Dock-based bike-sharing systems exhibit spatial imbalances between bicycle supply and user demand, often addressed through overnight truck-based rebalancing. This work studies static overnight rebalancing under demand uncertainty modeled as a tri-objective optimization problem. The objectives minimize total travel distance, expected unmet demand, and a robustness-oriented unmet demand measure over high-demand scenarios. Route plans are evaluated via a recourse simulation that enforces truck loads and station capacity constraints across multiple demand realizations. The robustness objective supports selecting plans that reduce peak-demand service degradation. Trade-off solutions are approximated with Non-dominated Sorting Genetic Algorithm II using a permutation--partition encoding and domain-specific relocation operators, including a biased best-improvement move for station relocation. Experiments on the real Barcelona Bicing system with 460 stations show well-distributed Pareto sets and substantial contributions to the reference non-dominated set. Greedy constructive baselines mainly yield extreme solutions and are often dominated.
Figures & tables
Figure 1. Example of solution encoding of a scenario with 9 stations and 3 trucks.
Figure 2. Diagram showing the operation of the AB2 operator. The red arrows indicate the step sequence.
Figure 3. BB1-MAX operator diagram. The red arrows indicate the step sequence.
Figure 4. Diagram of the Station Rebalancing using Roulette-Wheel Selection operator (BB2-MIN/MAX).
Figure 5. Instance map: the red points are the bike-shared stations and the blue is the depot.
Parameter
Domain
Crossover on R ( CR )
OX, PMX, ERX, EERX
Mutation on R ( MR )
IM, BMM, BSM, SM
Probability of mutation R ( PMR )
{0.01, 0.05, 0.1, 0.15, 0.20, 0.25}
Probability of crossover R ( PCR )
{0.1, 0.25, 0.5, 0.7, 0.9, 1}
Probability of mutation t ( PMT )
{0.01, 0.05, 0.1, 0.15, 0.20, 0.25}
Table 1. Candidates for the hyperparameters
Operator
CR
MR
PMR
PCR
PMT
AB2
PMX
SM
0.25
0.1
0.15
BB1-MIN
PMX
SM
0.25
0.1
0.20
BB1-MAX
PMX
BSM
0.01
0.1
0.25
BB2-MAX
PMX
SM
0.20
0.1
0.25
BB2-MIN
PMX
SM
0.20
0.1
0.15
Table 2. Parameter configurations for each operator.
Min
Median
IQR
Max
AB2
0.445
0.504
0.035
0.533
BB1-MAX
0.620
0.750
0.054
0.851
BB1-MIN
0.360
0.438
0.044
0.530
BB2-MAX
0.388
0.503
0.040
0.551
BB2-MIN
0.382
0.467
0.039
0.541
Table 3. Results of rhv for the studied instance.
IGD+
GD+
Min
Med
IQR
Max
Min
Med
IQR
Max
AB2
0.156
0.181
0.014
0.210
0.110
0.141
0.029
0.186
BB1-MAX
0.043
0.065
0.009
0.093
0.062
0.078
0.006
0.102
BB1-MIN
0.179
0.217
0.027
0.252
0.114
0.159
0.025
0.200
BB2-MAX
0.144
0.176
0.016
0.208
0.116
0.151
0.027
0.183
BB2-MIN
0.168
0.203
0.023
0.249
0.106
0.152
0.029
0.199
Table 4. Results for IGD+ and GD+ metrics.
Spread
#NDS
Min
Med
IQR
Max
Min
Med
IQR
Max
AB2
5.074
5.680
0.481
6.142
194
198
2.25
200
BB1-MAX
2.247
2.576
0.456
4.126
188
199
2.00
200
BB1-MIN
5.583
6.462
0.390
6.991
192
198
2.00
200
BB2-MAX
4.911
5.348
0.346
5.904
190
198
1.25
200
BB2-MIN
5.121
5.981
0.480
6.642
190
198
2.00
200
Table 5. Results for Spread and #NDS metrics.
Figure 6. Three-dimensional Pareto front obtained by the different mutation operators.
Figure 7. 2D front projection: distance vs. critical unmet demand.
rhv
gd+
igd+
spread
#nds
BB1-MAX
0.975
0.004
0.007
1.241
36
BB1-MIN
0.681
0.092
0.153
1.564
1
BB2-MAX
0.742
0.062
0.111
2.046
3
BB2-MIN
0.696
0.087
0.142
1.699
3
GLOBE_SD
0.402
0.007
0.127
0.414
2
GLOBE_Dist
0.251
0.048
0.180
0.377
0
Table 6. Results of MO metrics.
