Constrained optimisation represents a fundamental technique that has been successfully employed in Multi-Agent Systems (MAS) in order to face a number of multi-agent coordination challenges. These systems usually involve a large number of entities that interact with complex dynamics in unforeseen environmental conditions.
As a result, MAS coordination problems usually translate in hard constrained optimisation problems that have to be solved in a timely manner.
In this tutorial, we first provide a broad overview of the key aspects of constrained optimisation in the context of some widely studied real-world application, e.g., combinatorial auctions, ridesharing, and team formation. Subsequently, we propose some exact and approximated techniques that can deal with the computational complexity posed by these problem domains.
Finally, we conclude by highlighting open problems and possible future venues of research within this field.