Evolutionary algorithms for multi-center solutions

Large classes of multi-center supergravity solutions have been constructed in the study of supersymmetric black holes and their microstates. Many smooth multi-center solutions have the same charges as supersymmetric black holes, with all centers deep inside a long black-hole-like throat. These configurations are constrained by regularity, absence of closed timelike curves, and charge quantization. Due to these constraints, constructing explicit solutions with several centers in generic arrangements, and with all parameters in physically relevant ranges, is a hard task. In this work, an optimization algorithm, based on evolutionary algorithms and Bayesian optimization is presented, that systematically constructs numerical solutions satisfying all constraints. Explicit examples of novel five-center and seven-center machine-precision solutions are exhibited. (© 2023 The Authors. Fortschritte der Physik published by Wiley‐VCH GmbH)