High coverage and mutual exclusivity (HCME), which are considered two combinatorial properties of mutations in a collection of driver genes in cancers, have been used to develop mathematical programming models for distinguishing cancer driver gene sets. In this paper, we summarize a weak HCME pattern to justify the description of practical mutation datasets. We then present AWRMP, a method for identifying driver gene sets through the adaptive assignment of appropriate weights to gene candidates to tune the balance between coverage and mutual exclusivity. It embeds the genetic algorithm into the subsampling strategy to provide the optimization results robust against the uncertainty and noise in the data. Using biological datasets, we show that AWRMP can identify driver gene sets that satisfy the weak HCME pattern and outperform the state-of-arts methods in terms of robustness.