Figure 8. Two-dimensional Reference Pareto front projection: distance vs. critical unmet demand.
Figure 9. Histogram of the number of bikes needed per station in the non-rebalancing configuration (BASE), compared with the closest to ideal vector in normal and critical cases.
Figure 10. Total distance distribution of the solutions of our approach by number of trucks.
Figure 11. Unmet demand distribution of the solutions of our approach by number of trucks.
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 12. Heatmap of pairwise comparisons based on the rhv metric.
Figure 13. Heatmap of pairwise comparisons based on the gd+ metric.
Figure 14. Heatmap of pairwise comparisons based on the igd+ metric.
Figure 15. Heatmap of pairwise comparisons based on the spread metric.
Figure 16. Heatmap of pairwise comparisons based on the #nds metric.
This paper proposes a fully dynamic Deep Reinforcement Learning (DRL) method for rebalancing dockless bike-sharing systems, overcoming the limitations of periodic, system-wide interventions. We model the service through a graph-based simulator and cast rebalancing as a Markov decision process. A DRL agent routes a single truck in real time, executing localized pick-up, drop-off, and charging actions guided by spatiotemporal criticality scores. Experiments on real-world data show significant reductions in availability failures with a minimal fleet size, while limiting spatial inequality and mobility deserts. Our approach demonstrates the value of learning-based rebalancing for efficient and reliable shared micromobility.
Edoardo Scarpel, Alberto Pettena, Matteo Cederle +3
University of Padua, via Gradenigo 6/B, 35131, Padua, Italy
Urban bike-sharing systems require strategic station expansion to meet growing demand. Traditional allocation approaches rely on explicit demand modelling that may not capture the urban characteristics distinguishing successful stations. This study addresses the need to exploit patterns from existing stations to inform expansion decisions, particularly in data-constrained environments. We present a data-driven framework leveraging existing stations deemed desirable by operational metrics. A hybrid denoising autoencoder (HDAE) learns compressed latent representations from multi-source grid-level features (socio-demographic, built environment, and transport network), with a supervised classification head regularising the embedding space structure. Expansion candidates are selected via greedy allocation with spatial constraints based on latent-space similarity to existing stations. Evaluation on Trondheim's bike-sharing network demonstrates that HDAE embeddings yield more spatially coherent clusters and allocation patterns than raw features. Sensitivity analyses across similarity methods and distance metrics confirm robustness. A consensus-based procedure across multiple parametrisations distils 32 high-confidence extension zones where all parametrisations agree. The results demonstrate how representation learning captures complex patterns that raw features miss, enabling evidence-based expansion planning without explicit demand modelling. The consensus procedure strengthens recommendations by requiring agreement across parametrisations, while framework configurability allows planners to incorporate operational knowledge. The methodology generalises to any location-allocation problem where existing desirable instances inform the selection of new candidates.
Oluwaleke Yusuf, M. Tsaqif Wismadi, Adil Rasheed
Department of Engineering Cybernetics Norwegian University of Science and Technology (NTNU) NO-7491 Trondheim, Norway · Department of Architecture and Planning Norwegian University of Science and Technology (NTNU) NO-7491 Trondheim, Norway
Ride-hailing and autonomous mobility-on-demand operators reposition idle supply before future demand is fully observed. We study a retrieval-calibrated predict-then-optimize approach for this problem: historical demand regimes are matched to the current query block, combined into a calibrated demand prior, and passed to a fleet-balancing controller. The paper makes three contributions. First, we train a leakage-safe similarity gate whose objective penalizes demand error, pickup spatial mismatch, and queue shortage risk rather than retrieval rank alone. Second, we develop a spatial queue-regret decomposition for a stable queueing surrogate, linking demand-field error to wait through queueing sensitivity, allocator sensitivity, and Wasserstein pickup mismatch. Third, we evaluate learned retrieval and external-style rebalancing baselines in a common simulator. In the calibrated-demand gate experiment, across eight New York City scenarios and ten seeds, the spatial gate reduces mean wait to 82.3s, compared with 85.3s for hand-tuned similarity and 85.8s for a distributional-only baseline. In a separate replay-demand controller comparison, a scenario chance-MPC analog and a share-target transportation LP improve on Wen-style rebalancing (92.2s/92.2s vs. 100.1s), a reduced GPR chance-MPC comparator is intermediate at 94.4s, and an oracle MPC diagnostic is 91.3s.