Search for Common Minima in Joint Optimization of Multiple Cost Functions

TL;DR

This paper introduces the Combined Optimization Method (COM), a new approach for jointly optimizing multiple cost functions by finding their common minima, demonstrated on crystal structure prediction with improved success rates.

Contribution

The paper proposes a novel optimization technique that efficiently finds common minima across multiple cost functions without metaheuristics, enhancing crystal structure prediction accuracy.

Findings

Successfully predicted crystal structures of Si diamond, low quartz, and cristobalite.

Achieved higher success rates than previous methods.

Demonstrated effectiveness in materials science applications.

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.