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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.
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.