  Rerandomization discards undesired treatment assignments to ensure covariate
balance in randomized experiments. However, rerandomization based on
acceptance-rejection sampling is computationally inefficient, especially when
numerous independent assignments are required to perform randomization-based
statistical inference. Existing acceleration methods are suboptimal and are not
applicable in structured experiments, including stratified experiments and
experiments with clusters. Based on metaheuristics in combinatorial
optimization, we propose a novel variable neighborhood searching
rerandomization(VNSRR) method to draw balanced assignments in various
experiments efficiently. We derive the unbiasedness and a lower bound for the
variance reduction of the treatment effect estimator under VNSRR. Simulation
studies and a real data example indicate that our method maintains the
appealing statistical properties of rerandomization and can sample thousands of
treatment assignments within seconds, even in cases where existing methods
require an hour to complete the task.
