EV Orienteering Problem with V2G

• EVOP-V2G is a routing and energy management framework that merges mobility tasks with bidirectional grid interactions for profit maximization.
• It employs a mixed integer programming model alongside metaheuristics like evolutionary algorithms and large neighborhood search to address complex time, battery, and pricing constraints.
• Empirical findings demonstrate up to a 2x profit increase through coordinated mobility and V2G operations, highlighting its scalability for urban fleets.

The Electric Vehicle Orienteering Problem with Vehicle-to-Grid (EVOP-V2G) refers to the combined challenge of routing electric vehicles (EVs), scheduling their participation in mobility and delivery/ride-hailing tasks, and dynamically optimizing when and where those vehicles charge and discharge (through V2G) to maximize profit while satisfying routing, energy, and system constraints. Unlike traditional orienteering or vehicle routing problems, EVOP-V2G integrates the bidirectional flow of energy between vehicles and the power grid into the routing problem, requiring joint optimization of mobility and energy objectives under complex time, battery, and network constraints.

1. Problem Structure and Key Components

EVOP-V2G is formally defined as a profit-maximization problem for a single EV driver (applicable also to fleet or multi-agent versions), where the vehicle selects a subset of customer service requests (e.g., ride-hailing or delivery orders), manages routes and time windows, and decides when/where to charge or perform V2G discharging at charging stations with dynamic, time-dependent prices. The objective combines service income, energy trading revenue, and costs associated with charging operations, subject to time windows, battery constraints, and both mobility and energy system limits.

Key elements of the formulation:

• Nodes and Actions: Orders (pickup/delivery tasks), charging stations, and V2G (discharge) events are all represented as nodes in the routing/action sequence.
• Dynamic Energy Prices: Both charging (G2V) and discharging (V2G) prices depend on station, location, and time, requiring temporal and spatial awareness in the planning.
• Battery Constraints: The EV cannot deplete its battery below minimum thresholds or exceed capacity, and charging/discharging rates are bounded.
• Time Windows and Scheduling: Orders are only valid within specified windows, and the entire route must respect driver working hour restrictions.
• Profit Function: Maximizes order rewards plus V2G sale income minus charging costs.

This framework captures the essential coupling between trip selection/order sequencing and energy management, distinguishing EVOP-V2G from both standard vehicle routing and earlier energy dispatch models.

2. Mathematical Formulation (MIP Model)

The EVOP-V2G is modeled as a Mixed Integer Programming (MIP) problem, detailed as follows:

Decision variables:

• $x_{ij}$: binary, 1 if traveling directly from node $v_i$ to $v_j$.
• $rc_i^{t_k}$, $dc_i^{t_k}$: binary variables for (dis)charging at station $i$ in time slot $t_k$.
• $\tau_i$: arrival time at node $v_i$; $b_i$: battery level on reaching $v_i$.

Objective function:

$$\max \sum_{v_i \in V_{o}}\sum_{v_j} x_{ij} p_i + \sum_{v_i \in V_{c}}\sum_{t_k} [dc_i^{t_k} P_{i}^{D t_k} - rc_i^{t_k} P_{i}^{C t_k}]$$

where:

• First term: order/service profit (sum over completed customer requests),
• Second term: net V2G revenue at charging stations (revenue from discharging, cost from charging).

Constraints:

• Routing integrity: path from source to sink covers node/arc sequences and ensures proper arrival times at all orders;
• Service and time: each order's time window is strictly enforced;
• Energy management: battery level evolution with travel, task, and (dis)charging;
• Station operations: at most one charging or discharging operation per station/time slot, subject to capacity;
• All variables' logical and operational limits (binaries, non-negativity, bounds).

This MIP can capture both operational and energy profit trade-offs with complete fidelity, but typically becomes intractable for very large instances.

