Reasoning about Optimal Collections of Solutions

The problem of finding a collection of solutions to a combinatorial problem that is optimal in terms of an inter-solution objective function exists in many application settings. For example, maximizing diversity amongst a set of solutions in a product configuration setting is desirable so that a wide range of different options is offered to a customer. Given the computationally challenging nature of these multi-solution queries, existing algorithmic approaches either apply heuristics or combinatorial search, which does not scale to large solution spaces. However, in many domains compiling the original problem into a compact representation can support computationally efficient query answering. In this paper we present a new approach to find optimal collections of solutions when the problem is compiled into a multi-valued decision diagram. We demonstrate empirically that for real-world configuration problems, both exact and approximate versions of our methods are effective and are capable of significantly outperforming state-of-the-art search-based techniques.