Multi-Objective Optimization for Electric Vehicle Charging Infrastructure

This repository contains the codebase and optimization engine for the research paper: "An explainable multi-objective decision-support approach for grid-constrained EV charging infrastructure planning".

It proposes an end-to-end mathematical optimization and explainable machine learning framework for the strategic placement of Public Charging Stations (PCS) at national and regional scales (evaluated using 1,205 candidate sites in India).

---

Overview

Strategic planning of EV charging infrastructure presents a complex multi-objective optimization problem. Siting algorithms must balance user convenience (minimizing detours, maximizing demand coverage) with power grid stability (avoiding transformer/feeder overload) and spatial equity (ensuring fair infrastructure distribution).

This framework solves this problem by:

1. Demand Node Generation: Aggregating raw station and demographic data into representative demand centroids using a weighted K-Means clustering scheme.
2. Multi-Objective Siting: Optimizing station placement under deployment budget ($K=150$) and minimum service coverage constraints ($\theta=85%$) using:
   • Non-dominated Sorting Genetic Algorithm II (NSGA-II) to construct Pareto-optimal trade-off frontiers.
   • A single-objective Genetic Algorithm (GA) with auto-tuned trade-off weights.
3. Distributional Equity Assessment: Measuring spatial fairness of the layout using Gini coefficients and Lorenz curves.
4. Surrogate Explainability (XAI): Training tree-based surrogate classifiers (Random Forest and Gradient Boosted Trees) and applying SHAP (SHapley Additive exPlanations) to identify the causal drivers behind station selection decisions.

Mathematical Formulation

1. Spatial Demand Representation

Given $n$ candidate station locations, demand hotspots are aggregated into $m$ cluster centroids (demand nodes) $D = {1, 2, \dots, m}$. Each node $i \in D$ is assigned a demand weight $w_i > 0$ mapped from local population density, EV registrations, and transport intersections. $$\sum_{i \in D} w_i = 1$$

2. Objectives

A. Detour Distance Minimization $D(x)$ (User Convenience)

Minimizes the average travel detour distance from demand nodes to their nearest selected station using Haversine geodesic distance $d_{i, l}$: $$D(x) = \sum_{i \in D} w_i \cdot \min_{l \in L : x_l = 1} d_{i, l}$$ where $x = (x_1, \dots, x_n)$ is the binary selection vector ($x_l = 1$ if station $l$ is selected, $0$ otherwise).

B. Grid-Stress Penalty Minimization $\Psi(x)$ (Grid Reliability)

Penalizes placing stations in regions with high pre-existing grid stress. For region $j \in \Theta$: $$G_j = \frac{\text{EV charging load in region } j}{\text{installed capacity in region } j}$$ $$\Psi(x) = \sum_{j \in \Theta} G_j \left( \sum_{l \in L_j} x_l \right)$$ where $L_j$ is the set of candidate stations located in region $j$.

3. Multi-Objective Optimization

NSGA-II Formulation

The two competing objectives are optimized directly to generate a Pareto front of non-dominated solutions: $$\min_{x} \quad F(x) = \big( D(x), , \Psi(x) \big)$$ $$\text{subject to } \quad \sum_{l \in L} x_l = K \quad (\text{Cardinality constraint } K = 150)$$ $$\sum_{i \in D} w_i \cdot \mathbb{I}\big(\min_{l \in L : x_l = 1} d_{i,l} \le R\big) \ge \theta \quad (\text{Coverage constraint } \theta = 0.85, , R = 7.0\text{ km})$$

Scalarized Single-Objective GA Formulation

Converts the objectives into a single decision-intelligence cost function using auto-tuned weights $\alpha$ and $\beta$ ($\alpha + \beta = 1$): $$\min_{x} \quad J(x) = \alpha D(x) + \beta \Psi(x) + \lambda_{1} \max\left(0, \theta - \text{coverage}(x)\right)^2 + \lambda_{2} \left|\sum x_l - K\right|$$ where $\lambda_1, \lambda_2$ are large penalty scaling parameters ($10^5$) to discourage constraint violation.

4. Post-Hoc Explainability (Surrogate SHAP Analysis)

To resolve the "black-box" nature of metaheuristic siting, a machine learning surrogate classifier $\hat{f}$ is trained to predict whether a station $l$ is selected ($y_l = 1$) or not based on its spatial and regional characteristics: $$\hat{f}(z_l) = \phi_0 + \sum_{k} \phi_k(z_l)$$ where $z_l$ is the feature vector for candidate station $l$, and $\phi_k(z_l)$ is the SHAP attribution of feature $k$ to the prediction. Features include:

• station_demand_weight: The composite demand index of the station location.
• grid_index: Regional grid-stress $G_j$.
• demand_density: Sum of demand node weights within 50 km.
• min_distance & avg_weighted_distance: Proximity metrics to demand nodes.
• station_density_nearby: Count of existing stations within a 50 km neighborhood.

Key Results & Insights

• Optimized Performance: The GA-based placement reduces demand-weighted detour distance by ~22% and improves service coverage from 69.3% to 81.2% compared to existing configurations under identical deployment budgets ($K=150$).
• Grid Load Mitigation: The optimized layout reduces the grid-stress penalty by approximately 28%, actively diverting capacity additions away from saturated, high-voltage urban zones (e.g., Delhi, which gained only 12 stations out of 149 candidates) toward underserved growth corridors.
• Enhanced Spatial Equity: Lorenz curves demonstrate a significant redistribution of charging access. The state-wise allocation Gini coefficient decreases from 0.602 (existing network) to 0.519 (NSGA-II deployment), corresponding to a 13.8% reduction in spatial inequality.
• Explainable Drivers: Surrogate TreeSHAP analysis shows that accessibility metrics (min_distance and avg_weighted_distance) dominate optimization decisions, accounting for >80% of the surrogate model's explanatory power. Neighborhood density and grid stress act as secondary constraints to avoid congestion and over-loading.

---

Authors & Acknowledgment

• Mr. Abhigyan Pandey - Rajiv Gandhi Institute of Petroleum Technology (RGIPT), India
• Mr. Harsh Mishra - Rajiv Gandhi Institute of Petroleum Technology (RGIPT), India
• Dr. Akash Yadav - Rajiv Gandhi Institute of Petroleum Technology (RGIPT), India
• Mr. Vivek Raj - Rajiv Gandhi Institute of Petroleum Technology (RGIPT), India
• Mr. Vivek Kumar Thakur - Rajiv Gandhi Institute of Petroleum Technology (RGIPT), India
• Mr. Apurv Gupta - Rajiv Gandhi Institute of Petroleum Technology (RGIPT), India