As the transportation landscape evolves, autonomous shared electric vehicles (SAEVs) have emerged as a pivotal solution for sustainable urban mobility. This research addresses the dynamic operation of SAEVs by integrating ridesplitting and relay strategies, aiming to enhance operational efficiency and profitability. The following narrative unfolds the methodological framework, modeling approaches, and empirical insights from a first-person perspective, emphasizing the role of SAEVs in reshaping urban transportation systems.
Abstract
My investigation centers on optimizing SAEV operations by combining ridesplitting and relay tactics. Traditional single-ride models suffer from low vehicle utilization and limited economic benefits, prompting the need for a more adaptive framework. I propose a four-dimensional (time, space, battery level, passenger count) spatiotemporal network model, simplified to three dimensions through arc merging, and formulate a pure integer linear programming model to maximize operational profit. Using a rolling horizon optimization approach with GUROBI, I demonstrate that the integrated strategy boosts profits by 11.60% and 13.85% under uniform and non-uniform demand distributions, respectively, compared to single-ride models.
1. Introduction
1.1 The Promise of SAEVs
SAEVs represent a transformative force in urban transport, blending clean energy with shared mobility. My interest in this domain stems from their potential to mitigate traffic congestion, reduce carbon emissions, and enhance resource utilization. For instance, Baidu’s “Luobo Kuaipao” exemplifies how SAEVs can operationalize these benefits in real-world scenarios .
However, two critical challenges hinder SAEV scalability:
- Battery Constraints: Frequent charging demands conflict with continuous service, risking order abandonment due to limited range .
- Low Utilization: Traditional single-ride models fail to exploit vehicle capacity, leading to suboptimal profit margins .
1.2 Literature Gap
Reviewing existing studies, I noticed a pronounced gap: most research focuses on single-ride operations for human-driven vehicles, neglecting the synergistic potential of ridesplitting and relay in SAEVs. While works like [3-5] explore ridesplitting in two-dimensional networks, and [6-8] address relay in static models, none integrate these strategies dynamically for SAEVs. This motivated my pursuit of a unified framework.
2. Problem Description
2.1 Operational Scenario
My model envisions an SAEV system operating in a partitioned urban area, where each partition (site) \(i \in I\) is a 泰森多边形 (Voronoi diagram) node. Time is discretized into intervals \(t \in T\), battery levels into discrete layers \(l \in L\), and passenger counts into \(n \in N\) (up to \(n_{max}\)). This forms a four-dimensional network \(G=(V, \xi)\), where nodes \(v=(i, t, l, n)\) represent vehicle states, and arcs \(e=(i, t, l, n, j, t’, l’, n’)\) denote transitions .
Key operational dynamics include:
- Ridesplitting: Merging multiple single orders to a common destination into one trip.
- Relay: Transferring passengers from a low-battery vehicle to a high-battery one at a relay site to overcome range limitations .
- Safety Constraints: Vehicles must retain at least a safety battery level \(l_s\) post-service .
2.2 Network Topology
The four-dimensional network captures:
- Onboarding/Offboarding Arcs: State changes during passenger pickup/delivery.
- Movement Arcs: Travel between sites, consuming time \(TE_{i,j}\) and battery \(BE_{i,j}\).
- Charging Arcs: Battery replenishment at sites, limited by parking spots \(PA_{i,t}\).
- Relay Arcs: Two-stage transfers via relay sites, requiring coordination between vehicles .
3. Optimization Modeling
3.1 Network Reconstruction
The four-dimensional network’s exponential complexity necessitates simplification. By leveraging the fact that vehicles are empty before pickup and after delivery (\(n=0\)), I merge arcs to form a three-dimensional (time, space, battery) network \(G=(O, \varsigma)\). Key merges include:
- Direct Ride Arc \(s^{(z)}\): Chains onboarding, movement, and offboarding for n passengers:\(s^{(z)} = (i, t, l, j, t + 2n\Delta t + TE_{i,j}, l – 2n\Delta l – BE_{i,j})\)
- Relay Arc w: Two-stage direct rides via a relay site k:\(w = \left( (i, t, l, k, t + n\Delta t + TE_{i,k}, l – n\Delta l – BE_{i,k}), (k, t + n\Delta t + TE_{i,k}, q, j, t + 2n\Delta t + TE_{i,k} + TE_{k,j}, q – n\Delta l – BE_{k,j}) \right)\) This reduction significantly cuts model complexity while preserving operational fidelity .
