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

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 service start 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 ALNS, when used on small instances with 25 customers and with a much shorter running time. Our LP-based ALNS dominates the CP-based 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. We also adapt our algorithm to solve a well-studied variant of the problem, and the obtained results show that the algorithm provides good solutions as state-of-the-art approaches and improves four best known solutions. Crown Copyright (c) 2020 Published by Elsevier Ltd. All rights reserved.