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European Journal of Operational Research 2025年第2期326卷 220-233页

作者： Rolim, Gustavo Alencar Tomazella, Caio Paziani Nagano, Marcelo Seido Department of Production Engineering Sao Carlos School of Engineering University of Sao Paulo Sao Carlos Brazil Department of Applied Mathematics and Statistics Institute of Mathematical and Computer Sciences University of Sao Paulo Sao Carlos Brazil Department of Production Engineering Federal University of Sao Carlos Sao Carlos Brazil

Motivated by semiconductor applications, where wafer lots are grouped into families and processed on batch machines, this paper addresses a generalized unrelated parallel-batch scheduling problem. The goal is to minimize total completion time (flow time) while considering family- and machine-dependent setup times. We propose a mixed-integer programming formulation, establish a necessary condition for optimal schedules, and develop a polynomial-time heuristic for batching and sequencing. We also evaluate Q-Learning, a model-free reinforcement learning algorithm, for neighborhood selection within two Simulated Annealing-based metaheuristics: Stochastic Local Search (SLS) and Adaptive Large Neighborhood Search (ALNS). Results show that SLS and ALNS achieve better solutions and faster convergence compared to existing approaches. Finally, we conclude that while Q-Learning has the potential to improve solution quality in certain cases, it also increases the complexity of the algorithms, making them harder to configure and scale. © 2025 Elsevier B.V.

关键词： Simulated annealing

Hybrid Block Numerical Algorithm for Direct Solutions of Ordinary Differential Equations of the Third and Fourth Orders

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Hybrid Block Numerical Algorithm for Direct Solutions of Ord...

Science, engineering and Business for Sustainable Development Goals (SEB-SDG), International Conference on

作者： Ezekiel Olaoluwa Omole Ogunware Bankola Gbenga Florence Dami Ayegbusi Peter Onu Tosin Oreyeni Kehinde Peter Ajewole Department of Physical Science Mathematics Programme Landmark University Omu-Aran Nigeria Department of Mathematics and Statistics Joseph Ayo Babalola University Ikeji - Arakeji Nigeria Department of Mathematics First Technical University Ibadan Oyo State Nigeria Department of Mechanical Engineering (Mechatronics) Landmark University Omu-Aran Nigeria Department of Physical Science Mathematics Programme Unit Precious Cornerstone University Ibadan Oyo State Nigeria

ISBN: (数字)9798350358155

ISBN: (纸本)9798350358162

This article examines a single, effective hybrid block numerical technique for solving initial value problems of orders three and four. The novel technique was derived by using an interpolating polynomial that was the power series approximation solution, together with an interpolation and collocation approach. The block's numerical integrators were obtained by assessing the non-interpolating points in the chosen integration interval. The theoretical analysis of the techniques was examined in line with the already established rules, and the outcome shows that it is zero-stable and convergence. When the block's efficiency was put to the test on a few third- and fourth-order ordinary differential equations, the precision of the findings outperformed those of previous approaches.

关键词： Interpolation Accuracy Ordinary differential equations Polynomials Sustainable development Convergence Business

Assessing Potential of Organizations with Fuzzy Entropy

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Operations Research Forum 2023年第1期4卷 11页

作者： Aggarwal, Manish Krishankumar, R. Ravichandran, K.S. Senapati, T. Yager, R.R. School of Artificial Intelligence and Data Science IIT Jodhpur Jodhpur India Digital Humanities IIT Jodhpur Jodhpur India Department of Computer Science and Engineering Amrita School of Computing Amrita Vishwa Vidyapeetham Coimbatore India Department of Mathematics Amrita School of Physical Sciences Amrita Vishwa Vidyapeetham Coimbatore India School of Mathematics and Statistics Southwest University Chongqing Beibei 400715 China Machine Intelligence Institute Iona College New Rochelle 10801 NY United States

Assessing the performance of organizations in the near future has been a challenging problem because of the factors of subjective assessment of the uncertainty. To cater to such applications, a novel form of fuzzy entropy is proposed to unify the concepts of fuzzy entropy and the conventional Shannon’s entropy. The proposed entropy provides a direct and convenient framework to quantify the uncertainty associated with a firm in the near future. It is also shown that the proposed form is amenable in extending the fuzzy entropy functions to the probabilistic-fuzzy domain. Thus, the proposed form of fuzzy entropy finds a special significance in the human decision-making problems. A case study illustrates the applicability of the proposed functions in assessment of future performance of a firm. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

