We perform beamline design optimization for the High Intensity Muon Beams (HIMB) project at the Paul Scherrer Institute (PSI), which will deliver muon beams at the unprecedented rate of 10¹⁰ muons/s to next-generation intensity frontier particle physics and material science experiments. For optimization of the design and operational parameters to maximize the beamline transmission, we use the asynchronous Bayesian optimization package DeepHyper and a custom build of G4beamline with variance reduction and measured cross sections. We minimize the beam spot size at the final foci using a COSY INFINITY model with differential-algebraic system knobs, where we minimize the respective transfer map elements using the Levenberg-Marquardt and simulated annealing optimizers. We obtained a transmission of 1.34x10¹⁰ muons/s in a G4beamline model of HIMB’s MUH2 beamline into the experimental area.