The explosive growth of cellular networks makes their deployment and maintenance more and more complex, time consuming, and expensive. Self-Organizing Networks have been recognized as a promising way to alleviate this problem by minimizing human intervention in such processes. This paper introduces a novel multiobjective framework, based on evolutionary optimization, aiming at improving network performance and users Quality of Service. By tuning the transmitted power at each cell, average intercell interference levels are minimized. The design of the proposed scheme is feasible for distributed implementations in Long Term Evolution (LTE) and LTE-Advanced networks and its operation is compatible with current specifications. The framework is able to provide effective network-specific optimization and obtained results show that gains in terms of network capacity and cell edge performance are 5 and 10 %, respectively. Energy savings always accompanied such enhancements with reductions up to 35 %.