DecisionRules.io - Business rule engine that lets you create and deploy business rules, while all your rules run in a secure and scalable cloud. Unlike other rule engines, you can create your first rule in 5 minutes and make 100k decisions in a minute via API.

OptaPlanner - Mathematical optimization software

OpenRules - OpenRules is a Business Rules and Decision Management platform, offering a solution for building, deploying, executing, and monitoring Business Rules and Decision trees.

jsprit - jsprit is a java based, open source toolkit for solving rich vehicle routing problems.

Higson.io - Hyperon is a BRMS, that was created with very large decisions and hyper-performance in mind. It stands out with the concept of the business domain which organizes the whole configuration in easy to manage way.

MiniZinc - MiniZinc is a free and open-source constraint modeling language.