The paper proposes an efficient algebraic solution to the problem of forward kinematics for a general Stewart-Gough platform. The problem involves determining all possible postures of a mobile platform connected to a fixed base by six legs, given the leg lengths and the internal geometries of the platform and base. The problem is known to have 40 solutions (whether real or complex). The proposed algorithm consists of three main steps: (i) a specific sparse matrix of size 293x362 (the elimination template) is constructed from the coefficients of the polynomial system describing the platform's kinematics; (ii) the PLU decomposition of this matrix is used to construct a pair of 69x69 matrices; (iii) all 40 solutions (including complex ones) are obtained by computing the generalized eigenvectors of this matrix pair. The proposed algorithm is numerically robust, computationally efficient, and straightforward to implement - requiring only standard linear algebra decompositions. MATLAB, Julia, and Python implementations of the algorithm will be made publicly available.

--This paper presents the design of a pose estimator for a four wheel independent steer four wheel independent drive (4WIS4WID) wall climbing mobile robot, based on the fusion of multimodal measurements, including wheel odometry, visual odometry, and an inertial measurement unit (IMU) data using Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). The pose estimator is a critical component of wall climbing mobile robots, as their operational environment involves carrying precise measurement equipment and maintenance tools in construction, requiring information about pose on the building at the time of measurement. Due to the complex geometry and material properties of building fac ades, the use of traditional localization sensors such as laser, ultrasonic, or radar is often infeasible for wall-climbing robots. Moreover, GPS-based localization is generally unreliable in these environments because of signal degradation caused by reinforced concrete and electromagnetic interference. Consequently, robot odometry remains the primary source of velocity and position information, despite being susceptible to drift caused by both systematic and non-systematic errors. The calibrations of the robot's systematic parameters were conducted using nonlinear optimization and Levenberg-Marquardt methods as Newton-Gauss and gradient-based model fitting methods, while Genetic algorithm and Particle swarm were used as stochastic based methods for kinematic parameter calibration. Performance and results of the calibration methods and pose estimators were validated in detail with experiments on the experimental mobile wall climbing robot.

Even with the recent theoretical advancements that dramatically reduced the complexity of Integer Programming (IP), heuristics remain the dominant problem-solvers for this difficult category. This study seeks to establish the groundwork for Integer Evolution Strategies (IESs), a class of randomized search heuristics inherently designed for continuous spaces. IESs already excel in treating IP in practice, but accomplish it via discretization and by applying sophisticated patches to their continuous operators, while persistently using the $\ell_2$-norm as their operation pillar. We lay foundations for discrete search, by adopting the $\ell_1$-norm, accounting for the suitable step-size, and questioning alternative measures to quantify correlations over the integer lattice. We focus on mutation distributions for unbounded integer decision variables. We briefly discuss a couple of candidate discrete probabilities induced by the uniform and binomial distributions, which we show to possess less appealing theoretical properties, and then narrow down to the Truncated Normal (TN) and Double Geometric (DG) distributions. We explore their theoretical properties, including entropy functions, and propose a procedure to generate scalable correlated mutation distributions. Our investigations are accompanied by extensive numerical simulations, which consistently support the claim that the DG distribution is better suited for unbounded integer search. We link our theoretical perspective to empirical evidence indicating that an IES with correlated DG mutations outperformed other strategies over non-separable quadratic IP. We conclude that while the replacement of the default TN distribution by the DG is theoretically justified and practically beneficial, the truly crucial change lies in adopting the $\ell_1$-norm over the $\ell_2$-norm.