3.2 Mathematical Formulation
My objective is to maximize operational profit P, balancing revenue from ridesplitting/direct services against charging costs. The model is:
Objective Function:\(\max P = \sum_{n \in N} nP_nP_z \left(\sum_{s \in \varsigma_n(Z)} f_s\right) + \sum_{n \in N} nP_nP_w \left(\sum_{w \in \varsigma_n(W)} f_w\right) – \sum_{e \in \varsigma^{(C)}} P_c f_e\)
Constraints:
- Fleet size limit:\(\sum_{s \in \varsigma^{(SC)}} f_s \leq FS\)
- Parking capacity at site i and time t:\(\sum_{s \in \varsigma_{i,t}^{(S)} \cup \varsigma_{i,t}^{(C)}} f_s \leq PA_{i,t} \quad \forall i \in I, t \in T\)
- Flow balance at node o:\(\sum_{s \in \varsigma_o^{(-)}} f_s = \sum_{s \in \varsigma_o^{(+)}} f_s \quad \forall o \in O\)
- Demand satisfaction limit:\(\sum_{s \in \varsigma_{n,i,j,l}^{(Z)}} nf_s + \sum_{w \in \varsigma_{n,i,j,l}^{(W)}} nf_w \leq D_{i,j,t} \quad \forall i,j \in I, t \in T\)
- Non-negative integer flow:\(f_s \in \mathbb{N} \quad \forall s \in \varsigma\)
Here, \(P_z\) and \(P_w\) are profits per minute for direct and relay rides, \(P_n\) is the ridesplitting discount factor, and \(D_{i,j,t}\) is the demand from i to j at t .
4. Solution Algorithm: Rolling Horizon Optimization
4.1 Framework Design
Given the dynamic nature of SAEV operations, I adopt a rolling horizon approach to adapt to real-time demand fluctuations. The framework features:
- Multiple Time Windows: Shorter windows for relay orders (\(T_w\)) and longer for direct orders (\(T_z\)), due to relay’s higher resource consumption.
- Feasibility Guarantee: Subproblem length \(T_t\) must exceed the longest service time to ensure subsequent window viability .
4.2 Time Window Tuning
Through extensive testing, I determined optimal window lengths:
- Control period \(T_c = 5\) min
- Relay assignment window \(T_w = 5\) min
- Direct assignment window \(T_z = 45\) min
- Subproblem length \(T_t = 90\) min
Table 1 illustrates the impact of window lengths on profit and solution time:
| Direct Window (min) | Subproblem Length (min) | Profit (CNY) | Max Solve Time (s) | Order Fulfillment Rate |
|---|---|---|---|---|
| 30 | 60 | 33,678.20 | 10.3 | 60.00% |
| 30 | 75 | 33,798.68 | 10.99 | 60.50% |
| 30 | 90 | 34,067.34 | 14.59 | 60.59% |
| 45 | 60 | 36,934.73 | 151.06 | 66.47% |
| 45 | 75 | 37,497.03 | 223.64 | 67.46% |
| 45 | 90 | 37,242.28 | 456.81 | 67.04% |
| 60 | 60 | >300 s | – | – |
Table 1: Impact of rolling time window lengths on SAEV operations
5. Case Study: Chengdu Urban Network
5.1 Experimental Setup
I validated the model using Chengdu’s urban network, featuring:
- 30 zones with 600 SAEVs initialized at 70% battery.
- Operational period: 16:00–21:00, discretized into 5-minute intervals.
- Key parameters:
- Average speed: 30 km/h
- Battery capacity: 50 kWh
- Charging rate: 20 kW
- Safety battery level \(l_s = 20\%\)
- Direct ride profit \(P_z = 0.3\) CNY/min
- Relay profit \(P_w = 0.27\) CNY/min .
