The field of optimization and pattern detection is witnessing significant developments, driven by the integration of large language models (LLMs) and innovative algorithmic designs. Researchers are exploring novel approaches to solve complex combinatorial optimization problems, such as the Longest Run Subsequence and Longest Filled Common Subsequence problems, by leveraging LLMs to generate instance-driven heuristic biases and adaptive frameworks. These advancements have led to improved performance, scalability, and solution accuracy. Furthermore, the application of LLMs in meta-optimization is enabling the automated design of constrained evolutionary algorithms, while new algorithms for period detection in strings are being developed to efficiently handle noise and mismatches. Noteworthy papers in this area include:

• A study that introduced a novel framework integrating LLMs with a Biased Random-Key Genetic Algorithm to solve the NP-hard Longest Run Subsequence problem, achieving statistically significant improvements over the baseline.
• A paper that proposed an adaptive Construct, Merge, Solve, Adapt framework to solve the Longest Filled Common Subsequence problem, demonstrating state-of-the-art performance and exceptional scalability.
• Research that presented a large language model-assisted meta-optimizer for automated design of constrained evolutionary algorithms, showing potential for broad applicability and scalability.
• A work that developed a streaming algorithm for period detection in strings under the Hamming distance and edit distance, improving efficiency and handling noise and wildcards.
• A study that designed higher-order, generically complete, continuous, and polynomial-time isometry invariants of periodic sets, enabling the distinction of novel crystals from noisy perturbations of known materials.