--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.

As a promising physical layer security technique, physical layer key generation (PLKG) enables legitimate users to obtain secret keys from wireless channel without security infrastructures. However, in harsh propagation environments, the channel characteristic becomes unsatisfactory, the key generation rate (KGR) is significantly deteriorated. In this paper, we propose a novel fluid antenna (FA) enabled PLKG system to address this challenge. Specifically, we first derive the closed-form expression of the KGR for FA array, and then jointly optimize the precoding matrix and the antenna positions via a particle swarm optimization (PSO) algorithm. Next, to further reduce the computational complexity of the optimization procedure, we develop an alternating optimization (AO) algorithm, which combines the projected gradient descent (PGD) and the PSO. Simulation results demonstrate that by exploiting the additional spatial degree of freedom (DoF), our FA enabled PLKG system is superior to the benchmarks, such as the conventional fixed-position antenna (FPA) array and the reconfigurable intelligent surface (RIS). It is worth highlighting that compared to the conventional uniform planar antenna (UPA), the FA enabled PLKG achieves a 35.42\% KGR performance improvement under PSO algorithm and a 67.73\% KGR performance improvement under AO algorithm, respectively.

Reliable indoor navigation remains a significant challenge in complex environments, particularly where external positioning signals and dedicated infrastructures are unavailable. This research presents Grid2Guide, a hybrid navigation framework that combines the A* search algorithm with a Small Language Model (SLM) to generate clear, human-readable route instructions. The framework first conducts a binary occupancy matrix from a given indoor map. Using this matrix, the A* algorithm computes the optimal path between origin and destination, producing concise textual navigation steps. These steps are then transformed into natural language instructions by the SLM, enhancing interpretability for end users. Experimental evaluations across various indoor scenarios demonstrate the method's effectiveness in producing accurate and timely navigation guidance. The results validate the proposed approach as a lightweight, infrastructure-free solution for real-time indoor navigation support.

The move-acceptance hyper-heuristic was recently shown to be able to leave local optima with astonishing efficiency (Lissovoi et al., Artificial Intelligence (2023)). In this work, we propose two modifications to this algorithm that demonstrate impressive performances on a large class of benchmarks including the classic Cliff$_d$ and Jump$_m$ function classes. (i) Instead of randomly choosing between the only-improving and any-move acceptance operator, we take this choice via a simple two-state Markov chain. This modification alone reduces the runtime on Jump$_m$ functions with gap parameter $m$ from $Ω(n^{2m-1})$ to $O(n^{m+1})$. (ii) We then replace the all-moves acceptance operator with the operator that only accepts worsenings. Such a, counter-intuitive, operator has not been used before in the literature. However, our proofs show that our only-worsening operator can greatly help in leaving local optima, reducing, e.g., the runtime on Jump functions to $O(n^3 \log n)$ independent of the gap size. In general, we prove a remarkably good runtime of $O(n^{k+1} \log n)$ for our Markov move-acceptance hyper-heuristic on all members of a new benchmark class SEQOPT$_k$, which contains a large number of functions having $k$ successive local optima, and which contains the commonly studied Jump$_m$ and Cliff$_d$ functions for $k=2$.

The discovery of equations from observational data is one of the fundamental pillars of the traditional scientific method. From the work of Johannes Kepler, who inferred the laws of planetary motion from meticulous astronomical observations [1] collected by Tycho Brahe [2], to Isaac Newton's theoretical formulations that consolidated classical mechanics, the process of identifying mathematical relationships underlying natural phenomena has historically been characterized by its manual nature, based essentially on systematic trial-and-error procedures. However, in recent decades, the advent of Big Data, characterized by the production of an immense volume of complex, mostly nonlinear, data, in several fields has driven a new search for physical laws. Faced with the need to analyze these data sets to understand their intrinsic structure and derive symbolic representations that capture the integral behavior of a system, the demand for advanced analytical methods has become growing and indispensable. With the emergence of modern computational techniques, this process has undergone a radical transformation, driving the widespread development and use of various regression techniques.

In post-disaster scenarios, rapid and efficient delivery of medical resources is critical and challenging due to severe damage to infrastructure. To provide an optimized solution, we propose a cooperative trajectory optimization and task allocation framework leveraging unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs). This study integrates a Genetic Algorithm (GA) for efficient task allocation among multiple UAVs and UGVs, and employs an informed-RRT* (Rapidly-exploring Random Tree Star) algorithm for collision-free trajectory generation. Further optimization of task sequencing and path efficiency is conducted using Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Simulation experiments conducted in a realistic post-disaster environment demonstrate that our proposed approach significantly improves the overall efficiency of medical rescue operations compared to traditional strategies. Specifically, our method reduces the total mission completion time to 26.7 minutes for a 15-task scenario, outperforming K-Means clustering and random allocation by over 73%. Furthermore, the framework achieves a substantial 15.1% reduction in total traveled distance after CMA-ES optimization. The cooperative utilization of UAVs and UGVs effectively balances their complementary advantages, highlighting the system's scalability and practicality for real-world deployment.

Workforce scheduling in the healthcare sector is a significant operational challenge, characterized by fluctuating patient loads, diverse clinical skills, and the critical need to control labor costs while upholding high standards of patient care. This problem is inherently multi-objective, demanding a delicate balance between competing goals: minimizing payroll, ensuring adequate staffing for patient needs, and accommodating staff preferences to mitigate burnout. We propose a Multi-objective Genetic Algorithm (MOO-GA) that models the hospital unit workforce scheduling problem as a multi-objective optimization task. Our model incorporates real-world complexities, including hourly appointment-driven demand and the use of modular shifts for a multi-skilled workforce. By defining objective functions for cost, patient care coverage, and staff satisfaction, the GA navigates the vast search space to identify a set of high-quality, non-dominated solutions. Demonstrated on datasets representing a typical hospital unit, the results show that our MOO-GA generates robust and balanced schedules. On average, the schedules produced by our algorithm showed a 66\% performance improvement over a baseline that simulates a conventional, manual scheduling process. This approach effectively manages trade-offs between critical operational and staff-centric objectives, providing a practical decision support tool for nurse managers and hospital administrators.