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This study explores the Traveling Salesman Problem (TSP) by applying both deterministic and stochastic algorithms. The deterministic algorithms include the Greedy Algorithm (GrA), Brute Force (BF), Branch and Bound (B&B), Dynamic Programming (DP), and Nearest Neighbor (NN), while the stochastic algorithms include Genetic Algorithm (GA), Ant Colony Optimization (ACO), Simulated Annealing (SA), and Particle Swarm Optimization (PSO). The research addresses limitations in the practical application of optimization algorithms in the tourism industry by focusing on minimizing travel distance, time, and cost across eight tourist locations using multi-objective optimization. Unlike most studies that focus solely on theoretical models, this work offers a comprehensive real-world comparison of algorithm performance for tourism route planning. The analysis shows that BF, B&B, and DP achieve optimal results in distance, time, and cost. Among stochastic methods, SA performs competitively alongside GA and PSO for smaller datasets. Notably, DP emerges as the most practical solution for small to medium-sized TSP instances, balancing computational efficiency and optimality. This highlights DP's potential as an effective and efficient algorithm for real-world tourism applications, offering optimal solutions with minimal execution time.

In recent years, the collaborative operation of multiple unmanned aerial vehicles (UAVs) has been an important advancement in drone technology. The research on multi-UAV collaborative flight path planning has garnered widespread attention in the drone field, demonstrating unique advantages in complex task execution, large-scale monitoring, and disaster response. As one of the core technologies of multi-UAV collaborative operations, the research and technological progress in trajectory planning algorithms directly impact the efficiency and safety of UAV collaborative operations. This paper first reviews the application and research progress of path-planning algorithms based on centralized and distributed control, as well as heuristic algorithms in multi-UAV collaborative trajectory planning. It then summarizes the main technical challenges in multi-UAV path planning and proposes countermeasures for multi-UAV collaborative planning in government, business, and academia. Finally, it looks to future research directions, providing ideas for subsequent studies in multi-UAV collaborative trajectory planning technology.

Loss functions with a large number of saddle points are one of the major obstacles for training modern machine learning (ML) models efficiently. First-order methods such as gradient descent (GD) are usually the methods of choice for training ML models. However, these methods converge to saddle points for certain choices of initial guesses. In this paper, we propose a modification of the recently proposed Laplacian smoothing gradient descent (LSGD) [Osher et al., arXiv:1806.06317 ], called modified LSGD (mLSGD), and demonstrate its potential to avoid saddle points without sacrificing the convergence rate. Our analysis is based on the attraction region, formed by all starting points for which the considered numerical scheme converges to a saddle point. We investigate the attraction region’s dimension both analytically and numerically. For a canonical class of quadratic functions, we show that the dimension of the attraction region for mLSGD is$\\lfloor (n-1)/2\\rfloor$, and hence it is significantly smaller than that of GD whose dimension is$n-1$.

Tensor wheel (TW) decomposition combines the popular tensor ring and fully connected tensor network decompositions and has achieved excellent performance in tensor completion problem. A standard method to compute this decomposition is the alternating least squares (ALS). However, it usually suffers from slow convergence and numerical instability. In this work, the fast and robust SVD-based algorithms are investigated. Based on a result on TW-ranks, we first propose a deterministic algorithm that can estimate the TW decomposition of the target tensor under a controllable accuracy. Then, the randomized versions of this algorithm are presented, which can be divided into two categories and allow various types of sketching. Numerical results on synthetic and real data show that our algorithms have much better performance than the ALS-based method and are also quite robust. In addition, with one SVD-based algorithm, we also numerically explore the variability of TW decomposition with respect to TW-ranks and the comparisons between TW decomposition and other famous formats in terms of the performance on approximation and compression.

