Increased energy demands are driving the development of new power generation technologies with high efficient. Direct fired fuel cell turbine hybrid systems are one such development, which have the potential to dramatically increase power generation efficiency, quickly respond to transient loads (and are generally flexible), and offer fast start up times. However, traditional control techniques are often inadequate in these systems because of extremely high nonlinearities and coupling between system parameters. In this work, we develop multi-objective neural network controller via neuroevolution and the Pareto Concavity Elimination Transformation (PaCcET). In order for the training process to be computationally tractable, we develop a computationally efficient plant simulator based on physical plant data, allowing for rapid fitness assignment. Results demonstrate that the multi-objective algorithm is able to develop a Pareto front of control policies which represent tradeoffs between tracking desired turbine speed profiles and minimizing transient operation of the fuel cell.