关键词： Attitudinal character Entropy Fuzzy logic Probabilistic-fuzzy Uncertainty

LIPSCHITZ STABILITY OF LEAST-SQUARES PROBLEMS REGULARIZED BY FUNCTIONS WITH C2-CONE REDUCIBLE CONJUGATES

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arXiv 2024年

作者： Cui, Ying Hoheisel, Tim Nghia, Tran T.A. Sun, Defeng Department of Industrial Engineering and Operations Research University of California Berkeley BerkeleyCA94720 United States Department of Mathematics and Statistics McGill University MontréalQCH3A0B9 Canada Department of Mathematics and Statistics Oakland University RochesterMI48309 United States Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong

In this paper, we study Lipschitz continuity of the solution mappings of regularized least-squares problems for which the convex regularizers have (Fenchel) conjugates that are C2-cone reducible. Our approach, by using Robinson’s strong regularity on the dual problem, allows us to obtain new characterizations of Lipschitz stability that rely solely on first-order information, thus bypassing the need to explore second-order information (curvature) of the regularizer. We show that these solution mappings are automatically Lipschitz continuous around the points in question whenever they are locally single-valued. We leverage our findings to obtain new characterizations of full stability and tilt stability for a broader class of convex additive-composite *** Codes 49J52, 49J53, 49K40, 90C25, 90C31 © 2024, CC BY.

关键词： Mapping

cgNA + min: computation of sequence-dependent dsDNA energy-minimising minicircle configurations

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arXiv 2024年

作者： Singh, Raushan Glowacki, Jaroslaw Beaud, Marius Padovano, Federica Manning, Robert S. Maddocks, John H. Department of Mechanical Engineering IIT Madras Chennai600036 India Institute of Mathematics École Polytechnique Fédérale de Lausanne Lausanne1015 Switzerland Haverford College Department of Mathematics and Statistics HaverfordPA19041 United States

DNA minicircles are closed double-stranded DNA (dsDNA) fragments that have been demonstrated to be an important experimental tool to understand supercoiled, or stressed, DNA mechanics, such as nucleosome positioning and DNA-protein interactions. Specific minicircles can be simulated using Molecular Dynamics (MD) simulation. However, the enormous sequence space makes it unfeasible to exhaustively explore the sequence-dependent mechanics of DNA minicircles using either experiment or MD. For linear fragments, the cgNA+ model, a computationally efficient sequence-dependent coarse-grained model using enhanced Curves+ internal coordinates (rigid base plus rigid phosphate) of double-stranded nucleic acids (dsNAs), predicts highly accurate nonlocal sequence-dependent equilibrium distributions for an arbitrary sequence when compared with MD simulations. This article addresses the problem of modeling sequence-dependent topologically closed and, therefore, stressed fragments of dsDNA. We introduce cgNA + min, a computational approach within the cgNA+ framework, which extends the cgNA+ model applicability to compute the sequence-dependent energy minimising configurations of covalently closed dsDNA minicircles of various lengths and linking numbers (Lk). The main computational idea is to derive the appropriate chain rule to express the cgNA+ energy in absolute coordinates involving quaternions where the closure condition is simple to handle. We also present a semi-analytic method for efficiently computing sequence-dependent initial minicircles having arbitrary Lk and length. For different classes and lengths of sequences, we demonstrate that the dsDNA minicircle energies computed using cgNA+min agree well with the energies approximated from experimentally measured J-factor values. Utilizing computational efficiency of cgNA + min, finally, we present minicircle shape, energy, and multiplicity of Lk (and multiplicity of shapes/energies for fixed Lk) for more than 120K random DNA s

关键词： Coarse-grained modeling

Subjective Assessment of the Impact of a Content Adaptive Optimiser for Compressing 4K HDR Content With AV1

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Subjective Assessment of the Impact of a Content Adaptive Op...

IEEE International Conference on Image Processing

作者： Vibhoothi Angeliki Katsenou François Pitié Katarina Domijan Anil Kokaram Department of Electronic and Electrical Engineering Sigmedia Group Trinity College Dublin Ireland Department of Mathematics and Statistics Maynooth University Ireland

Since 2015 video dimensionality has expanded to higher spatial and temporal resolutions and a wider colour gamut. This High Dynamic Range (HDR) content has gained traction in the consumer space as it delivers an enhanced quality of experience. At the same time, the complexity of codecs is growing. This has driven the development of tools for content-adaptive optimisation that achieve optimal rate-distortion performance for HDR video at 4K resolution. While improvements of just a few percentage points in BD-Rate (1-5%) are significant for the streaming media industry, the impact on subjective quality has been less studied especially for HDR/AV1. In this paper, we conduct a subjective quality assessment (42 subjects) of 4K HDR content with a per-clip optimisation strategy. We correlate these subjective scores with existing popular objective metrics used in standard development and show that some perceptual metrics correlate surprisingly well even though they are not tuned for HDR. We find that the DSQCS protocol is too insensitive to categorically compare the methods but the data allows us to make recommendations about the use of experts vs non-experts in HDR studies, and explain the subjective impact of film grain in HDR content under compression.

