MIQCP and MISOCP-Based Solution Methods for the Multi-Layer Thin Films Problem

TL;DR

This paper introduces exact MIQCP and MISOCP-based optimization methods to design multi-layer coatings for metallic substrates, achieving high reflectance across multiple wavelengths, improving upon heuristic approaches.

Contribution

The work develops a novel nonconvex MIQCP model and a relaxation-based MISOCP approach for multi-wavelength coating design, advancing optimization techniques in materials science.

Findings

Achieved an average reflectance of 99% over the visible spectrum.

Attained 95% average reflectance over the broad spectrum (300-3000 nm).

MISOCP relaxation offers computational advantages over MIQCP.

Abstract

The Multi-Layer Thin Films Problem is a materials science problem that aims to enhance the reflectance of a metallic substrate by designing multi-layer coatings composed of different dielectric materials and thicknesses. While previous studies on the problem mostly rely on heuristic approaches and are designed for single wavelength applications, this work addresses the problem using global optimization techniques for multiple wavelengths. We develop an exact nonconvex mixed-integer quadratically constrained programming (MIQCP) model to solve this problem. We also develop a mixed-integer second-order cone programming relaxation that has computational advantage over the MIQCP model. Our numerical experiments yield solutions that have average reflectance of 99% over the visible spectrum (380-770 nm) and 95% over the broad spectrum (300-3000 nm).