Large Language Models (LLMs) such as GPT-4 have demonstrated their ability to understand natural language and generate complex code snippets. This paper introduces a novel Large Language Model Evolutionary Algorithm (LLaMEA) framework, leveraging GPT models for the automated generation and refinement of algorithms. Given a set of criteria and a task definition (the search space), LLaMEA iteratively generates, mutates and selects algorithms based on performance metrics and feedback from runtime evaluations. This framework offers a unique approach to generating optimized algorithms without requiring extensive prior expertise. We show how this framework can be used to generate novel black-box metaheuristic optimization algorithms for box-constrained, continuous optimization problems automatically. LLaMEA generates multiple algorithms that outperform state-of-the-art optimization algorithms (Covariance Matrix Adaptation Evolution Strategy and Differential Evolution) on the 5-dimensional black box optimization benchmark (BBOB). The algorithms also show competitive performance on the 10-and 20-dimensional instances of the test functions, although they have not seen such instances during the automated generation process. The results demonstrate the feasibility of the framework and identify future directions for automated generation and optimization of algorithms via LLMs.

Thirty years, 1993–2023, is a huge time frame in science. We address some major developments in the field of evolutionary algorithms, with applications in parameter optimization, over these 30 years. These include the covariance matrix adaptation evolution strategy and some fast-growing fields such as multimodal optimization, surrogate-assisted optimization, multiobjective optimization, and automated algorithm design. Moreover, we also discuss particle swarm optimization and differential evolution, which did not exist 30 years ago, either. One of the key arguments made in the paper is that we need fewer algorithms, not more, which, however, is the current trend through continuously claiming paradigms from nature that are suggested to be useful as new optimization algorithms. Moreover, we argue that we need proper benchmarking procedures to sort out whether a newly proposed algorithm is useful or not. We also briefly discuss automated algorithm design approaches, including configurable algorithm design frameworks, as the proposed next step toward designing optimization algorithms automatically, rather than by hand.

Background: There is great interest in agentic LLMs, large language models that act as agents. Objectives: We review the growing body of work in this area and provide a research agenda. Methods: Agentic LLMs are LLMs that (1) reason, (2) act, and (3) interact. We organize the literature according to these three categories. Results: The research in the first category focuses on reasoning, reflection, and retrieval, aiming to improve decision making; the second category focuses on action models, robots, and tools, aiming for agents that act as useful assistants; the third category focuses on multi-agent systems, aiming for collaborative task solving and simulating interaction to study emergent social behavior. We find that works mutually benefit from results in other categories: retrieval enables tool use, reflection improves multi-agent collaboration, and reasoning benefits all categories. Conclusions: We discuss applications of agentic LLMs and provide an agenda for further research. Important applications are in medical diagnosis, logistics and financial market analysis. Meanwhile, self-reflective agents playing roles and interacting with one another augment the process of scientific research itself. Further, agentic LLMs provide a solution for the problem of LLMs running out of training data: inference-time behavior generates new training states, such that LLMs can keep learning without needing ever larger datasets. We note that there is risk associated with LLM assistants taking action in the real world—safety, liability and security are open problems—while agentic LLMs are also likely to benefit society.

Large language models (LLMs) with billions of parameters exhibit in-context learning abilities, enabling few-shot learning on tasks that the model was not specifically trained for. Traditional models achieve breakthrough performance on language tasks, but do not perform well on basic reasoning benchmarks. However, a new in-context learning approach, Chain-of-thought, has demonstrated strong multi-step reasoning abilities on these benchmarks. The research on LLM reasoning abilities started with the question whether LLMs can solve grade school math word problems, and has expanded to other tasks in the past few years. This article reviews the field of multi-step reasoning with LLMs. We propose a taxonomy that identifies different ways to generate, evaluate, and control multi-step reasoning. We provide an in-depth coverage of core approaches and open problems, and we propose a research agenda for the near future. We find that multi-step reasoning approaches have progressed beyond math word problems, and can now successfully solve challenges in logic, combinatorial games, and robotics, sometimes by first generating code that is then executed by external tools. Many studies in multi-step methods use reinforcement learning for finetuning, external optimization loops, in-context reinforcement learning, and self-reflection.

Explainable Artificial Intelligence (XAI) is an increasingly important field of research required to bring AI to the next level in real-world applications. Global sensitivity analysis (GSA) methods play an important role in XAI, as they can provide an understanding of which (groups of) parameters have high influence in the predictions of machine learning models and the output of simulators and real-world processes. In this paper, we conduct a survey into global sensitivity methods in an XAI context and present both a qualitative and a quantitative analysis of these methods under different conditions. In addition to the overview and comparison, we propose an open source application, GSAreport, that allows you to easily generate extensive reports using a carefully selected set of global sensitivity analysis methods depending on the number of dimensions and samples, to gain a deep understanding of the role of each feature for a given model or data set. We finally present the methods discussed in a complex real-world application of genomic prediction and draw conclusions about when to use which GSA methods.

KrigingorGaussian Process Regressionis applied in many fields as a non-linear regression model as well as a surrogate model in the field of evolutionary computation. However, the computational and space complexity of Kriging, that is cubic and quadratic in the number of data points respectively, becomes a major bottleneck with more and more data available nowadays. In this paper, we propose a general methodology for the complexity reduction, called cluster Kriging, where the whole data set is partitioned into smaller clusters and multiple Kriging models are built on top of them. In addition, four Kriging approximation algorithms are proposed as candidate algorithms within the new framework. Each of these algorithms can be applied to much larger data sets while maintaining the advantages and power of Kriging. The proposed algorithms are explained in detail and compared empirically against a broad set of existing state-of-the-art Kriging approximation methods on a well-defined testing framework. According to the empirical study, the proposed algorithms consistently outperform the existing algorithms. Moreover, some practical suggestions are provided for using the proposed algorithms.