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Bilevel optimization for the deployment of refuelling stations for electric vehicles on road networks

Ramón Piedra-de-la-Cuadra, Francisco Ortega

TL;DR

Problem: deploy EV charging points along road networks to guarantee reinforced coverage and satisfy demand within a budget. Approach: a bilevel optimization framework with an upper-level coverage objective and a lower-level demand-maximization objective, complemented by a heuristic that decouples CCP and knapsack subproblems; and single-level reformulations via primal–dual (E1) and hierarchy-exchange (E2). Contributions: formalization of reinforced coverage for EV charging with a mixed CCP/knapsack structure, development of a scalable heuristic, and comparative analysis of exact single-level reformulations against the bilevel approach. Significance: demonstrates practical pathways to scale EV charging deployment on real networks, balancing administration-friendly coverage guarantees with private-sector profitability, and provides insights into solver performance on large NP-hard instances.

Abstract

This work consists of a procedure to optimally select, among a group of candidate sites where gas stations were already located, a sufficient number of charging points in order to guarantee that an electric vehicle can make its journey without a problem of energy autonomy and that each selected charging station has another one that serves as useful support in case of failure (reinforced coverage service). For this purpose, we propose a bilevel model that, in a former level, minimizes the number of refuelling points necessary to guarantee a reinforced service coverage for all users who transit from their origin to destination and, as a second level, maximize the volume of demand that can be satisfied subject to budgetary restrictions. With the first of the objectives we are addressing the typical requirement of the administration, which consists of guaranteeing the viability of the solutions, and the second of the objectives is a criterion typically used by the private sector initiative, compatible with the profit maximization.

Bilevel optimization for the deployment of refuelling stations for electric vehicles on road networks

TL;DR

Problem: deploy EV charging points along road networks to guarantee reinforced coverage and satisfy demand within a budget. Approach: a bilevel optimization framework with an upper-level coverage objective and a lower-level demand-maximization objective, complemented by a heuristic that decouples CCP and knapsack subproblems; and single-level reformulations via primal–dual (E1) and hierarchy-exchange (E2). Contributions: formalization of reinforced coverage for EV charging with a mixed CCP/knapsack structure, development of a scalable heuristic, and comparative analysis of exact single-level reformulations against the bilevel approach. Significance: demonstrates practical pathways to scale EV charging deployment on real networks, balancing administration-friendly coverage guarantees with private-sector profitability, and provides insights into solver performance on large NP-hard instances.

Abstract

This work consists of a procedure to optimally select, among a group of candidate sites where gas stations were already located, a sufficient number of charging points in order to guarantee that an electric vehicle can make its journey without a problem of energy autonomy and that each selected charging station has another one that serves as useful support in case of failure (reinforced coverage service). For this purpose, we propose a bilevel model that, in a former level, minimizes the number of refuelling points necessary to guarantee a reinforced service coverage for all users who transit from their origin to destination and, as a second level, maximize the volume of demand that can be satisfied subject to budgetary restrictions. With the first of the objectives we are addressing the typical requirement of the administration, which consists of guaranteeing the viability of the solutions, and the second of the objectives is a criterion typically used by the private sector initiative, compatible with the profit maximization.

Paper Structure

This paper contains 13 sections, 19 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Model development
  4. Input data
  5. Preprocess
  6. Conditional Covering and Knapsack Models
  7. Bilevel optimization model and solution algortihm
  8. Our case study
  9. Others perspectives
  10. Single level reformulation with primal-dual problems
  11. Single level reformulation with exchange in the hierarchy criteria
  12. Computational results
  13. Conclusions

Figures (5)

  • Figure 1: Example of adapted gas station
  • Figure 2: Example of an area with 27 existing gas stations
  • Figure 3: Selected nodes at Step 1 and Step 2.
  • Figure 4: Selected nodes at Step 9.
  • Figure 5: Example of an area with 57 existing gas stations.

Theorems & Definitions (1)

  • Definition 1