Model-Based Approaches to Multi-attribute Diverse Matching

Abstract

Bipartite b-matching is a classical model that is used for utility maximization in various applications such as marketing, healthcare, education, and general resource allocation. Multi-attribute diverse weighted bipartite b-matching (MDWBM) balances the quality of the matching with its diversity. The recent paper by Ahmadi et al. (2020) introduced the MDWBM but presented an incorrect mixed integer quadra-tic program (MIQP) and a flawed local exchange algorithm. In this work, we develop two constraint programming (CP) models, a binary quadratic programming (BQP) model, and a quadratic unconstrained binary optimization (QUBO) model for both the unconstrained and constrained MDWBM. A thorough empirical evaluation using commercial solvers and specialized QUBO hardware shows that the hardware-based QUBO approach dominates, finding best-known solutions on all tested instances up to an order of magnitude faster than the other approaches. CP is able to achieve better solutions than BQP on unconstrained problems but under-performs on constrained problems.