appendix

Results for the VRPTW

In order to demonstrate the effectiveness and efficiency of the proposed HACO algorithm, we use the HACO algorithm to solve the classical Solomon VRPTW benchmark instances. Small size problems with 25 customers and large size problems with 100 customers are used as the test instances. For each instance, we run the program for 10 times, and the computing results are presented in the following Tables 11 and 12. It is obvious that the results highlight the effectiveness and efficiency of the proposed HACO algorithm.

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Luo, H., Dridi, M. & Grunder, O. An ACO-based heuristic approach for a route and speed optimization problem in home health care with synchronized visits and carbon emissions. Soft Comput 25, 14673–14696 (2021). https://doi.org/10.1007/s00500-021-06263-6

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Keywords

  • Home health care
  • Synchronized visits
  • Carbon emissions
  • ACO-based heuristic
  • Dynamic programming