Simulator-based surrogate optimisation employing adaptive uncertainty-aware sampling

Optimisation problems involving computationally expensive, black-box functions derived from high-fidelity engineering simulations remain challenging. To efficiently bridge the simulators and optimisation processes, we introduce an adaptive framework for surrogate modelling and optimisation. Our method employs low-discrepancy sequence sampling to select points, followed by training a surrogate model using a piecewise linear neural network (NN) with rectified linear unit (ReLU) activation. Using mixed-integer programming (MIP), we reformulate the ReLU NN as embedded components of an optimisation problem and solve it to find an optimal simulator input. This is achieved by iteratively refining the solution via resampling the simulator, retraining the surrogate model, and rebuilding and resolving the MIP problem. For resampling, an infill strategy that incorporates uncertainty assessment and a solution pool is employed, balancing exploration and exploitation. Moreover, computational efficiency is boosted by bound tightening, lossless model compression, and memory structure reuse. Validation on practical engineering applications confirms significant optimisation efficiency gains from the domain-refined strategy.