To further validate the algorithm's convergence and robustness, we repeated the damage identification process 10 times for each test scenario. As an example, the best objective function value per generation for the Legs 4 and 5 missing scenario is shown in Figure 1. Across the 10 identification runs, the resulting morphology was either identical or differed by a single link within the identified damaged legs, a discrepancy discussed before. The most frequently identified morphology is reported in Table III, representing the most probable morphological configuration based on the algorithm's convergence behavior. As shown in Figure 1, the algorithm converged to three distinct morphologies over 10 attempts.

Heuristic algorithms play a vital role in solving combinatorial optimization (CO) problems, yet traditional designs depend heavily on manual expertise and struggle to generalize across diverse instances. We introduce \textbf{HeurAgenix}, a two-stage hyper-heuristic framework powered by large language models (LLMs) that first evolves heuristics and then selects among them automatically. In the heuristic evolution phase, HeurAgenix leverages an LLM to compare seed heuristic solutions with higher-quality solutions and extract reusable evolution strategies. During problem solving, it dynamically picks the most promising heuristic for each problem state, guided by the LLM's perception ability. For flexibility, this selector can be either a state-of-the-art LLM or a fine-tuned lightweight model with lower inference cost. To mitigate the scarcity of reliable supervision caused by CO complexity, we fine-tune the lightweight heuristic selector with a dual-reward mechanism that jointly exploits singals from selection preferences and state perception, enabling robust selection under noisy annotations. Extensive experiments on canonical benchmarks show that HeurAgenix not only outperforms existing LLM-based hyper-heuristics but also matches or exceeds specialized solvers. Code is available at https://github.com/microsoft/HeurAgenix.

Hyperparameter optimization (HPO) aims to identify an optimal hyperparameter configuration (HPC) such that the resulting model generalizes well to unseen data. As the expected generalization error cannot be optimized directly, it is estimated with a resampling strategy, such as holdout or cross-validation. This approach implicitly assumes that minimizing the validation error leads to improved generalization. However, since validation error estimates are inherently stochastic and depend on the resampling strategy, a natural question arises: Can excessive optimization of the validation error lead to overfitting at the HPO level, akin to overfitting in model training based on empirical risk minimization? In this paper, we investigate this phenomenon, which we term overtuning, a form of overfitting specific to HPO. Despite its practical relevance, overtuning has received limited attention in the HPO and AutoML literature. We provide a formal definition of overtuning and distinguish it from related concepts such as meta-overfitting. We then conduct a large-scale reanalysis of HPO benchmark data to assess the prevalence and severity of overtuning. Our results show that overtuning is more common than previously assumed, typically mild but occasionally severe. In approximately 10% of cases, overtuning leads to the selection of a seemingly optimal HPC with worse generalization error than the default or first configuration tried. We further analyze how factors such as performance metric, resampling strategy, dataset size, learning algorithm, and HPO method affect overtuning and discuss mitigation strategies. Our results highlight the need to raise awareness of overtuning, particularly in the small-data regime, indicating that further mitigation strategies should be studied.

Solving systems of ordinary differential equations (ODEs) is essential when it comes to understanding the behavior of dynamical systems. Yet, automated solving remains challenging, in particular for nonlinear systems. Computer algebra systems (CASs) provide support for solving ODEs by first simplifying them, in particular through the use of Lie point symmetries. Finding these symmetries is, however, itself a difficult problem for CASs. Recent works in symbolic regression have shown promising results for recovering symbolic expressions from data. Here, we adapt search-based symbolic regression to the task of finding generators of Lie point symmetries. With this approach, we can find symmetries of ODEs that existing CASs cannot find.

Electromagnetic structure (EMS) design plays a critical role in developing advanced antennas and materials, but remains challenging due to high-dimensional design spaces and expensive evaluations. While existing methods commonly employ high-quality predictors or generators to alleviate evaluations, they are often data-intensive and struggle with real-world scale and budget constraints. To address this, we propose a novel method called Progressive Quadtree-based Search (PQS). Rather than exhaustively exploring the high-dimensional space, PQS converts the conventional image-like layout into a quadtree-based hierarchical representation, enabling a progressive search from global patterns to local details. Furthermore, to lessen reliance on highly accurate predictors, we introduce a consistency-driven sample selection mechanism. This mechanism quantifies the reliability of predictions, balancing exploitation and exploration when selecting candidate designs. We evaluate PQS on two real-world engineering tasks, i.e., Dual-layer Frequency Selective Surface and High-gain Antenna. Experimental results show that our method can achieve satisfactory designs under limited computational budgets, outperforming baseline methods. In particular, compared to generative approaches, it cuts evaluation costs by 75-85%, effectively saving 20.27-38.80 days of product designing cycle.

