In this study, we perform a multi-objective parametric study for an array of three miniature wind turbines subjected to active yaw control (AYC), with the objectives of maximizing the power and minimizing the fatigue loads. Using the time series extracted from large-eddy simulation (LES), we compute the mean power and the yaw-moment damage equivalent load (DEL) at every point of a finite decision space spanned by the yaw angles of the first two turbines. The mean power outputs simulated with LES are compared with those measured in the wind tunnel, and a good agreement is found between the two. The Pareto front of different yaw configurations is extracted in the objective space of AYC and the Pareto-optimal strategies are identified in the decision space. We find that most of the Pareto-optimal strategies share the characteristic of moderately decremental yaw angles. We also find that the strategies with a small yaw angle for the first wind turbine are inefficient since they incur significant increases in fatigue while only achieving marginal power gains. The results indicate that the decision space of algorithms searching for optimal AYC strategies can be significantly reduced a priori with the consideration of load mitigation in the optimization.