A Simulated Annealing for Optimizing Assignment of E-Scooters to Freelance Chargers
Abstract
:1. Introduction
2. Problem Statement and Formulation
2.1. Notation
2.2. Objective Function
2.3. Constraints
3. The SA-Based Assignment Algorithm
- the solution representation
- the neighborhood structure
- the local search method within the neighborhood
- acceptance-reject criteria
Algorithm 1. Procedure of the proposed SA for E-Scooter-Charger Allocation |
|
4. Computational Experiments
4.1. Simulated Instances
- (i)
- Chargers can collect a maximum of six e-scooters; thereby, no competition can occur.
- (ii)
- This proposed algorithm heuristically minimizes the objective function, leading to a reduction in the distance traveled by the chargers.
4.2. Real-World Benchmark Instances
5. Discussion
- How to extend the model in such a way that it is generally applicable based on real data acquired from a large number of places in Australia, including Queensland.
- How to discover a decent (near optimum) solution for major e-scooter operators who may have to address this problem for thousands of e-scooters.
6. Conclusions
- We used a static ESCA approach that does not account for time-variations in the location of e-scooters or chargers.
- Our method assumes that the chargers would accept the assignment solution, which may or may not be the case
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
City | S | R | No. of Selected Chargers | Mean Total Dist. (km) | Std. of Total Dist. | Average Dist. per Charger (km) | Mean (s) | Std. (s) |
---|---|---|---|---|---|---|---|---|
Bari | 13 | 3 | 3 | 17.42 | 0.6925 | 5.81 | 24.2825 | 0.6536 |
4 | 3 | 16.48 | 0.4590 | 5.49 | 26.6802 | 2.8873 | ||
5 | 3 | 16.04 | 0.2366 | 5.35 | 26.4121 | 0.9359 | ||
6 | 3 | 15.89 | 0.2132 | 5.30 | 25.8882 | 0.2477 | ||
Denver | 51 | 10 | 9 | 93.77 | 4.2992 | 10.43 | 7.6649 | 0.0925 |
15 | 9 | 84.85 | 5.6836 | 9.43 | 7.6642 | 0.0688 | ||
20 | 9 | 83.16 | 4.8102 | 9.24 | 7.7522 | 0.1255 | ||
25 | 9 | 77.19 | 4.1236 | 8.57 | 7.7465 | 0.0920 | ||
Rio De Janeiro | 55 | 10 | 10 | 156.03 | 4.2809 | 15.60 | 7.8684 | 0.1018 |
15 | 10 | 130.51 | 4.0688 | 13.05 | 8.4486 | 0.5078 | ||
20 | 10 | 126.63 | 5.8542 | 12.66 | 8.4389 | 0.1110 | ||
25 | 10 | 118.21 | 6.9748 | 11.82 | 9.0633 | 0.1438 | ||
Boston | 59 | 10 | 10 | 149.53 | 1.8104 | 14.95 | 7.9769 | 0.1624 |
15 | 10 | 118.66 | 3.7801 | 11.87 | 8.1854 | 0.1057 | ||
20 | 10 | 107.24 | 3.4410 | 10.72 | 8.7185 | 0.2075 | ||
25 | 10 | 97.59 | 3.1160 | 9.76 | 9.0540 | 0.2089 | ||
Torino | 75 | 15 | 13 | 82.49 | 2.6982 | 6.35 | 9.3305 | 0.5826 |
