Selection of Filters for Photonic Crystal Spectrometer Using Domain-Aware Evolutionary Algorithms

TL;DR

The paper tackles Optimal Filter Selection (OFS) for a photonic-crystal trace-gas spectrometer by casting it as a stochastic combinatorial optimization problem solved on a noisy TGMD simulator. It evaluates a broad suite of solvers from evolutionary, response-surface, and model-based families, identifying leading performers and then enhancing them with domain-aware distance metrics to exploit filter-space structure. A key contribution is the Distance-Driven UMDA variant (UMDA-U-PLS-Dist) using distance metrics on the filter library, which, with the $d_1$ metric, yields the most robust and efficient solutions within a fixed evaluation budget. Additional innovations include a Distance-Driven Mutation framework (DDA-EA) for solving inverse linear assignment subproblems and a thorough analysis of high-performing, diverse filter multisets that significantly improve methane retrieval precision over a baseline. The work demonstrates that filters with large local transmission differences and smooth transmission profiles can substantially boost device performance, with practical implications for compact, high-precision trace-gas sensing in earth observation and related imaging domains.

Abstract

This work addresses the critical challenge of optimal filter selection for a novel trace gas measurement device. This device uses photonic crystal filters to retrieve trace gas concentrations affected by photon and read noise. The filter selection directly influences the accuracy and precision of the gas retrieval and, therefore, is a crucial performance driver. We formulate the problem as a stochastic combinatorial optimization problem and develop a simulator modeling gas retrieval with noise. Metaheuristics representing various families of optimizers are used to minimize the retrieval error objective function. We improve the top-performing algorithms using our novel distance-driven extensions, which employ metrics on the space of filter selections. This leads to a new adaptation of the Univariate Marginal Distribution Algorithm (UMDA), called the Univariate Marginal Distribution Algorithm Unified by Probabilistic Logic Sampling driven by Distance (UMDA-U-PLS-Dist), equipped with one of the proposed distance metrics as the most efficient and robust solver among the considered ones. We apply this algorithm to obtain a diverse set of high-performing solutions and analyze them to draw general conclusions about better combinations of transmission profiles. The analysis reveals that filters with large local differences in transmission improve the device performance. Moreover, the obtained top-performing solutions show significant improvement compared to the baseline.

Figures (19)

• Figure 1: Illustration of the trace gas measurement device concept. Sunlight travels through the Earth's atmosphere, is reflected and is measured by the trace gas measurement device by a camera with different photonic crystal filters. As the instrument flies over the earth, each ground pixel is measured with each filter.
• Figure 2: Diagram of the trace gas measurement device description.
• Figure 3: Convergence plot for every algorithm $A \in \mathbb{A}_1$. Part (a) represents the approximated mean of $\mathrm{f}$ defined in Eq. \ref{['eq:cr1']} as the quality of the solution considered by algorithm $A$ when computational budget $t$ is spent. Part (b) represents the approximated mean and standard deviation of $\mathrm{g}$ defined in Eq. \ref{['eq:cr2']} as the quality of best-so-far solution found by algorithm $A$ when computational budget $t$ is spent. The number of independent runs per algorithm is $n = 20$.
• Figure 4: Distance-driven optimization. Left: Standard mutation (a) samples points on contours $d_1,d_2,d_3$ of $F(\bm{x})$; distance-driven mutation (b) “flattens” objective values on closer contours to the reference point $\bm{\widehat{x}}$ in the transformed landscape. Right: To generate a new candidate $\bm{z}$ in the transformed landscape, (c) draw step‐size $s \sim \mathscr{D}(m)$ (see Section \ref{['sec:step-size-distr']}), (d) learn scaling parameter $\gamma$ (see Section \ref{['sec:gamma']}), (e) rescale the step-size $S = {\sqrt{-\ln(1-s)}}/{\gamma},$ (see Section \ref{['sec:gamma']}) and (f) solve $\min_{\bm{z}}\bigl|d(\bm{\widehat{x}},\bm{ z})-S\bigr|$ to place $\bm{ z}$ exactly at distance $S$ from $\bm{\widehat{x}}$ (see Section \ref{['sec:internal-opt']}).
• Figure 5: Proposed DD-$(\mu/2 + \lambda)$ EA, equipped with a distance-driven heuristic for integer programming, where objective function $F: \mathbb{L}^M \to \mathbb{R}$ is minimized. Points in its domain have dimensionality $M$. Value at every component of every point is an integer from the set $\mathbb{L} \coloneqq \overline{1,L}$, which is a metric space with distance $d_{\mathbb{L}}$. The maximal number of $F$ evaluations is limited by constant $b$. On top of that, the algorithm uses integer constants $\mu, \lambda, R$ and a real constant $0\le m \le 1$.

Theorems & Definitions (5)

• Definition 1
• Definition 2
• Definition 3: Metric Space
• Proposition 1
• proof