Discovering diverse visual patterns in continuous cellular automata (CA) is challenging due to the vastness and redundancy of high-dimensional behavioral spaces. Traditional exploration methods like Novelty Search (NS) expand locally by mutating known novel solutions but often plateau when local novelty is exhausted, failing to reach distant, unexplored regions. We introduce Expedition and Expansion (E&E), a hybrid strategy where exploration alternates between local novelty-driven expansions and goal-directed expeditions. During expeditions, E&E leverages a Vision-Language Model (VLM) to generate linguistic goals--descriptions of interesting but hypothetical patterns that drive exploration toward uncharted regions. By operating in semantic spaces that align with human perception, E&E both evaluates novelty and generates goals in conceptually meaningful ways, enhancing the interpretability and relevance of discovered behaviors. Tested on Flow Lenia, a continuous CA known for its rich, emergent behaviors, E&E consistently uncovers more diverse solutions than existing exploration methods. A genealogical analysis further reveals that solutions originating from expeditions disproportionately influence long-term exploration, unlocking new behavioral niches that serve as stepping stones for subsequent search. These findings highlight E&E's capacity to break through local novelty boundaries and explore behavioral landscapes in human-aligned, interpretable ways, offering a promising template for open-ended exploration in artificial life and beyond.

In this respect, existing selection hyper-heuristics primarily focus on an adaptive selection of low-level heuristics (LLHs) from a predefined set. In contrast, we concentrate on the composition of this set and its strategic transformations. We systematically analyze transformations based on three key principles: solution acceptance, LLH repetitions, and perturbation intensity, i.e., the proportion of a solution affected by a perturbative LLH. We demonstrate the raw effects of our transformations on a trivial unbiased random selection mechanism. With an appropriately constructed transformation, this trivial method outperforms all available state-of-the-art hyper-heuristics on three challenging real-world domains and finds 11 new best-known solutions. The same method is competitive with the winner of the CHeSC competition, commonly used as the standard cross-domain benchmark. Moreover, we accompany several recent hyper-heuristics with such strategic transformations. Using this approach, we outperform the current state-of-the-art methods on both the CHeSC benchmark and real-world domains while often simplifying their designs.

Large Language Models (LLMs) excel at generating synthetic data, but ensuring its quality and diversity remains challenging. We propose Genetic Prompt, a novel framework that combines genetic algorithms with LLMs to augment synthetic data generation. Our approach treats semantic text attributes as gene sequences and leverages the LLM to simulate crossover and mutation operations. This genetic process enhances data quality and diversity by creating novel attribute combinations, yielding synthetic distributions closer to real-world data. To optimize parent selection, we also integrate an active learning scheme that expands the offspring search space. Our experiments on multiple NLP tasks reveal several key findings: Genetic Prompt not only significantly outperforms state-of-the-art baselines but also shows robust performance across various generator model sizes and scales. Moreover, we demonstrate that fusing our synthetic data with the original training set significantly boosts downstream model performance, particularly for class-imbalanced scenarios. Our findings validate that Genetic Prompt is an effective method for producing high-quality synthetic data for a wide range of NLP applications.

--Appointment scheduling is a great challenge in healthcare operations management. Appointment rules (AR) provide medical practitioners with a simple yet effective tool to determine patient appointment times. Genetic programming (GP) can be used to evolve ARs. However, directly applying GP to design ARs may lead to rules that are difficult for end-users to interpret and trust. A key reason is that GP is unaware of the dimensional consistency, which ensures that the evolved rules align with users' domain knowledge and intuitive understanding. In this paper, we develop a new dimensionally aware GP algorithm with dimension repair to evolve ARs with dimensional consistency and high performance. A key innovation of our method is the dimension repair procedure, which optimizes the dimensional consistency of an expression tree while minimizing structural changes and ensuring that its output dimension meets the problem's requirements. We formulate the task as a mixed-integer linear programming model that can be efficiently solved using common mathematical programming methods. With the support of the dimension repair procedure, our method can explore a wider range of AR structures by temporarily breaking the dimensional consistency of individuals, and then restoring it without altering their overall structure, thereby identifying individuals with greater potential advantages. We evaluated the proposed method in a comprehensive set of simulated clinics. The experimental results demonstrate that our approach managed to evolve high-quality ARs that significantly outperform not only the manually designed ARs but also existing state-of-the-art dimensionally aware GP methods in terms of both objective values and dimensional consistency. In addition, we analyzed the semantics of the evolved ARs, providing insight into the design of more effective and interpretable ARs. PPOINTMENT scheduling plays a crucial role in healthcare systems, impacting clinical, operational, and financial performance. A well-designed appointment system can improve the efficiency of medical providers and patient satisfaction by smoothing demand and mitigating uncertainty in patient arrivals [1]. Patients expect fast and timely service and find long wait times increasingly difficult to tolerate. Medical providers face pressure to efficiently utilize resources, including doctors' availability and expensive diagnostic machines.

