Title: Search for Common Minima in Joint Optimization of Multiple Cost Functions,
Abstract: We present a novel optimization method, named the Combined Optimization
Method (COM), for the joint optimization of two or more cost functions. Unlike
the conventional joint optimization schemes, which try to find minima in a
weighted sum of cost functions, the COM explores search space for common minima
shared by all the cost functions. Given a set of multiple cost functions that
have qualitatively different distributions of local minima with each other, the
proposed method finds the common minima with a high success rate without the
help of any metaheuristics. As a demonstration, we apply the COM to the crystal
structure prediction in materials science. By introducing the concept of data
assimilation, i.e., adopting the theoretical potential energy of the crystal
and the crystallinity, which characterizes the agreement with the theoretical
and experimental X-ray diffraction patterns, as cost functions, we show that
the correct crystal structures of Si diamond, low quartz, and low cristobalite
can be predicted with significantly higher success rates than the previous
methods.