Annals of Mathematics and Artificial Intelligence最新文献

The continuous Hopfield network (CHN) has provided a powerful approach to optimization problems and has shown good performance in different domains. However, two primary challenges still remain for this network: defining appropriate parameters and hyperparameters. In this study, our objective is to address these challenges and achieve optimal solutions for combinatorial optimization problems, thereby improving the overall performance of the continuous Hopfield network. To accomplish this, we propose a new technique for tuning the parameters of the CHN by considering its stability. To evaluate our approach, three well-known combinatorial optimization problems, namely, weighted constraint satisfaction problems, task assignment problems, and the traveling salesman problem, were employed. The experiments demonstrate that the proposed approach offers several advantages for CHN parameter tuning and the selection of optimal hyperparameter combinations.

Finding a collision-free feasible path for mobile robots is very important because they are essential in many fields such as healthcare, military, and industry. In this paper, a novel Clustering Obstacles (CO)-based path planning algorithm for mobile robots is presented using a quintic trigonometric Bézier curve and its two shape parameters. The CO-based algorithm forms clusters of geometrically shaped obstacles and finds the cluster centers. Moreover, the proposed waypoint algorithm (WP) finds the waypoints of the predefined skeleton path in addition to the start and destination points in an environment. Based on all these points, the predefined quintic trigonometric Bézier path candidates, taking the skeleton path as their convex hull, are then generated using the shape parameters of this curve. Moreover, the performance of the proposed algorithm is compared with K-Means and agglomerative hierarchical algorithms to obtain the quintic trigonometric Bézier paths desired by the user. The experimental results show that the CO-based path planning algorithm achieves better cluster centers and consequently better collision-free predefined paths.

The k-nearest neighbors (k/NN) algorithm is a simple yet powerful non-parametric classifier that is robust to noisy data and easy to implement. However, with the growing literature on k/NN methods, it is increasingly challenging for new researchers and practitioners to navigate the field. This review paper aims to provide a comprehensive overview of the latest developments in the k/NN algorithm, including its strengths and weaknesses, applications, benchmarks, and available software with corresponding publications and citation analysis. The review also discusses the potential of k/NN in various data science tasks, such as anomaly detection, dimensionality reduction and missing value imputation. By offering an in-depth analysis of k/NN, this paper serves as a valuable resource for researchers and practitioners to make informed decisions and identify the best k/NN implementation for a given application.

A digitized rigid motion is called digitally continuous if two neighbor pixels still stay neighbors after the motion. This concept plays important role when people or computers (artificial intelligence, machine vision) need to recognize the object shown in the image. In this paper, digital rotations of a pixel with its closest neighbors are of our interest. We compare the neighborhood motion map results among the three regular grids, when the center of rotation is the midpoint of a main pixel, a grid point (corner of a pixel) or an edge midpoint. The first measure about the quality of digital rotations is based on bijectivity, e.g., measuring how many of the cases produce bijective and how many produce not bijective neighborhood motion maps (Avkan et. al, 2022). Now, a second measure is investigated, the quality of bijective digital rotations is measured by the digital continuity of the resulted image: we measure how many of the cases are bijective and also digitally continuous. We show that rotations on the triangular grid prove to be digitally continuous at many more real angles and also as a special case, many more integer angles compared to the square grid or to the hexagonal grid with respect to the three different rotation centers.

A digital plane is a digitization of a Euclidean plane. A plane is specified by its normal, which is a 3D vector with integer coordinates, as considered in this case. It is established here that a 3D digital straight line segment, shifted by an integer amount, can produce the digitized plane. 3D plane’s normals are classified based on the Greatest Common Divisor (GCD) of its components, and the net code is calculated separately for each case. Experimental results are provided for several normals. Also, we show that the digital plane segment generated is a connected digital plane. The proposed method mainly involves integer arithmetic.

Hedonic games are a prominent model of coalition formation, in which each agent’s utility only depends on the coalition she resides. The subclass of hedonic games that models the formation of general partnerships (Larson 2018), where all affiliates receive the same utility, is referred to as hedonic games with common ranking property (HGCRP). Aside from their economic motivation, HGCRP came into prominence since they are guaranteed to have core stable solutions that can be found efficiently (Farrell and Scotchmer Q. J. Econ. 103(2), 279–297 1988). We improve upon existing results by proving that every instance of HGCRP has a solution that is Pareto optimal, core stable, and individually stable. The economic significance of this result is that efficiency is not to be totally sacrificed for the sake of stability in HGCRP. We establish that finding such a solution is NP-hard even if the sizes of the coalitions are bounded above by 3; however, it is polynomial time solvable if the sizes of the coalitions are bounded above by 2. We show that the gap between the total utility of a core stable solution and that of the socially-optimal solution (OPT) is bounded above by n, where n is the number of agents, and that this bound is tight. Our investigations reveal that computing OPT is inapproximable within better than (O(n^{1-epsilon })) for any fixed (epsilon > 0), and that this inapproximability lower bound is polynomially tight. However, OPT can be computed in polynomial time if the sizes of the coalitions are bounded above by 2.