3. Solution Approaches: Metaheuristics and Scalability

Exact MIP solvers find optimal solutions only for small instances due to combinatorial complexity. Two classes of metaheuristic optimization algorithms are implemented for realistic, scalable, near-optimal solution:

Evolutionary Algorithm (EA)

• Maintains a population of candidate order-charging action sequences (chromosomes).
• Employs selection, crossover, and multiple domain-specific mutation operators to evolve superior action sequences over generations.
• Chromosomes encode order selection and (dis)charging actions (variable-length sequences).
• Fitness evaluated as total profit, subject to full route, time, and battery constraints.

Large Neighborhood Search (LNS)

• Starts from a feasible solution, then iteratively destroys (removes a set of actions/orders) and repairs (re-inserts best candidates based on profit, time, and battery constraints).
• Uses multiple, adaptive destroy and repair operators (regret-k, max-profit insertion, cluster- and Shaw-based removal).
• After each repair, a sub-MIP is solved locally for charging/discharging sequence optimization.
• Adaptive Large Neighborhood Search (ALNS) version selects operators based on performance.

Empirical results:

• On small benchmarks: LNS and EA approach MIP-optimal profits.
• On large urban datasets (up to 900 orders/70 stations): LNS outperforms EA in speed and profit, doubling driver profit versus greedy baselines and achieving robust scalability.
• LNS typically converges more quickly and reliably; EA continues to bring value, especially in exploring diverse solution basins.

4. Empirical Findings and System Impact

Driver and Grid Profitability:

• Both EA and LNS metaheuristics can more than double driver profit compared to greedy or naively energy-agnostic baselines.
• V2G activities, under current real-world pricing and charging infrastructure, contribute approximately 20% of driver profit; in scenarios with higher energy prices or reduced ride fares, V2G can dominate, accounting for up to 99% of profit when energy arbitrage is favorable.
• Order pool size, order spatial dispersion, and window flexibility significantly affect achievable profit; denser markets and larger order pools increase both routing and V2G value.

Scalability:

• The proposed algorithms remain tractable for large city-scale problem sizes.
• LNS is especially efficient, capable of handling datasets with over 68,000 orders and dozens of charging stations.

Sensitivity Analysis:

• Greater charging station density and faster charge/discharge rates increase total system profit and the role of V2G.
• Price variability and higher energy market prices shift profit sources from rides/deliveries toward grid services.

5. Integration of Mobility and Energy Services

The EVOP-V2G formulation demonstrates that optimized, bidirectional charging introduces a powerful new lever for both driver profitability and grid resilience:

• For the grid: Efficient driver routing produces valuable load-shifting, peak shaving, and distributed energy storage, especially when drivers’ energy decisions align with grid needs (e.g., discharging during price peaks).
• For drivers: Strategic participation in energy markets, beyond mobility, can supplement or even outstrip ride income as infrastructure and market signals evolve.

A plausible implication is that as charging/discharging rates and price volatility increase, and with wider V2G access, energy arbitrage by ride-hailing/delivery drivers will become an increasingly major component of the urban energy ecosystem.

6. Practical and Future Implications

Key takeaways from the documented research include:

• Optimization algorithms (especially metaheuristics) are essential to operationalize joint routing and V2G scheduling at urban scale.
• The EVOP-V2G framework provides an extensible template for new energy-mobility business models, where vehicles serve as both mobility and grid assets.
• Realizing the full potential of EVOP-V2G in practice will require expanded high-rate V2G infrastructure, dynamic pricing, and real-time data flow among vehicles, platforms, and grid operators.
• This approach lays the foundation for smart, scalable, and profitable EV-based mobility systems that actively support energy grid stability and decarbonization objectives.

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Table: Summary of EVOP-V2G and Solution Approaches

Aspect	Description	Algorithms
Problem	Routing and order/service selection for an EV, with dynamic charging/discharging	MIP (exact), EA, LNS
Objective	Maximize combined profit from customer service and V2G activities (minus energy cost)
Key Constraints	Route/time windows, battery and energy dynamics, charging station/time, pricing
Metaheuristics	EA (population-based), LNS (adaptive destruction/repair with local MIP)
Empirical Impact	Up to 2x profit increase, scalable to thousands of orders/stations
V2G Role	Currently 20% of profit; could dominate in future with favorable rates/infrastructure