The High Intensity Muon Beams (HIMB) project at the Paul Scherrer Institute (PSI) will provide muon intensities of the order of 10¹⁰ muons/s for particle physics and material science experiments, two orders of magnitude higher than the state of the art, which is currently available also at PSI. In particle transport simulations for the HIMB, we use G4beamline with measured ⁺ cross-sections and with variance reduction. We also use the codes COSY INFINITY, TRANSPORT, and TURTLE for some studies. We perform asynchronous Bayesian optimisation of the beamlines on a computing cluster using G4beamline and the optimisation package DeepHyper. We performed numerous studies for the design of the HIMB, and we produced various results, including the muon transmission, beam phase space, polarisation, and momentum spectrum.