This paper introduces the concept of a mean for trajectories and multi-object trajectories (defined as sets or multi-sets of trajectories) along with algorithms for computing them. Specifically, we use the Fréchet mean, and metrics based on the optimal sub-pattern assignment (OSPA) construct, to extend the notion of average from vectors to trajectories and multi-object trajectories. Further, we develop efficient algorithms to compute these means using greedy search and Gibbs sampling. Using distributed multi-object tracking as an application, we demonstrate that the Fréchet mean approach to multi-object trajectory consensus significantly outperforms state-of-the-art distributed multi-object tracking methods.

We propose an efficient motion planning method designed to efficiently find collision-free trajectories for multiple manipulators. While multi-manipulator systems offer significant advantages, coordinating their motions is computationally challenging owing to the high dimensionality of their composite configuration space. Conflict-Based Search (CBS) addresses this by decoupling motion planning, but suffers from subsequent conflicts incurred by resolving existing conflicts, leading to an exponentially growing constraint tree of CBS. Our proposed method is based on repulsive trajectory modification within the two-level structure of CBS. Unlike conventional CBS variants, the low-level planner applies a gradient descent approach using an Artificial Potential Field. This field generates repulsive forces that guide the trajectory of the conflicting manipulator away from those of other robots. As a result, subsequent conflicts are less likely to occur. Additionally, we develop a strategy that, under a specific condition, directly attempts to find a conflict-free solution in a single step without growing the constraint tree. Through extensive tests including physical robot experiments, we demonstrate that our method consistently reduces the number of expanded nodes in the constraint tree, achieves a higher success rate, and finds a solution faster compared to Enhanced CBS and other state-of-the-art algorithms.

Bio-inspired algorithms utilize natural processes such as evolution, swarm behavior, foraging, and plant growth to solve complex, nonlinear, high-dimensional optimization problems. However, a plethora of these algorithms require a more rigorous review before making them applicable to the relevant fields. This survey categorizes these algorithms into eight groups: evolutionary, swarm intelligence, physics-inspired, ecosystem and plant-based, predator-prey, neural-inspired, human-inspired, and hybrid approaches, and reviews their principles, strengths, novelty, and critical limitations. We provide a critique on the novelty issues of many of these algorithms. We illustrate some of the suitable usage of the prominent algorithms in machine learning, engineering design, bioinformatics, and intelligent systems, and highlight recent advances in hybridization, parameter tuning, and adaptive strategies. Finally, we identify open challenges such as scalability, convergence, reliability, and interpretability to suggest directions for future research. This work aims to serve as a resource for both researchers and practitioners interested in understanding the current landscape and future directions of reliable and authentic advancement of bio-inspired algorithms.

Discovering valid and meaningful mathematical equations from observed data plays a crucial role in scientific discovery. While this task, symbolic regression, remains challenging due to the vast search space and the trade-off between accuracy and complexity. In this paper, we introduce DiffuSR, a pre-training framework for symbolic regression built upon a continuous-state diffusion language model. DiffuSR employs a trainable embedding layer within the diffusion process to map discrete mathematical symbols into a continuous latent space, modeling equation distributions effectively. Through iterative denoising, DiffuSR converts an initial noisy sequence into a symbolic equation, guided by numerical data injected via a cross-attention mechanism. We also design an effective inference strategy to enhance the accuracy of the diffusion-based equation generator, which injects logit priors into genetic programming. Experimental results on standard symbolic regression benchmarks demonstrate that Dif-fuSR achieves competitive performance with state-of-the-art autoregressive methods and generates more interpretable and diverse mathematical expressions.

The performance of Conflict-Driven Clause Learning solvers hinges on internal heuristics, yet the heterogeneity of SA T problems makes a single, universally optimal configuration unattainable. While prior automated methods can find specialized configurations for specific problem families, this dataset-specific approach lacks generalizability and requires costly re-optimization for new problem types. We introduce DaSA Thco, a framework that addresses this challenge by learning a generalizable mapping from instance features to tailored heuristic ensembles, enabling a train-once, adapt-broadly model. Our framework uses a Large Language Model, guided by systematically defined Problem Archetypes, to generate a diverse portfolio of specialized heuristic ensembles and subsequently learns an adaptive selection mechanism to form the final mapping. Experiments show that DaSA Thco achieves superior performance and, most notably, demonstrates robust out-of-domain generalization where non-adaptive methods show limitations. Our work establishes a more scalable and practical path toward automated algorithm design for complex, configurable systems.

There are currently two well established domains for studying general problem solving. The first describes strategies used by humans on both experimental and real-world tasks. Human problem solving is captured through a number of frameworks including skill acquisition [1] and automaticity [2], the application of expert knowledge [3, 4], the use of heuristics [5, 6], reinforcement learning and conditioning [7, 8], Bayesian inference [9, 10], analogy making [11, 12], collective intelligence and cognition [13, 14], simulation intelligence [15], the use of external representations [16, 17] and the synergy of mind and matter through exbodiment [18]. The second domain, computational problem solving, investigates algorithms that enable computers to tackle problems effectively . Within this domain, two branches especially pertinent to the present question are: (i) computational complexity theory, which analyzes the resources (time, memory, etc.) required to solve problems as functions of input size, typically in the asymptotic limit; and (ii) the study of search algorithms, which seeks efficient solutions to specific tasks (e.g., games and puzzles) by exploiting the combinatorial structure of state spaces, often via heuristics [19-22].

