Optimizing the parameters of physics-based simulators is crucial in the design process of engineering and scientific systems. This becomes challenging when the simulator is stochastic, computationally expensive, black-box, multi-modal, and has a high-dimensional parameter space, such as when simulating complex climate models that involve numerous interacting variables and uncertain parame- ters. Many traditional optimization methods rely on gradient information, which is frequently unavailable in legacy black-box codes. To address these challenges, we present SCOUT-Nd (Stochastic Constrained Optimization for N dimensions), an algorithm designed to efficiently estimate gradients, reduce noise in the gradient estimator, and enhance convergence properties through the use of natural gradients. SCOUT-Nd also incorporates multi-fidelity schemes and an adaptive number of samples to minimize computational effort. We validate our approach using stan- dard benchmark analytical problems, demonstrating its superior performance in parameter optimization compared to existing methods. Additionally, we showcase the algorithm’s efficacy in a complex real-world application: optimizing wind farm layout.