SPIE

SPIE Computational Optics 2024: Quality-Diversity Driven Robust Evolutionary Optimization of Optical Designs Abstract: Developing optical systems, particularly those consisting of spherical lenses, is relevant for various applications such as lithographic scanners and metrology equipment. The design process of an optical system typically involves the optimization of specific objectives to ensure the best performance. As a common example of such an objective, we consider the problem of determining the lens curvatures that result in a sufficiently small root mean square (RMS) spot size. Optimization algorithms are commonly employed to solve this problem by heuristically eliminating sub-optimal optical designs. This class of algorithms includes the damped least squares (DLS) widely applied in commercial software and advanced methods like Saddle Point Construction. However, within a restricted computational budget, these optimizers are limited in exploring potentially promising novel solutions since they heavily rely on the initial specific designs that must conform to complex or unknown requirements. In this work, we address the considered problem with a modified Hill-Valley Evolutionary Algorithm (HillVallEA), which proved itself as one of the best state-of-the-art metaheuristics for multimodal black-box optimization. We demonstrate that our algorithm locates a diverse set of high-quality optical designs with four lenses in a single run even when initialized with random starting curvatures. This is the first result in this domain when an optimization algorithm that does not take specific optical properties into account can still generate relevant and high-performing optical systems. Furthermore, we show the benefits of the proposed methodology for the diversity of the obtained set of solutions, while maintaining a solution of the same quality as the one found by the most prominent algorithm in the domain. We provide analyses of the obtained solutions according to: 1) tolerance to the alignment of lenses, 2) susceptibility to small variations of lens curvatures.

Chapter

“The Prism-Net Search Space Representation for Multi-objective Building Spatial Design” Abstract

A building spatial design (BSD) determines external and internal walls and ceilings of a building. The design space has a hierarchical structure, in which decisions on the existence or non-existence of spatial components determine the existence of variables related to these spaces, such as sizing and angles. In the optimization of BSDs it is envisioned to optimize various performance indicators from multiple disciplines in concert, such as structural, functional, thermal, and daylight performance. Existing representations of design spaces suffer from severe limitations, such as only representing orthogonal designs or representing the structures in parametric superstructure, allowing only for limited design variations. This paper proposes prism nets - a new way of representing the search space of BSDs based on triangulations defining space filling collections of triangular prisms that can be combined via coloring parameters to spaces. Prism nets can accommodate for non-orthogonal designs and are flexible in terms of topological variations. We follow the guidelines for representation and operator design proposed in the framework of metric-based evolutionary algorithms. The main contribution of the paper is a detailed discussion of the search space representation and corresponding mutation operators. Moreover, a proof of concept example demonstrates the integration into multi-objective evolutionary algorithms and provides first results on a simple, but reproducible, benchmark problem.

https://link.springer.com/chapter/10.1007/978-3-031-27250-9_34