  The emergence of data-driven science has opened up new avenues for
understanding the thermophysical properties of materials. For decades, alloys
are known to possess very low thermal conductivity, but the extreme thermal
conductivity can be achieved by alloying has never been identified. In this
work, we combine the Bayesian optimization with a high throughput thermal
conductivity calculation to search for the lowest thermal conductivity atomic
configuration of $\rm{Si_{0.5}Ge_{0.5}}$ alloy. It is found layered structures
are most beneficial for reducing the thermal conductivity among all atomic
configurations, which is attributed to the strong branch-folding effect.
Furthermore, the roles of interface roughness and layer thicknesses in
producing the lowest thermal conductivity are investigated. Through another
comprehensive search using Bayesian optimization, the layered structure with
smooth interfaces and optimized layer thickness arrangement is identified as
the optimal structure with the lowest thermal conductivity.