20 | 13 | 76.46 | 3.6623 | 5.88 | 9.1847 | 0.1975 | ||
25 | 13 | 71.20 | 1.7541 | 5.48 | 9.2049 | 0.1094 | ||
30 | 13 | 70.67 | 1.7714 | 5.44 | 9.8359 | 0.3867 | ||
Toronto | 80 | 15 | 14 | 85.46 | 1.6811 | 6.10 | 10.0570 | 0.3215 |
20 | 14 | 80.92 | 3.1012 | 5.78 | 10.5567 | 0.5761 | ||
25 | 14 | 77.06 | 3.0354 | 5.50 | 11.3008 | 0.6557 | ||
30 | 14 | 74.27 | 4.7503 | 5.30 | 10.6710 | 0.4708 | ||
Miami | 82 | 15 | 14 | 225.59 | 5.4343 | 16.11 | 26.4689 | 1.5830 |
20 | 14 | 159.78 | 4.9159 | 11.41 | 26.2428 | 0.7857 | ||
25 | 14 | 112.97 | 5.3943 | 8.07 | 23.9292 | 1.2262 | ||
30 | 14 | 89.82 | 4.7962 | 6.41 | 19.5331 | 6.9275 | ||
Ciudad De Mexico | 90 | 20 | 15 | 116.93 | 2.9714 | 7.80 | 26.1773 | 3.1219 |
25 | 15 | 101.66 | 1.9904 | 6.78 | 26.5732 | 1.9891 | ||
30 | 15 | 93.97 | 3.0322 | 6.26 | 26.9500 | 1.1487 | ||
35 | 15 | 86.37 | 2.1399 | 5.76 | 27.5016 | 0.5540 | ||
Minneapolis | 116 | 25 | 20 | 265.37 | 4.8507 | 13.27 | 16.0412 | 0.4177 |
30 | 20 | 247.41 | 8.1364 | 12.37 | 16.1741 | 0.3450 | ||
35 | 20 | 239.35 | 8.9119 | 11.97 | 16.2944 | 0.2845 | ||
40 | 20 | 230.90 | 5.2024 | 11.54 | 16.2057 | 0.2166 |
City | S | R | No. of Selected Chargers | Mean Total Distance (km) | Std. of Total Distance | Average Dist. per Charger (km) | Mean (s) | Std. (s) |
---|---|---|---|---|---|---|---|---|
Brisbane | 150 | 30 | 25 | 157.26 | 5.5674 | 6.29 | 70.6994 | 0.7181 |
35 | 25 | 156.90 | 6.5932 | 6.28 | 71.1903 | 0.5602 | ||
40 | 25 | 155.55 | 8.3422 | 6.22 | 71.1579 | 0.2525 | ||
45 | 25 | 150.21 | 4.5519 | 6.01 | 72.2431 | 0.1981 | ||
Milano | 184 | 40 | 31 | 170.24 | 3.7002 | 5.49 | 78.6649 | 0.6661 |
50 | 31 | 168.73 | 5.3349 | 5.44 | 78.9016 | 0.2877 | ||
60 | 31 | 166.53 | 5.0347 | 5.37 | 79.2027 | 0.3343 | ||
70 | 31 | 167.87 | 4.2611 | 5.42 | 79.3685 | 0.5798 | ||
Lille | 200 | 40 | 34 | 404.63 | 12.1092 | 11.90 | 82.1638 | 0.3132 |
50 | 34 | 397.18 | 19.0258 | 11.68 | 82.4724 | 0.4127 | ||
60 | 34 | 334.06 | 19.7114 | 9.83 | 82.8899 | 0.2982 | ||
70 | 34 | 280.17 | 20.6407 | 8.24 | 83.8384 | 4.2350 | ||
Toulouse | 240 | 40 | 40 | 320.26 | 8.3525 | 8.01 | 66.9241 | 0.6171 |
50 | 40 | 300.72 | 8.6194 | 7.52 | 69.5375 | 0.5668 | ||
60 | 40 | 291.34 | 10.2889 | 7.28 | 78.2493 | 0.4577 | ||
70 | 40 | 279.78 | 8.8202 | 6.99 | 70.2105 | 0.8201 | ||
Sevilla | 258 | 50 | 43 | 360.48 | 8.5747 | 8.38 | 72.4298 | 2.7409 |
60 | 43 | 324.76 | 12.1106 | 7.55 | 74.1808 | 1.3228 | ||
70 | 43 | 312.89 | 11.3318 | 7.28 | 74.0912 | 1.0718 | ||
80 | 43 | 307.98 | 10.4338 | 7.16 | 73.1707 | 0.3482 | ||
Valencia | 276 | 50 | 46 | 485.54 | 10.1946 | 10.55 | 75.2697 | 5.1969 |
60 | 46 | 439.79 | 9.9710 | 9.56 | 79.2874 | 3.0556 | ||