A solver’s runtime and the quality of the solutions it generates are strongly influenced by its parameter settings. Finding good parameter configurations is a formidable challenge, even for fixed problem instance distributions. However, when the instance distribution can change over time, a once effective configuration may no longer provide adequate performance. Realtime algorithm configuration (RAC) offers assistance in finding high-quality configurations for such distributions by automatically adjusting the configurations it recommends based on instances seen so far. Existing RAC methods treat the solver as a black box, meaning the solver is given a configuration as input, and it outputs either a solution or runtime as an objective function for the configurator. However, analyzing intermediate output from the solver can enable configurators to avoid wasting time on poorly performing configurations. We propose a gray-box approach that utilizes intermediate output during evaluation and implement it within the RAC method Contextual Preselection with Plackett-Luce (CPPL blue). We apply cost-sensitive machine learning with pairwise comparisons to determine whether ongoing evaluations can be terminated to free resources. We compare our approach to a black-box equivalent on several experimental settings and show that our approach reduces the total solving time in several scenarios and improves solution quality in an additional scenario.

In this paper, we develop two SVM-based classifiers named stable nested one-class support vector machines (SN-1SVMs) and decoupled margin-moment based SVMs (DMMB-SVMs), to predict the specific type of pancreatic carcinoma using quantitative histopathological signatures of images. For each patient, the diagnosis can produce hundreds of images, which can be used to classify the pancreatic tissues into three classes: chronic pancreatitis, intraductal papillary mucinous neoplasms, and pancreatic carcinoma. The proposed two approaches tackle the classification problems from two different perspectives: the SN-1SVM treats each image as a classification point in a nested fashion to predict malignancy of the tissues, while the DMMB-SVM treats each patient as a classification point by assembling information across images. One attractive feature of the DMMB-SVM is that, in addition to utilizing the mean information, it also takes into account the covariance of features extracted from images for each patient. We conduct numerical experiments to evaluate and compare performance of the two methods. It is observed that the SN-1SVM can take advantage of the data structure more effectively, while the DMMB-SVM demonstrates better computational efficiency and classification accuracy. To further improve interpretability of the final classifier, we also consider the (ell _1)-norm in the DMMB-SVM to handle feature selection.

There is a parameter ubiquitous throughout the deep learning world: learning rate. There is likewise a ubiquitous question: what should that learning rate be? The true answer to this question is often tedious and time consuming to obtain, and a great deal of arcane knowledge has accumulated in recent years over how to pick and modify learning rates to achieve optimal training performance. Moreover, the long hours spent carefully crafting the perfect learning rate can come to nothing the moment your network architecture, optimizer, dataset, or initial conditions change ever so slightly. But it need not be this way. We propose a new answer to the great learning rate question: the Autonomous Learning Rate Controller. Find it at https://github.com/fastestimator/ARC/tree/v2.0.

Strategic spatial planning is becoming more popular around the world as a decision-making way to build a unified vision for directing the medium- to long-term development of land/marine areas. Recently, the study of marine areas in terms of spatial planning such as Marine Spatial Planning (MSP) has received much attention. One of the challenging issues in MSP is to make a balance between determining the ideal zone for a new activity while also considering the locations of existing activities. This spatial zoning problem for multi-uses with multiple objectives could be formulated as optimization models. This paper presents and compares the results of two multi-objective evolutionary-based algorithms (MOEAs), Synchronous Hypervolume-based non-dominated sorting genetic algorithm-II (SH-NSGA-II) which is an extension of NSGA-II and a memetic algorithm (MA) in which SH-NSGA-II is enhanced with a local search. These proposed algorithms are used to solve the multi-objective spatial zoning optimization problem, which seeks to maximize the zone interest value assigned to the new activity while simultaneously maximizing its spatial compactness. We introduce several innovations in these proposed algorithms to address the problem constraints and to improve the robustness of the traditional NSGA-II and MA approaches. Unlike traditional ones, a different stop condition, multiple crossover, mutation, and repairing operators, and also a local search operator are developed. A comparative study is presented between the results obtained using both algorithms. To guarantee robust results for both algorithms, their parameters are calibrated and tuned using the Multi-Response Surface Methodology (MRSM) method. The effective and non-effective components, as well as the validity of the regression models, are determined using analysis of variance (ANOVA). Although SH-NSGA-II has revealed a good efficiency, its performance is still improved using a local search scheme within SH-NSGA-II, which is specially tailored to the problem characteristics. The two methods are designed for raster data.