The issue of optimal power allocation in wireless cellular networks with interfering multiple-access channels (IMAC) attracted a lot of attention in recent decades. Although several model-based algorithms have been investigated in this problem, most of them require analytically tractable mathematical models and have high computational complexity. In this context, we compared different model-free stochastic algorithms and proposed a genetic algorithm-based method to minimize signal interference and maximize spectral efficiency. The simulation result shows the superiority of GA-based algorithms against the conventional baseline algorithms.