  In this paper we are interested in optimizing the shape of multi-flagellated
helical microswimmers. Mimicking the propagation of helical waves along the
flagella, they self-propel by rotating their tails. The swimmer's dynamics is
computed using the Boundary Element Method, implemented in the open source
Matlab library $Gypsilab$. We exploit a Bayesian optimization algorithm to
maximize the swimmer's speeds through their shape optimization. Our results
show that the optimal tail shapes are helices with large wavelength, such that
the shape periodicity is disregarded. Moreover, the best propulsion speed is
achieved for elongated heads when the swimmer has one or two flagella.
Surprisingly, a round head is obtained when more flagella are considered. Our
results indicate that the position and number of flagella modify the propulsion
pattern and play a significant role in the optimal design of the head. It
appears that Bayesian optimization is a promising method for performance
improvement in microswimming.