Standard evaluation protocols in robotic manipulation typically assess policy performance over curated, in-distribution test sets, offering limited insight into how systems fail under plausible variation. We introduce Geometric Red-Teaming (GRT), a red-teaming framework that probes robustness through object-centric geometric perturbations, automatically generating CrashShapes -- structurally valid, user-constrained mesh deformations that trigger catastrophic failures in pre-trained manipulation policies. The method integrates a Jacobian field-based deformation model with a gradient-free, simulator-in-the-loop optimization strategy. Across insertion, articulation, and grasping tasks, GRT consistently discovers deformations that collapse policy performance, revealing brittle failure modes missed by static benchmarks. By combining task-level policy rollouts with constraint-aware shape exploration, we aim to build a general purpose framework for structured, object-centric robustness evaluation in robotic manipulation. We additionally show that fine-tuning on individual CrashShapes, a process we refer to as blue-teaming, improves task success by up to 60 percentage points on those shapes, while preserving performance on the original object, demonstrating the utility of red-teamed geometries for targeted policy refinement. Finally, we validate both red-teaming and blue-teaming results with a real robotic arm, observing that simulated CrashShapes reduce task success from 90% to as low as 22.5%, and that blue-teaming recovers performance to up to 90% on the corresponding real-world geometry -- closely matching simulation outcomes. Videos and code can be found on our project website: https://georedteam.github.io/ .

Image-to-image translation has emerged as a powerful technique in medical imaging, enabling tasks such as image denoising and cross-modality conversion. However, it suffers from limitations in handling out-of-distribution samples without causing performance degradation. To address this limitation, we propose a novel Test-Time Adaptation (TTA) framework that dynamically adjusts the translation process based on the characteristics of each test sample. Our method introduces a Reconstruction Module to quantify the domain shift and a Dynamic Adaptation Block that selectively modifies the internal features of a pretrained translation model to mitigate the shift without compromising the performance on in-distribution samples that do not require adaptation. We evaluate our approach on two medical image-to-image translation tasks: low-dose CT denoising and T1 to T2 MRI translation, showing consistent improvements over both the baseline translation model without TTA and prior TTA methods. Our analysis highlights the limitations of the state-of-the-art that uniformly apply the adaptation to both out-of-distribution and in-distribution samples, demonstrating that dynamic, sample-specific adjustment offers a promising path to improve model resilience in real-world scenarios. The code is available at: https://github.com/Sample-Aware-TTA/Code.

We propose FACTORS, a framework that combines design of experiments with Shapley decomposition to address performance and stability issues that are sensitive to combinations of training factors. Our approach consistently estimates main effects and two-factor interactions, then integrates them into a risk-adjusted objective function that jointly accounts for uncertainty and cost, enabling reliable selection of configurations under a fixed budget. Effect estimation is implemented through two complementary paths: a plug-in path based on conditional means, and a least-squares path that reconstructs Shapley contributions from samples. These paths are designed to work complementarily even when design density and bias levels differ. By incorporating standardization of estimates, bias correction, and uncertainty quantification, our procedure ensures comparability across heterogeneous factor spaces and designs, while a lightweight search routine yields configurations within practical time even for large factor spaces. On the theoretical side, we provide error decompositions, sample complexity analysis, and upper bounds on optimality gaps. On the interpretive side, we summarize main effects and interactions in map form, highlighting adjustment priorities and safe improvement pathways. Across diverse datasets and design conditions, our approach improves rank preservation and optimal configuration identification, reduces decision-making risks, and offers a tuning foundation that delivers interpretable justification alongside stable performance gains even under budget constraints.

Complex networks have become essential tools for understanding diverse phenomena in social systems, traffic systems, biomolecular systems, and financial systems. Identifying critical nodes is a central theme in contemporary research, serving as a vital bridge between theoretical foundations and practical applications. Nevertheless, the intrinsic complexity and structural heterogeneity characterizing real-world networks, with particular emphasis on dynamic and higher-order networks, present substantial obstacles to the development of universal frameworks for critical node identification. This paper provides a comprehensive review of critical node identification techniques, categorizing them into seven main classes: centrality, critical nodes deletion problem, influence maximization, network control, artificial intelligence, higher-order and dynamic methods. Our review bridges the gaps in existing surveys by systematically classifying methods based on their methodological foundations and practical implications, and by highlighting their strengths, limitations, and applicability across different network types. Our work enhances the understanding of critical node research by identifying key challenges, such as algorithmic universality, real-time evaluation in dynamic networks, analysis of higher-order structures, and computational efficiency in large-scale networks. The structured synthesis consolidates current progress and highlights open questions, particularly in modeling temporal dynamics, advancing efficient algorithms, integrating machine learning approaches, and developing scalable and interpretable metrics for complex systems.