Background Linking mothers to their newborns in health records is crucial for understanding the impact of policies, programs, and medical treatments on intergenerational health outcomes. While previous studies have used shared identifiers for linkage, such data are often unavailable in Medicaid records due to privacy concerns. Existing algorithms are not sufficiently flexible to accommodate Medicaid data from all states and from both Medicaid Analytic Extract (MAX) and Transformed Analytical Files (TAF) data systems. Methods We present a scalable framework and linking algorithm that connects deliveries and infants without relying on names, addresses, or linkage to vital records. First, we confirm our ability to identify newborn beneficiaries and deliveries resulting in live birth across states and over time by comparing our findings to the total number of Medicaid births recorded in the National Vital Statistics System (NVSS). Second, we confirm that our algorithm accommodates variations in Medicaid records over time and across states for MAX and TAF data, supporting matches at different levels of stringency. Finally, we assess the extent to which our algorithm is effective across demographic groups. Results Using data from all 50 states over 9 years, our algorithm linked 11.68 million mother-infant dyads, covering 68% of Medicaid-enrolled infants, over 30% of all U.S. infants. Our linked cohort is approximately representative of the broader population of Medicaid beneficiaries on key observable characteristics including race and ethnicity, age, gender, and region. However, linked beneficiaries are more likely to be white and from the Midwest or Northeast relative to those we are unable to link. Conclusions Despite substantial variation in the nature of Medicaid data across states and over time, it is possible to identify family units in all states between 2011 and 2019 without linking claims to vital records. This algorithm will facilitate research on social determinants of health and the intergenerational effects of medical interventions and public policy.

We provide a new algorithm (called the grid algorithm) designed to generate the image of the attractor of a generalized iterated function system on a finite dimensional space and we compare it with the deterministic algorithm regarding generalized iterated function systems presented by Jaros et al. (Numer. Algorithms 73 , 477–499, 2016 ).

Most works on Support Vector Regression (SVR) focus on kernel or loss functions, with the corresponding support vectors obtained using a fixed-radius ε -tube, affording good predictive performance on datasets. However, the fixed radius limitation prevents the adaptive selection of support vectors according to the data distribution characteristics, compromising the performance of the SVR-based methods. Therefore, this study proposes an “Alterable ε i -Support Vector Regression” ( A ε i -SVR) model by applying a novel ε , named “Alterable ε i ,” to the SVR model. Based on the data point sparsity at each location, the model solves the different ε i at the corresponding position, and thus zoom-in or zoom-out the ε -tube by changing its radius. Such a variable ε -tube strategy diminishes noise and outliers in the dataset, enhancing the prediction performance of the A ε i -SVR model. Therefore, we suggest a novel non-deterministic algorithm to iteratively solve the complex problem of optimizing ε i associated with every location. Extensive experimental results demonstrate that our approach can improve the accuracy and stability on simulated and real data compared with the baseline methods.

We investigated nearest-neighbor density-based clustering for hyperspectral image analysis. Four existing techniques were considered that rely on a K-nearest neighbor (KNN) graph to estimate local density and to propagate labels through algorithm-specific labeling decisions. We first improved two of these techniques, a KNN variant of the density peaks clustering method dpc, and a weighted-mode variant of knnclust, so the four methods use the same input KNN graph and only differ by their labeling rules. We propose two regularization schemes for hyperspectral image analysis: (i) a graph regularization based on mutual nearest neighbors (MNN) prior to clustering to improve cluster discovery in high dimensions; (ii) a spatial regularization to account for correlation between neighboring pixels. We demonstrate the relevance of the proposed methods on synthetic data and hyperspectral images, and show they achieve superior overall performances in most cases, outperforming the state-of-the-art methods by up to 20% in kappa index on real hyperspectral images.

Gathering is a key task in distributed and mobile systems, which becomes significantly harder if some agents are subject to Byzantine faults, known as being the worst ones. We propose here to study the task of Byzantine gathering in an arbitrary graph: despite the presence of Byzantine agents, the goal is to ensure that all the other (good) agents, executing the same algorithm, eventually meet at the same node and stop. Initially, each agent gets as input a different label and some global knowledge that is common to all agents. The agents move in synchronous rounds and communicate with each other only when located at the same node. There are f Byzantine agents. These agents act in an unpredictable way, e.g., they may convey arbitrary informations or forge any label. In the literature, the gathering algorithms working in such a context all have an exponential time complexity in the number n of nodes and the labels of the good agents. In this paper, we design a deterministic algorithm to solve Byzantine gathering in time polynomial in n and the logarithm ℓ of the smallest label of a good agent, provided the agents are a strong team i.e., a team where the number of good agents is at least some quadratic polynomial in f. Our algorithm requires global knowledge that can be coded in O(logloglogn) bits: we prove this size is of optimal order of magnitude to obtain a polynomial time complexity in n and ℓ with strong teams.