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VRP
Chris Groer's VRPH library
An open source library for solving the capacitated vehicle routing problem written in C++.
OptaPlanner
OptaPlanner is a lightweight, embeddable planning engine written in Java™. It can be used to solve the capacitated vehicle routing problem (with time windows).
Open-VRP
Open-VRP is a framework to model and solve various vehicle routing problems.
VROOM
VROOM is an optimization engine written in C++14 that aim at providing good solutions to various real-life vehicle routing problems within a small computing time. It is free software, distributed under the term of the GNU General Public License V3.
Hipster4j
Hipster is an easy to use yet powerful and flexible type-safe library for heuristic search, written in pure Java. It relies on a flexible model with generic operators to define search problems. So you can also model and solve vehicle routing problems.
OscaR
OscaR, an Open Source Toolbox for Optimising Logistics and Supply Chain Systems.
Territory Design
OpenDoorLogistics
Open Door Logistics Studio is an easy-to-use standalone open source application for performing geographic analysis of your customer base and sales territory design, mapping and management.
If you know another promising open source implementation, report it.