In this work, we investigate how autonomous agents, organized into tribes, learn to use communication signals to coordinate their activities and enhance their collective efficiency. Using the NEC-DAC (Neurally Encoded Culture - Distributed Autonomous Communicators) system, where each agent is equipped with its own neural network for decision-making, we demonstrate how these agents develop a shared behavioral system -- akin to a culture -- through learning and signalling. Our research focuses on the self-organization of culture within these tribes of agents and how varying communication strategies impact their fitness and cooperation. By analyzing different social structures, such as authority hierarchies, we show that the culture of cooperation significantly influences the tribe's performance. Furthermore, we explore how signals not only facilitate the emergence of culture but also enable its transmission across generations of agents. Additionally, we examine the benefits of coordinating behavior and signaling within individual agents' neural networks.

Fully re-orientable small spacecraft are now supported by commercial technologies, allowing them to point their instruments in any direction and capture images, with short notice. When combined with improved onboard processing, and implemented on a constellation of inter-communicable satellites, this intelligent agility can significantly increase responsiveness to transient or evolving phenomena. We demonstrate a ground-based and onboard algorithmic framework that combines orbital mechanics, attitude control, inter-satellite communication, intelligent prediction and planning to schedule the time-varying, re-orientation of agile, small satellites in a constellation. Planner intelligence is improved by updating the predictive value of future space-time observations based on shared observations of evolving episodic precipitation and urban flood forecasts. Reliable inter-satellite communication within a fast, dynamic constellation topology is modeled in the physical, access control and network layer. We apply the framework on a representative 24-satellite constellation observing 5 global regions. Results show appropriately low latency in information exchange (average within 1/3rd available time for implicit consensus), enabling the onboard scheduler to observe ~7% more flood magnitude than a ground-based implementation. Both onboard and offline versions performed ~98% better than constellations without agility.

Recent deep reinforcement learning methods have achieved remarkable success in solving multi-objective combinatorial optimization problems (MOCOPs) by decomposing them into multiple subproblems, each associated with a specific weight vector. However, these methods typically treat all subproblems equally and solve them using a single model, hindering the effective exploration of the solution space and thus leading to suboptimal performance. To overcome the limitation, we propose POCCO, a novel plug-and-play framework that enables adaptive selection of model structures for subproblems, which are subsequently optimized based on preference signals rather than explicit reward values. Specifically, we design a conditional computation block that routes subproblems to specialized neural architectures. Moreover, we propose a preference-driven optimization algorithm that learns pairwise preferences between winning and losing solutions. We evaluate the efficacy and versatility of POCCO by applying it to two state-of-the-art neural methods for MOCOPs. Experimental results across four classic MOCOP benchmarks demonstrate its significant superiority and strong generalization.

Training Artificial Neural Networks (ANNs) with Stochastic Gradient Descent (SGD) frequently encounters difficulties, including substantial computing expense and the risk of converging to local optima, attributable to its dependence on partial weight gradients. Therefore, this work investigates Particle Swarm Optimization (PSO) and Genetic Algorithms (GAs) - two population-based Metaheuristic Optimizers (MHOs) - as alternatives to SGD to mitigate these constraints. A hybrid PSO-SGD strategy is developed to improve local search efficiency. The findings indicate that the hybrid PSO-SGD technique decreases the median training MSE by 90 to 95 percent relative to conventional GA and PSO across various network sizes (e.g., from around 0.02 to approximately 0.001 in the Sphere function). RMHC attains substantial enhancements, reducing MSE by roughly 85 to 90 percent compared to GA. Simultaneously, RS consistently exhibits errors exceeding 0.3, signifying subpar performance. These findings underscore that hybrid and evolutionary procedures significantly improve training efficiency and accuracy compared to conventional optimization methods and imply that the Building Block Hypothesis (BBH) may still be valid, indicating that advantageous weight structures are retained during evolutionary search.

Drawing inspiration from our human brain that designs different neurons for different tasks, recent advances in deep learning have explored modifying a network's neurons to develop so-called task-driven neurons. Prototyping task-driven neurons (referred to as NeuronSeek) employs symbolic regression (SR) to discover the optimal neuron formulation and construct a network from these optimized neurons. Along this direction, this work replaces symbolic regression with tensor decomposition (TD) to discover optimal neuronal formulations, offering enhanced stability and faster convergence. Furthermore, we establish theoretical guarantees that modifying the aggregation functions with common activation functions can empower a network with a fixed number of parameters to approximate any continuous function with an arbitrarily small error, providing a rigorous mathematical foundation for the NeuronSeek framework. Extensive empirical evaluations demonstrate that our NeuronSeek-TD framework not only achieves superior stability, but also is competitive relative to the state-of-the-art models across diverse benchmarks. The code is available at https://github.com/HanyuPei22/NeuronSeek.