In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven framework for discovering fractional differential equations (FDEs) directly from data. FDEs, known for their capacity to model non-local dynamics with fewer parameters than integer-order derivatives, can represent complex systems with long-range interactions. Our framework applies deep neural networks as surrogate models for denoising and reconstructing sparse and noisy observations while using Gaussian-Jacobi quadrature to handle the challenges posed by singularities in fractional derivatives. To optimize both the sparse coefficients and fractional order, we employ an alternating optimization approach that combines sparse regression with global optimization techniques. We validate the framework across various datasets, including synthetic anomalous diffusion data, experimental data on the creep behavior of frozen soils, and single-particle trajectories modeled by L\'{e}vy motion. Results demonstrate the framework's robustness in identifying the structure of FDEs across diverse noise levels and its capacity to capture integer-order dynamics, offering a flexible approach for modeling memory effects in complex systems.

However, despite their size and complexity, these models still face challenges in multi-step reasoning, particularly in tasks that require arithmetic, logic, and/or mathematical reasoning [Cobbe et al. 2021; Rae et al. 2021]. To address this limitation, recent works have focused on enhancing the reasoning abilities of LLMs. A significant advancement in this direction is the chain-of-thought (CoT) prompting method [Wei et al. 2022b]. This approach involves guiding LLMs to articulate intermediate reasoning steps in a manner akin to human thought processes, leading to more accurate and interpretable solutions. This method has shown substantial improvements on complex tasks, including mathematics and commonsense reasoning [Lu et al. 2022b; Suzgun et al. 2022; Wei et al. 2022b]. The advancement of the CoT prompting has opened new pathways in the design of effective CoT prompts [Fu et al. 2022; Jiang et al. 2023; Kojima et al. 2022; Zhou et al. 2022].

The rising popularity of the microservice architectural style has led to a growing demand for automated testing approaches tailored to these systems. EvoMaster is a state-of-the-art tool that uses Evolutionary Algorithms (EAs) to automatically generate test cases for microservices' REST APIs. One limitation of these EAs is the use of unit-level search heuristics, such as branch distances, which focus on fine-grained code coverage and may not effectively capture the complex, interconnected behaviors characteristic of system-level testing. To address this limitation, we propose a new search heuristic (MISH) that uses real-time automaton learning to guide the test case generation process. We capture the sequential call patterns exhibited by a test case by learning an automaton from the stream of log events outputted by different microservices within the same system. Therefore, MISH learns a representation of the systemwide behavior, allowing us to define the fitness of a test case based on the path it traverses within the inferred automaton. We empirically evaluate MISH's effectiveness on six real-world benchmark microservice applications and compare it against a state-of-the-art technique, MOSA, for testing REST APIs. Our evaluation shows promising results for using MISH to guide the automated test case generation within EvoMaster.

Path Planning methods for autonomously controlling swarms of unmanned aerial vehicles (UAVs) are gaining momentum due to their operational advantages. An increasing number of scenarios now require autonomous control of multiple UAVs, as autonomous operation can significantly reduce labor costs. Additionally, obtaining optimal flight paths can lower energy consumption, thereby extending battery life for other critical operations. Many of these scenarios, however, involve obstacles such as power lines and trees, which complicate Path Planning. This paper presents an evolutionary computation-based system employing genetic algorithms to address this problem in environments with obstacles. The proposed approach aims to ensure complete coverage of areas with fixed obstacles, such as in field exploration tasks, while minimizing flight time regardless of map size or the number of UAVs in the swarm. No specific goal points or prior information beyond the provided map is required. The experiments conducted in this study used five maps of varying sizes and obstacle densities, as well as a control map without obstacles, with different numbers of UAVs. The results demonstrate that this method can determine optimal paths for all UAVs during full map traversal, thus minimizing resource consumption. A comparative analysis with other state-of-the-art approach is presented to highlight the advantages and potential limitations of the proposed method.

In this work, we propose a minimalistic swarm flocking approach for multirotor unmanned aerial vehicles (UAVs). Our approach allows the swarm to achieve cohesively and aligned flocking (collective motion), in a random direction, without externally provided directional information exchange (alignment control). The method relies on minimalistic sensory requirements as it uses only the relative range and bearing of swarm agents in local proximity obtained through onboard sensors on the UAV. Thus, our method is able to stabilize and control the flock of a general shape above a steep terrain without any explicit communication between swarm members. To implement proximal control in a three-dimensional manner, the Lennard-Jones potential function is used to maintain cohesiveness and avoid collisions between robots. The performance of the proposed approach was tested in real-world conditions by experiments with a team of nine UAVs. Experiments also present the usage of our approach on UAVs that are independent of external positioning systems such as the Global Navigation Satellite System (GNSS). Relying only on a relative visual localization through the ultraviolet direction and ranging (UVDAR) system, previously proposed by our group, the experiments verify that our system can be applied in GNSS-denied environments. The degree achieved of alignment and cohesiveness was evaluated using the metrics of order and steady-state value.

