  Superomniphobic textures are at the frontier of surface design for vast
arrays of applications. Despite recent significant advances in fabrication
methods for reentrant and doubly reentrant microstructures, design optimisation
remains a major challenge. We overcome this in two stages. Firstly, we develop
readily-generalisable computational methods to systematically survey three key
wetting properties: contact angle hysteresis, critical pressure, and minimum
energy wetting barrier. For each, we uncover multiple competing mechanisms,
leading to the development of new quantitative models, and correction of
inaccurate assumptions in prevailing models. Secondly, we combine these
analyses simultaneously, demonstrating the power of this strategy by optimizing
structures that are well-suited to overcome challenges faced by two emerging
applications: membrane distillation and digital microfluidics. As the wetting
properties are antagonistically coupled, this multifaceted approach is
essential for optimal design. When large surveys are impractical, we show that
genetic algorithms enable efficient optimisation, offering speedups of up to
10,000x.
