Combining Optimization and Machine Learning for the Formation of Collectives

This thesis considers the problem of forming collectives of agents for real-world applications aligned with Sustainable Development Goals (e.g., shared mobility and cooperative learning). Such problems require fast approaches that can produce solutions of high quality for hundreds of agents. With this goal in mind, existing solutions for the formation of collectives focus on enhancing the optimization approach by exploiting the characteristics of a domain. However, the resulting approaches rely on specific domain knowledge and are not transferable to other collective formation problems. Therefore, approaches that can be applied to various problems need to be studied in order to obtain general approaches that do not require prior knowledge of the domain. Along these lines, this thesis proposes a general approach for the formation of collectives based on a novel combination of machine learning and an \emph{Integer Linear Program}. More precisely, a machine learning component is trained to generate a set of promising collectives that are likely to be part of a solution. Then, such collectives and their corresponding utility values are introduced into an \emph{Integer Linear Program} which finds a solution to the collective formation problem. In that way, the machine learning component learns the structure shared by ``good'' collectives in a particular domain, making the whole approach valid for various applications. In addition, the empirical analysis conducted on two real-world domains (i.e., ridesharing and team formation) shows that the proposed approach provides solutions of comparable quality to state-of-the-art approaches specific to each domain. Finally, this thesis also shows that the proposed approach can be extended to problems that combine the formation of collectives with other optimization objectives. Thus, this thesis proposes an extension of the collective formation approach for assigning pickup and delivery locations to robots in a warehouse environment. The experimental evaluation shows that, although it is possible to use the collective formation approach for that purpose, several improvements are required to compete with state-of-the-art approaches. Overall, this thesis aims to demonstrate that machine learning can be successfully intertwined with classical optimization approaches for the formation of collectives by learning the structure of a domain, reducing the need for ad-hoc algorithms devised for a specific application.