Two demand scenarios were tested:
- Tidal Demand (Scenario 1): High demand at transport hubs and industrial zones.
- Uniform Demand (Scenario 2): Balanced demand across zones .
5.2 Results and Analysis
Table 2 compares single-ride and integrated strategies:
| Scenario | Order Type | Total Profit (CNY) | Profit Increase | Fulfillment Rate | Relay Rate | Ridesplitting Rate |
|---|---|---|---|---|---|---|
| 1 | Single Ride | 33,011.20 | – | 58.47% | 0% | 0% |
| 1 | Ridesplitting+Relay | 36,840.87 | 11.60% | 66.35% | 11.87% | 18.52% |
| 2 | Single Ride | 33,504.70 | – | 59.86% | 0% | 0% |
| 2 | Ridesplitting+Relay | 38,147.60 | 13.85% | 68.44% | 11.23% | 17.21% |
Table 2: Operational performance under different demand distributions
Key insights from the case study:
- Profit Enhancement: The integrated strategy consistently outperforms single-ride models, with higher gains under non-uniform demand (13.85%) versus uniform (11.60%). This confirms its adaptability to urban traffic patterns .
- Fulfillment Rate: Ridesplitting and relay increase order satisfaction by 8–10%, leveraging vehicle capacity and overcoming battery constraints.
- Relay Efficiency: Relay is most effective when demand exceeds fleet capacity, allowing low-battery vehicles to contribute via 接力 (relay), thus reducing order abandonment .
5.3 Impact of Ridesplitting Capacity
Testing varying passenger limits \(n_{max}\) under different demand pressures (RN) revealed:
- Low Demand (\(RN=0.6\)): Allowing \(n_{max}=3\) slightly boosts fulfillment (70%) but reduces profit due to deeper discounts.
- High Demand (\(RN=1.0\)): Higher \(n_{max}\) significantly improves profit (41,488 CNY at \(n_{max}=3\)) by serving more orders .
Table 3 summarizes these findings:
| \(n_{max}\) | RN | Profit (CNY) | Relay Rate | Ridesplitting Rate | Fulfillment Rate |
|---|---|---|---|---|---|
| 1 | 0.6 | 28,685.87 | 10.35% | 0% | 65.94% |
| 1 | 0.8 | 36,009.14 | 11.46% | 0% | 61.73% |
| 1 | 1.0 | 39,363.82 | 13.24% | 0% | 54.23% |
| 2 | 0.6 | 27,855.12 | 10.13% | 13.46% | 66.48% |
| 2 | 0.8 | 36,840.87 | 11.87% | 18.53% | 66.35% |
| 2 | 1.0 | 40,328.53 | 12.96% | 24.26% | 59.30% |
| 3 | 0.6 | 29,502.62 | 9.95% | 9.85% | 70.00% |
| 3 | 0.8 | 37,615.78 | 10.98% | 14.52% | 67.67% |
| 3 | 1.0 | 41,488.04 | 11.86% | 16.99% | 61.11% |
Table 3: Effect of ridesplitting capacity on SAEV operations
6. Conclusions and Future Directions
6.1 Key Contributions
Through this research, I have demonstrated that:
- Integrating ridesplitting and relay in SAEV operations significantly enhances profitability (11.6–13.85% gain) and order fulfillment (6–10% increase) .
- The four-dimensional spatiotemporal network, simplified to three dimensions, provides an efficient modeling framework for dynamic SAEV scheduling.
- Rolling horizon optimization with adaptive time windows ensures real-time responsiveness, with subproblem solve times under 500 seconds, meeting operational deadlines .
6.2 Future Work
My ongoing research will address:
- Multi-person Orders: Extending the model to handle group bookings and optimize mixed-party ridesplitting.
- V2G Integration: Incorporating vehicle-to-grid capabilities to optimize charging schedules for grid stability and cost reduction.
- Uncertainty Modeling: Developing stochastic frameworks to handle demand prediction errors and traffic congestion variability.