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In this paper we are interested in optimizing the shape of multi-flagellatedhelical microswimmers. Mimicking the propagation of helical waves along theflagella, they self-propel by rotating their tails. The swimmer's dynamics iscomputed using the Boundary Element Method, implemented in the open sourceMatlab library $Gypsilab$. We exploit a Bayesian optimization algorithm tomaximize the swimmer's speeds through their shape optimization. Our resultsshow that the optimal tail shapes are helices with large wavelength, such thatthe shape periodicity is disregarded. Moreover, the best propulsion speed isachieved for elongated heads when the swimmer has one or two flagella.Surprisingly, a round head is obtained when more flagella are considered. Ourresults indicate that the position and number of flagella modify the propulsionpattern and play a significant role in the optimal design of the head. Itappears that Bayesian optimization is a promising method for performanceimprovement in microswimming.

Shapes enhancing the propulsion of multiflagellated helical microswimmers