Simulation-based test functions for optimization algorithms

When designing or developing optimization algorithms, test functions are crucial to evaluate performance. Often, test functions are not sufficiently difficult, diverse, flexible or relevant to real-world applications. Previously, test functions with real-world relevance were generated by training a machine learning model based on real-world data. The model estimation is used as a test function. We propose a more principled approach using simulation instead of estimation. Thus, relevant and varied test functions are created which represent the behavior of real-world fitness landscapes. Importantly, estimation can lead to excessively smooth test functions while simulation may avoid this pitfall. Moreover, the simulation can be conditioned by the data, so that the simulation reproduces the training data but features diverse behavior in unobserved regions of the search space. The proposed test function generator is illustrated with an intuitive, one-dimensional example. To demonstrate the utility of this approach it is applied to a protein sequence optimization problem. This application demonstrates the advantages as well as practical limits of simulation-based test functions.