70 | 46 | 402.61 | 7.9594 | 8.75 | 79.3139 | 1.5698 | ||
80 | 46 | 396.40 | 8.8915 | 8.62 | 81.5518 | 1.4524 | ||
Bruxelles | 304 | 60 | 51 | 486.90 | 16.2957 | 9.55 | 82.0023 | 3.2712 |
70 | 51 | 448.17 | 16.9597 | 8.79 | 84.6469 | 1.9173 | ||
80 | 51 | 439.38 | 14.4431 | 8.62 | 82.4134 | 1.1279 | ||
90 | 51 | 428.26 | 9.7240 | 8.40 | 184.4216 | 55.3400 | ||
Lyon | 336 | 60 | 56 | 589.37 | 12.5426 | 10.52 | 93.4295 | 4.3040 |
70 | 56 | 538.87 | 7.5401 | 9.62 | 97.1009 | 6.8603 | ||
80 | 56 | 508.91 | 10.7859 | 9.09 | 88.6171 | 2.0332 | ||
90 | 56 | 492.42 | 11.8251 | 8.79 | 91.0158 | 1.5686 | ||
Barcelona | 410 | 70 | 69 | 610.01 | 6.0656 | 8.84 | 101.2063 | 2.7764 |
80 | 69 | 548.78 | 9.6474 | 7.95 | 102.5639 | 2.8394 | ||
90 | 69 | 510.66 | 8.1314 | 7.40 | 103.1610 | 1.9283 | ||
100 | 69 | 491.63 | 12.9522 | 7.13 | 103.7572 | 1.4365 |
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The Baseline | SA | |||||
---|---|---|---|---|---|---|
No. of Chargers | Mean (km) | Std (km) | Mean (km) | Std (km) | p-Value | |
20 | 213.58 | 66.08 | 82.68 | 4.51 | 0.61 | |
30 | 307.68 | 115.97 | 69.20 | 4.15 | 0.78 | |
40 | 301.04 | 86.06 | 68.03 | 3.85 | 0.77 | |
50 | 322.01 | 110.85 | 67.17 | 4.45 | 0.79 |
The Baseline | MILP (Optimal) | ACA | BHO | SA | |
---|---|---|---|---|---|
# of Chargers | Total Dis. | Total Dis. | Total Dis. | Total Distance | Total Distance |
20 | 213.58 | 76.7 | 98.2 | 131.9 | 82.68 |
30 | 307.68 | 65.6 | 85.9 | 122.6 | 69.20 |
40 | 301.04 | 61.4 | 81.0 | 129.7 | 68.03 |
50 | 322.01 | 60.4 | 79.3 | 130.1 | 67.17 |
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Masoud, M.; Elhenawy, M.; Liu, S.Q.; Almannaa, M.; Glaser, S.; Alhajyaseen, W. A Simulated Annealing for Optimizing Assignment of E-Scooters to Freelance Chargers. Sustainability 2023, 15, 1869. https://doi.org/10.3390/su15031869
Masoud M, Elhenawy M, Liu SQ, Almannaa M, Glaser S, Alhajyaseen W. A Simulated Annealing for Optimizing Assignment of E-Scooters to Freelance Chargers. Sustainability. 2023; 15(3):1869. https://doi.org/10.3390/su15031869
Chicago/Turabian StyleMasoud, Mahmoud, Mohammed Elhenawy, Shi Qiang Liu, Mohammed Almannaa, Sebastien Glaser, and Wael Alhajyaseen. 2023. "A Simulated Annealing for Optimizing Assignment of E-Scooters to Freelance Chargers" Sustainability 15, no. 3: 1869. https://doi.org/10.3390/su15031869
APA StyleMasoud, M., Elhenawy, M., Liu, S. Q., Almannaa, M., Glaser, S., & Alhajyaseen, W. (2023). A Simulated Annealing for Optimizing Assignment of E-Scooters to Freelance Chargers. Sustainability, 15(3), 1869. https://doi.org/10.3390/su15031869