This paper proposes a solution for energy-efficient communication in reconfigurable intelligent surface (RIS)-assisted unmanned aerial vehicle (UAV) networks. The limited battery life of UAVs is a major concern for their sustainable operation, and RIS has emerged as a promising solution to reducing the energy consumption of communication systems. The paper formulates the problem of maximizing the energy efficiency of the network as a mixed integer non-linear program, in which UAV placement, UAV beamforming, On-Off strategy of RIS elements, and phase shift of RIS elements are optimized. The proposed solution utilizes the block coordinate descent approach and a combination of continuous and binary genetic algorithms. Moreover, for optimizing the UAV placement, Adam optimizer is used. The simulation results show that the proposed solution outperforms the existing literature. Specifically, we compared the proposed method with the successive convex approximation (SCA) approach for optimizing the phase shift of RIS elements.