Pickup & Delivery with Time Windows and Transfers: combining decomposition with metaheuristics

TL;DR

This paper advances the Pickup and Delivery Problem with time windows and vehicle transfers by introducing a novel LBBD method and an adaptable LNS algorithm, significantly improving solution quality and scalability for larger problem instances.

Contribution

It presents a new LBBD approach and an enhanced LNS algorithm for complex pickup and delivery problems with transfers and time windows, along with a new benchmark generator.

Findings

LBBD closes optimality gaps on benchmark problems.

LNS provides near-optimal solutions and scales well to larger instances.

The new instance generator enables extensive testing and comparison.

Abstract

This paper examines the generalisation of the Pickup and Delivery Problem that allows mid-route load exchanges among vehicles and obeys strict time-windows at all locations. We propose a novel Logic-Based Benders Decomposition (LBBD) that improves optimality gaps for all benchmarks in the literature and scales up to handle larger ones. To tackle even larger instances, we introduce a refined Large Neighborhood Search (LNS) algorithm that improves the adaptability of LNS beyond case-specific configurations appearing in related literature. To bridge the gap in benchmark availability, we develop an instance generator that allows for extensive experimentation. For moderate datasets (25 and 50 requests), we evaluate the performance of both LBBD and LNS, the former being able to close the gap and the latter capable of providing near-optimal solutions. For larger instances (75 and 100 requests), we recreate indicative state-of-the-art metaheuristics to highlight the improvements introduced by our LNS refinements, while establishing its scalability.