Container virtualization is an emerging technology in cloud computing mainly due to its portability and lightweight features. Scheduling is a key task, performed by container management tool, which indirectly affects the characteristics of distributed software system in terms of availability, realizability, scalability, resources utilization, as well as power consumption. However, current schedulers only focus on some of the aforementioned aspects but not all. In this paper, a Many-Objective Genetic Algorithm Scheduler (MOGAS) is proposed to handle all such objectives to realize solutions with better characteristics. The proposed scheduler is compared with the Ant Colony Optimization (ACO)-based scheduler. Based on the proposed objective functions, simulation results show that MOGAS is better than the ACO scheduler in equally distributing tasks by 50%, assigning unique set of tasks per node by 40%, and reducing power consumption by 7%, on average.