Adversarial attacks pose significant challenges in many machine learning applications, particularly in the setting of distributed training and federated learning, where malicious agents seek to corrupt the training process with the goal of jeopardizing and compromising the performance and reliability of the final models. In this paper, we address the problem of robust federated learning in the presence of such attacks by formulating the training task as a bi-level optimization problem. We conduct a theoretical analysis of the resilience of consensus-based bi-level optimization (CB$^2$O), an interacting multi-particle metaheuristic optimization method, in adversarial settings. Specifically, we provide a global convergence analysis of CB$^2$O in mean-field law in the presence of malicious agents, demonstrating the robustness of CB$^2$O against a diverse range of attacks. Thereby, we offer insights into how specific hyperparameter choices enable to mitigate adversarial effects. On the practical side, we extend CB$^2$O to the clustered federated learning setting by proposing FedCB$^2$O, a novel interacting multi-particle system, and design a practical algorithm that addresses the demands of real-world applications. Extensive experiments demonstrate the robustness of the FedCB$^2$O algorithm against label-flipping attacks in decentralized clustered federated learning scenarios, showcasing its effectiveness in practical contexts.

Methods for generative design of robot physical configurations can automatically find optimal and innovative solutions for challenging tasks in complex environments. The vast search-space includes the physical design-space and the controller parameter-space, making it a challenging problem in machine learning and optimisation in general. Evolutionary algorithms (EAs) have shown promising results in generating robot designs via gradient-free optimisation. Morpho-evolution with learning (MEL) uses EAs to concurrently generate robot designs and learn the optimal parameters of the controllers. Two main issues prevent MEL from scaling to higher complexity tasks: computational cost and premature convergence to sub-optimal designs. To address these issues, we propose combining morpho-evolution with intrinsic motivations. Intrinsically motivated behaviour arises from embodiment and simple learning rules without external guidance. We use a homeokinetic controller that generates exploratory behaviour in a few seconds with reduced knowledge of the robot's design. Homeokinesis replaces costly learning phases, reducing computational time and favouring diversity, preventing premature convergence. We compare our approach with current MEL methods in several downstream tasks. The generated designs score higher in all the tasks, are more diverse, and are quickly generated compared to morpho-evolution with static parameters.

Learning problems in which multiple conflicting objectives must be considered simultaneously often arise in various fields, including engineering, drug design, and environmental management. Traditional methods for dealing with multiple black-box objective functions, such as scalarization and identification of the Pareto set under the componentwise order, have limitations in incorporating objective preferences and exploring the solution space accordingly. While vector optimization offers improved flexibility and adaptability via specifying partial orders based on ordering cones, current techniques designed for sequential experiments either suffer from high sample complexity or lack theoretical guarantees. To address these issues, we propose Vector Optimization with Gaussian Process (VOGP), a probably approximately correct adaptive elimination algorithm that performs black-box vector optimization using Gaussian process bandits. VOGP allows users to convey objective preferences through ordering cones while performing efficient sampling by exploiting the smoothness of the objective function, resulting in a more effective optimization process that requires fewer evaluations. We establish theoretical guarantees for VOGP and derive information gain-based and kernel-specific sample complexity bounds. We also conduct experiments on both real-world and synthetic datasets to compare VOGP with the state-of-the-art methods.

The emergence of LLMs, like ChatGPT and Gemini, has marked the modern era of artificial intelligence applications characterized by high-impact applications generating text, images, and videos. However, these models usually ensue with one critical challenge called hallucination: confident presentation of inaccurate or fabricated information. This problem attracts serious concern when these models are applied to specialized domains, including healthcare and law, where the accuracy and preciseness of information are absolute conditions. In this paper, we propose EvoLLMs, an innovative framework inspired by Evolutionary Computation, which automates the generation of high-quality Question-answering (QA) datasets while minimizing hallucinations. EvoLLMs employs genetic algorithms, mimicking evolutionary processes like selection, variation, and mutation, to guide LLMs in generating accurate, contextually relevant question-answer pairs. Comparative analysis shows that EvoLLMs consistently outperforms human-generated datasets in key metrics such as Depth, Relevance, and Coverage, while nearly matching human performance in mitigating hallucinations. These results highlight EvoLLMs as a robust and efficient solution for QA dataset generation, significantly reducing the time and resources required for manual curation.

Artificial Intelligence (AI) has witnessed significant advances with the emergence of powerful neural network (NN) models. Examples include large language models [1] and image generation models such as DALL-E [2], Imagen [3], and Parti [4]. Each has achieved previously unseen capabilities as powerful individuals through recent technical breakthroughs. On the other hand, the biological evolutionary strategy focuses more on the direction of collective intelligence compared to individual ability, especially for species living in populations [5]. Unlike individual intelligence, which deals with challenges independently, collective intelligence necessitates the ability to process information, operate in a decentralized manner, and adaptively integrate information based on context. This distinction is evident in social insects, such as ants and bees, where collective behavior with role differentiation emerges not from highly complex individuals but through simple interactions among members.