Constrained Local Search for Last-Mile Routing

Abstract

Last-mile routing refers to the final step in a supply chain, delivering packages from a depot station to the homes of customers. At the level of a single van driver, the task is a traveling salesman problem. But the choice of route may be constrained by warehouse sorting operations, van-loading processes, driver preferences, and other considerations rather than a straightforward minimization of tour length. We propose a simple and efficient penalty-based local search algorithm for route optimization in the presence of such constraints, adopting a technique developed by Helsgaun to extend the Lin–Kernighan–Helsgaun algorithm for the traveling salesman problem to general vehicle routing problems. We apply his technique to handle combinations of constraints obtained from an analysis of historical routing data, enforcing properties that are desired in high-quality solutions. Our code is available under the open-source Massachusetts Institute of Technology license. An earlier version of the code received the $100,000 top prize in the Amazon Last Mile Routing Research Challenge organized in 2021.

Adaptive Composite Online Optimization: Predictions in Static and Dynamic Environments

“…Another piece of information in the dataset is that time window targets for package delivery are included for a subset of the stops. As observed by some contestants of the challenge (e.g., [Arslan and Abay, 2021;Cook et al, 2022]), these constraints are often trivially satisfied, and ignoring them altogether had minimal impact on their final score. Therefore, time windows are ignored in our approach.…”

“…Wu et al [2022] uses a sequential probability model to encode the drivers' behavior and uses a policy iteration method to sample zone sequences from the learned probability model. The model that won the Amazon Challenge [Cook et al, 2022] is based on a constrained local search method. In this approach, given a new delivery request, they extract precedence and clustering constraints by analyzing similar historical human routes in the training dataset.…”

Probability estimation and structured output prediction for learning preferences in last mile delivery

“…Routing Research Challenge 1 . The winning approach in this challenge was presented in [12], where the team developed a k-opt local search heuristic. This heuristic considers both the length of the routes and a penalization for constraints not satisfied at each iteration.…”