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Analysis of perturbation factors and fractional order derivatives for the novel singular model using the fractional Meyer wavelet neural networks

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Chaos, Solitons and Fractals: X 2023年 11卷

作者： Sabir, Zulqurnain Ali, Mohamed R. Department of Mathematics and Statistics Hazara University Mansehra Pakistan Faculty of Engineering and Technology Future University in Egypt New Cairo11835 Egypt Department of Computer Science and Mathematics Lebanese American University Beirut Lebanon Basic Engineering Science Department Benha Faculty of Engineering Benha University Banha Egypt

In this study, an analysis of the perturbation factors and fractional order derivatives is performed for the novel singular model. The design of the perturbed fractional order singular model is presented by using the traditional form of the Lane-Emden along with the detail of singular points, fractional order, shape, and perturbed factors. The analysis of the perturbation factors and fractional order terms for the singular model is provided in two steps by taking three different values of the perturbed term as well as fractional order derivatives. The numerical analysis of the perturbation and fractional order terms for the novel fractional Meyer wavelet neural network (FMWNN) along with the global and local search effectiveness of the genetic algorithm (GA) and active-set algorithm (ASA) called as FMWNN-GAASA. The modeling of the FMWNN is presented in terms of mean square error, while the optimization is performed through the GAASA. The authentication, validation, excellence, and correctness of the singular model are observed by using the comparative performances of the obtained and the reference solutions. The stability of the proposed stochastic scheme is observed through the statistical performances for taking large datasets to present the analysis of the perturbation and fractional order terms. © 2023

关键词： Mean square error

SUBJECTIVE ASSESSMENT OF THE IMPACT OF A CONTENT ADAPTIVE OPTIMISER FOR COMPRESSING 4K HDR CONTENT WITH AV1

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arXiv 2023年

作者： Vibhoothi Katsenou, Angeliki Pitié, François Domijan, Katarina Kokaram, Anil Sigmedia Group Department of Electronic and Electrical Engineering Trinity College Dublin Ireland Department of Mathematics and Statistics Maynooth University Ireland

关键词： Electric distortion

Transformer-based Multivariate Time Series Anomaly Localization

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arXiv 2025年

作者： Shimillas, Charalampos Malialis, Kleanthis Fokianos, Konstantinos Polycarpou, Marios M. KIOS Research and Innovation Center of Excellence Nicosia Cyprus Department of Electrical and Computer Engineering University of Cyprus Nicosia Cyprus Department of Mathematics and Statistics University of Cyprus Nicosia Cyprus

With the growing complexity of Cyber-Physical Systems (CPS) and the integration of Internet of Things (IoT), the use of sensors for online monitoring generates large volume of multivariate time series (MTS) data. Consequently, the need for robust anomaly diagnosis in MTS is paramount to maintaining system reliability and safety. While significant advancements have been made in anomaly detection, localization remains a largely underexplored area, though crucial for intelligent decision-making. This paper introduces a novel transformer-based model for unsupervised anomaly diagnosis in MTS, with a focus on improving localization performance, through an in-depth analysis of the self-attention mechanism’s learning behavior under both normal and anomalous conditions. We formulate the anomaly localization problem as a three-stage process: time-step, window, and segment-based. This leads to the development of the Space-Time Anomaly Score (STAS), a new metric inspired by the connection between transformer latent representations and space-time statistical models. STAS is designed to capture individual anomaly behaviors and inter-series dependencies, delivering enhanced localization performance. Additionally, the Statistical Feature Anomaly Score (SFAS) complements STAS by analyzing statistical features around anomalies, with their combination helping to reduce false alarms. Experiments on real world and synthetic datasets illustrate the model’s superiority over state-of-the-art methods in both detection and localization tasks. © 2025, CC BY-SA.

关键词： Time series

Learning algorithms for mean field optimal control

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arXiv 2025年

作者： Soner, H. Mete Teichmann, Josef Yan, Qinxin Department of Operations Research and Financial Engineering Princeton University PrincetonNJ08540 United States Department of Mathematics ETH Zürich Switzerland Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States

We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model by an N-particle system and leverage the exchangeability of the particles to obtain substantial computational efficiency. In addition to several numerical examples, a convergence analysis is provided. We also developed a universal approximation theorem on Wasserstein *** Codes 35Q89, 35D40, 49L25, 60G99 © 2025, CC BY-NC-ND.

关键词： Optimal control systems