Neural architecture search (NAS) is an attractive approach to automate the design of optimized architectures but is constrained by high computational budget, especially when optimizing for multiple, important conflicting objectives. To address this, an adaptive Co-Kriging-assisted multi-fidelity multi-objective NAS algorithm is proposed to further reduce the computational cost of NAS by incorporating a clustering-based local multi-fidelity infill sampling strategy, enabling efficient exploration of the search space for faster convergence. This algorithm is further accelerated by the use of a novel continuous encoding method to represent the connections of nodes in each cell within a generalized cell-based U-Net backbone, thereby decreasing the search dimension (number of variables). Results indicate that the proposed NAS algorithm outperforms previously published state-of-the-art methods under limited computational budget on three numerical benchmarks, a 2D Darcy flow regression problem and a CHASE_DB1 biomedical image segmentation problem. The proposed method is subsequently used to create a wind velocity regression model with application in urban modelling, with the found model able to achieve good prediction with less computational complexity. Further analysis revealed that the NAS algorithm independently identified principles undergirding superior U-Net architectures in other literature, such as the importance of allowing each cell to incorporate information from prior cells.

Microbiomes not only underpin Earth's biogeochemical cycles but also play crucial roles in both engineered and natural ecosystems, such as the soil, wastewater treatment, and the human gut. However, microbiome engineering faces significant obstacles to surmount to deliver the desired improvements in microbiome control. Here, we use the backpropagation neural network (BPNN), optimized through differential evolution (DE-BP), to predict the microbial composition of activated sludge (AS) systems collected from wastewater treatment plants (WWTPs) located worldwide. Furthermore, we introduce a novel clustering algorithm termed Directional Position Nonlinear Emotional Preference Migration Behavior Clustering (DPNG-EPMC). This method is applied to conduct a clustering analysis of WWTPs across various feature attributes. Finally, we employ the Similar Time Generative Adversarial Networks (SiTime-GAN), to synthesize novel microbial compositions and feature attributes data. As a result, we demonstrate that the DE-BP model can provide superior predictions of the microbial composition. Additionally, we show that the DPNG-EPMC can be applied to the analysis of WWTPs under various feature attributes. Finally, we demonstrate that the SiTime-GAN model can generate valuable incremental synthetic data. Our results, obtained through predicting the microbial community and conducting analysis of WWTPs under various feature attributes, develop an understanding of the factors influencing AS communities.

In this paper, we propose an evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed Operator learning Network, which is a novel operator learning network to efficiently solve parametric partial differential equations. In forward and inverse settings, this operator learning network only admits minimum requirement of noisy observational data. While physics-informed neural networks and operator learning approaches such as Deep Operator Networks and Fourier Neural Operators offer promising alternatives to traditional numerical solvers, they struggle with balancing operator and physics losses, maintaining robustness under noisy or sparse data, and providing uncertainty quantification. The proposed framework addresses these limitations by integrating: (i) evolutionary multi-objective optimization to adaptively balance operator and physics-based losses in the Pareto front; (ii) replica exchange stochastic gradient Langevin dynamics to improve global parameter-space exploration and accelerate convergence; and (iii) built-in Bayesian uncertainty quantification from stochastic sampling. The proposed operator learning method is tested numerically on several different problems including one-dimensional Burgers equation and the time-fractional mixed diffusion-wave equation. The results indicate that our framework consistently outperforms the general operator learning methods in accuracy, noise robustness, and the ability to quantify uncertainty.