A new constraint programming model and a linear programming-based adaptive large neighborhood search for the vehicle routing problem with synchronization constraints

TL;DR

This paper introduces a new constraint programming model and an LP-based adaptive large neighborhood search for a vehicle routing problem with synchronization constraints, demonstrating improved solution quality and efficiency.

Contribution

It presents a novel combination of CP and LP techniques for a complex vehicle routing problem with synchronization, with acceleration methods to enhance computational performance.

Findings

The CP model outperforms existing CP-based ALNS on small instances.

The LP-based ALNS yields better solutions than the CP-based approach across all tested instances.

Using LP in ALNS improves solution quality for problems with tight constraints.

Abstract

We consider a vehicle routing problem which seeks to minimize cost subject to time window and synchronization constraints. In this problem, the fleet of vehicles is categorized into regular and special vehicles. Some customers require both vehicles' services, whose starting service times at the customer are synchronized. Despite its important real-world application, this problem has rarely been studied in the literature. To solve the problem, we propose a Constraint Programming (CP) model and an Adaptive Large Neighborhood Search (ALNS) in which the design of insertion operators is based on solving linear programming (LP) models to check the insertion feasibility. A number of acceleration techniques is also proposed to significantly reduce the computational time. The computational experiments show that our new CP model finds better solutions than an existing CP-based ANLS, when used on small instances with 25 customers and with a much shorter running time. Our LP-based ALNS dominates the cp-ALNS, in terms of solution quality, when it provides solutions with better objective values, on average, for all instance classes. This demonstrates the advantage of using linear programming instead of constraint programming when dealing with a variant of vehicle routing problems with relatively tight constraints, which is often considered to be more favorable for CP-based methods.