Managing complex Cyber-Physical Energy Systems (CPES) requires solving various optimization problems with multiple objectives and constraints. As distributed control architectures are becoming more popular in CPES for certain tasks due to their flexibility, robustness, and privacy protection, multi-objective optimization must also be distributed. For this purpose, we present MO-COHDA, a fully distributed, agent-based algorithm, for solving multi-objective optimization problems of CPES. MO-COHDA allows an easy and flexible adaptation to different use cases and integration of custom functionality. To evaluate the effectiveness of MO-COHDA, we compare it to a central NSGA-2 algorithm using multi-objective benchmark functions from the ZDT problem suite. The results show that MO-COHDA can approximate the reference front of the benchmark problems well and is suitable for solving multi-objective optimization problems. In addition, an example use case of scheduling a group of generation units while optimizing three different objectives was evaluated to show how MO-COHDA can be easily applied to real-world optimization problems in CPES.