Adaptive Operator Selection (AOS) is a strategy in Evolutionary Algorithms (EAs) that dynamically adjusts the application frequency of operators to enhance search efficiency based on online performance feedback. This paper introduces LAOS, an AOS framework driven by Large Language Models (LLMs). We design a meta-prompt to provide optimization state information (such as optimization progress, best fitness, and population diversity) and operator credit assignment, assisting LLMs in making adaptive decisions. Furthermore, LAOS maintains a dual-layer replay buffer structure: the offline layer records historical experiences under fixed operator strategies, while the online layer accumulates dynamically generated experiences during execution. By employing a similar experience sampling strategy, the framework can provide decision-making support for LLMs, enhancing both the efficiency and accuracy of search strategies. Experimental results on continuous numerical optimization and three categories of combinatorial optimization problems validate the effectiveness and generalization capability of LAOS. This study demonstrates the feasibility of leveraging LLMs for AOS, showcasing their potential in enhancing optimization performance and supporting automated algorithm design.

Parameter setting is a critical challenge in Evolutionary Algorithms (EAs) as it directly impacts optimization performance. However, fixed parameter configurations often fail to guarantee optimal algorithm behavior throughout the optimization process. Despite numerous dynamic parameter control methods, no universal solution has emerged. In this work, we introduce Large Language Model-Powered Adaptive Parameter Control (LAPC), a novel framework for adaptive parameter control in EAs. Our framework leverages an innovative prompt design that incorporates key optimization metrics, including progress, mean fitness, and mean pairwise distance. Additionally, a replay buffer is employed to sample similar optimization experiences, helping guide large language models (LLMs) in selecting appropriate parameter control strategies. To reduce search space and inference complexity, we also design a discrete parameter output strategy. We apply LAPC to control parameters in (1 + 1)-ES and Genetic Algorithms (GAs), targeting numerical optimization problems and the Traveling Salesman Problem (TSP), respectively. Experimental results demonstrate that LAPC consistently outperforms existing methods, such as the one-fifth rule and Deep Q-Networks (DQN). Moreover, we present comparative studies on the effectiveness of the LAPC module, the impact of parameter update intervals, and the effect of the dimensionality of the discrete parameter output. Our results highlight the potential of LLMs as general-purpose tools for complex decision-making tasks.

Recently, several robust principal component analysis (RPCA) models were presented to enhance the robustness of PCA by exploiting the robust norms as their loss functions. But an important problem is that they have no ability to discriminate outliers from correct samples. To solve this problem, we propose a RPCA method based on discriminant information (RPCA-DI). RPCA-DI disentangles the robust PCA with a two-step fashion: the identification and the processing of outliers. To identity outliers, a sample representation model based on entropy regularization is constructed to analyze the membership of data belonging to the principal component space(PC) and its orthogonal complement(OC), the discriminative information of data will be extracted based on measuring the differences of retained information on PC(or OC) of data. By this way, we can discriminate correct samples when we deal with outliers, which is more reasonable for robustness learning respective to previous works. In the noise processing step, in addition to considering the levels of noise, the resistance of the sample points to noise is also considered to prevent overfitting, thereby improving the generalization performance of RPCA-DI. Finally, an iterative algorithm is designed to solve the corresponding model. Compared with some state-of-art RPCA methods on artificial datasets, UCI datasets and face databases that verifies the effectiveness of RPCA-DI.