A Bi-criterion Steiner Traveling Salesperson Problem with Time Windows for Last-Mile Electric Vehicle Logistics (2409.14848v1)

Abstract: This paper addresses the problem of energy-efficient and safe routing of last-mile electric freight vehicles. With the rising environmental footprint of the transportation sector and the growing popularity of E-Commerce, freight companies are likely to benefit from optimal time-window-feasible tours that minimize energy usage while reducing traffic conflicts at intersections and thereby improving safety. We formulate this problem as a Bi-criterion Steiner Traveling Salesperson Problem with Time Windows (BSTSPTW) with energy consumed and the number of left turns at intersections as the two objectives while also considering regenerative braking capabilities. We first discuss an exact mixed-integer programming model with scalarization to enumerate points on the efficiency frontier for small instances. For larger networks, we develop an efficient local search-based heuristic, which uses several operators to intensify and diversify the search process. We demonstrate the utility of the proposed methods using benchmark data and real-world instances from Amazon delivery routes in Austin, US. Comparisons with state-of-the-art solvers shows that our heuristics can generate near-optimal solutions within reasonable time budgets, effectively balancing energy efficiency and safety under practical delivery constraints.

• The paper presents a novel dual-objective model for EV last-mile delivery that minimizes energy consumption and left-turn frequency.
• It employs a mixed integer programming formulation for smaller networks and a local search heuristic for larger, time-constrained instances.
• Benchmark tests on Amazon routes demonstrate the method’s ability to generate 66 diverse optimal tours, promising sustainable urban logistics.

Overview of "A Bi-criterion Steiner Traveling Salesperson Problem with Time Windows for Last-Mile Electric Vehicle Logistics"

This paper addresses the problem of optimizing last-mile delivery routes for electric freight vehicles (EVs), focusing on two primary objectives: minimizing energy consumption and reducing the number of left turns at intersections. This dual-objective optimization, known as the Bi-criterion Steiner Traveling Salesperson Problem with Time Windows (BSTSPTW), is particularly relevant in the context of E-commerce's rapid growth and the need to reduce the transportation sector's environmental impact.

Problem Formulation

The authors formulate the BSTSPTW by considering the two objectives of energy efficiency and safety, specifically targeting the reduction of left turns. The problem is modeled as a variant of the well-known Traveling Salesperson Problem (TSP), specifically the Steiner TSP where only a subset of nodes (terminals) need to be visited, combined with time window constraints. This model also incorporates the regenerative braking capabilities of EVs, which allows for energy recovery on certain road segments.

Methodology

The authors propose two approaches to solve the BSTSPTW:

1. Mixed Integer Programming (MIP): The MIP formulation is designed for smaller instances of the problem. It employs scalarization to generate points on the efficiency frontier, capturing Pareto-optimal solutions. The MIP model incorporates decision variables that allow for potential node and edge revisits, essential for finding optimal routes in complex networks. This formulation addresses the time window constraints and utilizes an exact solver to explore the solution space methodically.
2. Local Search Heuristics: Given the computational challenges of scaling the MIP approach to larger networks, the authors develop an efficient local search-based heuristic. This method uses several operators, including S3Opt, S3OptTW, RepairTW, FixedPerm, Quad, and RandPermute, to explore the solution space. These operators help in both intensifying the search and diversifying it to escape local optima. The initial solution generation employs a scalarization technique combined with state-of-the-art solvers like Lin-Kernighan-Helsgaun (LKH) to bootstrap the heuristic procedure.

Performance Evaluation

The proposed methods are evaluated using benchmark datasets and real-world instances from Amazon delivery routes in Austin, USA. The MIP approach provides exact solutions for smaller networks, while the local search heuristic effectively balances energy efficiency and safety under practical delivery constraints for larger networks.

• Benchmark Results: The local search heuristic often outperforms the MIP approach in terms of the number of Pareto-optimal solutions found. This is particularly evident when the proportion of nodes designated as terminals increases or when allowing multiple revisits to nodes.
• Real-world Application: The heuristic is applied to 87 routes from the Amazon dataset, demonstrating its capability to generate around 66 diverse tours within a two-hour computational budget. This diverse set of optimal routes offers practical flexibility for drivers and logistics managers.

Implications and Future Directions

The BSTSPTW model and its solutions have significant implications for urban logistics and sustainable transportation. By efficiently minimizing energy consumption and enhancing safety, freight companies can reduce their carbon footprint and operational costs.

The research opens several avenues for further exploration:

• Incorporation of More Realistic Constraints: Future work could include factors such as load-dependent energy consumption, the impact of traffic density, and charging station availability.
• Multi-depot and Fleet Heterogeneity: Extending the model to multi-depot scenarios and heterogeneous fleets could provide more comprehensive solutions to complex logistics problems.
• Adaptive and Real-time Routing: The developed methods could be integrated with real-time data for dynamic routing adjustments, further enhancing efficiency and robustness.

In summary, this paper makes substantial contributions to the optimization of last-mile EV logistics by addressing the dual objectives of energy efficiency and safety. The proposed MIP formulation and local search heuristics effectively generate optimal and near-optimal solutions, providing valuable insights and tools for sustainable urban freight transportation.