It is usually difficult to characterize the alternative hypothesis precisely in a log-likelihood ratio (LLR)-based speaker verification system. In a previous work, we proposed using a weighted arithmetic combination (WAC) or a weighted geometric combination (WGC) of the likelihoods of the background models instead of heuristic combinations, such as the arithmetic mean and the geometric mean, to better characterize the alternative hypothesis. In this paper, we further propose learning the parameters associated with WAC or WGC via an evolutionary minimum verification error (MVE) training method, such that both the false acceptance probability and the false rejection probability can be minimized. Our experiment results show that the proposed methods outperform conventional LLR-based approaches.