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Optimal Mating Combination for Directed Breeding in a Racially Composite Cattle Population

JOURNAL OF ANIMAL BREEDING AND GENETICS 2025年第0期 2025 Mar 11页

作者： Teodoro, Joao Vitor Mourao, Gerson Barreto Carvalho, Rachel Santos Bueno de Mattos, Elisangela Chicaroni Ferraz, Jose Bento Sterman Eler, Joanir Pereira Univ Fed Triangulo Mineiro Iturama MG Brazil Univ Sao Paulo Pirassununga Brazil Univ Sao Paulo Piracicaba Brazil

Evaluating optimal mating combinations in large populations poses significant combinatorial and computational challenges. To address this, we propose a method to optimise mating combinations in composite cattle populations, incorporating heterosis and genetic variability. Leveraging integer linear programming, our approach maximises expected offspring merit, outperforming random mating systems. A robust mathematical model and specialised software were developed to implement the method, demonstrating its effectiveness on a real dataset. Notably, results reveal a 14.8% superiority over random mating averages and a 12.4% advantage over random mating maxima. The method's flexibility and adaptability enable constraint inclusion and application to diverse species and genomic data, making it an indispensable tool for enhancing mating selection efficiency and effectiveness in composite beef cattle breeding programmes.

关键词： composite cattle computational mathematics cross-breeding genetic improvement integer linear programming

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A new method of large integer prime decomposition for network public key cryptosystem

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International Journal of Security and Networks 2024年第3期19卷 159-167页

作者： Sun, Wenbo Wang, Wei Bai, Chenguang College of Sciences Xi’an Shiyou University Xi’an710065 China

This paper takes prime numbers as the research object. Firstly, a dynamic password authentication scheme based on prime modulus is proposed by using prime modulus as an identity identifier, combined with the Chinese remainder theorem in number theory and RSA public key system, and its security is analysed. Secondly, this paper establishes prime-base linear spaces and corresponding positive rational logarithmic linear spaces. It obtains the matrix of natural logarithmic function linear isomorphism mapping under the corresponding basis through logarithmic isomorphism linear mapping between spaces based on the important role that prime numbers play in theory. Thirdly, by transforming the problem of large integer prime factorisation into the problem of factorisation over polynomial rings, several new methods of large integer prime factorisation based on the theory of polynomial rings are proposed. It provides a theoretical basis for further improving the security of network public key encryption systems. Copyright © 2024 Inderscience Enterprises Ltd.

关键词： integer linear programming

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On the Existence of Small Strictly Neumaier Graphs

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GRAPHS AND COMBINATORICS 2024年第3期40卷 51-51页

作者： Abiad, Aida De Boeck, Maarten Zeijlemaker, Sjanne Eindhoven Univ Technol Dept Math & Comp Sci Eindhoven Netherlands Univ Ghent Dept Math Anal Log & Discrete Math Ghent Belgium Vrije Univ Brussel Dept Math & Data Sci Brussels Belgium Univ Memphis Dept Math Sci Memphis TN USA Univ Ghent Dept Math Algebra & Geometry Ghent Flanders Belgium

A Neumaier graph is a non-complete edge-regular graph containing a regular clique. In this work, we prove several results on the existence of small strictly Neumaier graphs. In particular, we present a theoretical proof of the uniqueness of the smallest strictly Neumaier graph with parameters (16, 9, 4;2, 4), we establish the existence of a strictly Neumaier graph with parameters (25, 12, 5;2, 5), and we disprove the existence of strictly Neumaier graphs with parameters (25, 16, 9;3, 5), (28, 18, 11;4, 7), (33, 24, 17;6, 9), (35, 2212;3, 5), (40, 30, 22;7, 10) and (55, 34, 18;3, 5). Our proofs use combinatorial techniques and a novel application of integer programming methods.

关键词： Neumaier graphs Edge-regular graphs Regular cliques Latin squares integer linear programming

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RIBAP: a comprehensive bacterial core genome annotation pipeline for pangenome calculation beyond the species level

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GENOME BIOLOGY 2024年第1期25卷 1页

作者： Lamkiewicz, Kevin Barf, Lisa-Marie Sachse, Konrad Hoelzer, Martin Friedrich Schiller Univ Jena RNA Bioinformat & High Throughput Anal Leutragraben 1 D-07743 Jena Germany Robert Koch Inst Genome Competence Ctr MF1 D-13353 Berlin Germany

Microbial pangenome analysis identifies present or absent genes in prokaryotic genomes. However, current tools are limited when analyzing species with higher sequence diversity or higher taxonomic orders such as genera or families. The Roary ILP Bacterial core Annotation Pipeline (RIBAP) uses an integer linear programming approach to refine gene clusters predicted by Roary for identifying core genes. RIBAP successfully handles the complexity and diversity of Chlamydia, Klebsiella, Brucella, and Enterococcus genomes, outperforming other established and recent pangenome tools for identifying all-encompassing core genes at the genus level. RIBAP is a freely available Nextflow pipeline at ***/hoelzer-lab/ribap and ***/doi/10.5281/zenodo.10890871.

关键词： Bacteria Pangenome Prokaryote Core genes Clustering integer linear programming Nextflow Pipeline

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Educational timetabling problem with teaching load assignment using preferences and compactness

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ANNALS OF OPERATIONS RESEARCH 2024年 1-26页

作者： Maya-Padron, C. Arratia-Martinez, N. M. Univ Politecn Garcia Dept Comp Syst Engn 16 Septiembre Garcia 66004 Nuevo Leon Mexico Univ Americas Puebla Dept Business Adm Ex Hacienda Sant Catarina Martir Cholula 72810 Puebla Mexico

The educational timetabling problem is well known for its complexity and difficulty, making it a time-consuming task for many institutions. Consequently, a variety of approaches have been developed to address this problem. This research presents a novel integer linear programming model that incorporates features to maintain a sustainable relationship between the institution and its professors in the long term. These features involve faculty considerations and preferences. The mathematical model is applied to solve a course timetabling problem at a Mexican university, where the faculty is mainly composed of part-time professors. In addition to determining the allocation of professors to courses within specific time slots for groups of students, we also address the issue of teaching load, which is determined by the number of courses assigned to each professor. This results in a specific number of class hours per week, a value constrained to ensure the compactness of professors' schedules and the balancing of assigned courses and class hours for the same group. These conditions are treated as hard constraints to emphasize their importance and ensure compliance. The final timetable maximizes the total preference of course-professor assignments based on professors' preferences and previous academic performance evaluations. In all cases, an optimal solution was obtained in a short time (seconds), significantly reducing the time required to process this task and providing solutions with optimal preference in course-professor assignments. An analysis and discussion comparing the obtained solution with the handmade case are presented.

关键词： Educational timetabling problem Course timetabling problem Mathematical modeling Assignment problem integer linear programming

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Improving reliability with optimal allocation of maintenance resources: an application to power distribution networks

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ANNALS OF OPERATIONS RESEARCH 2024年第1期340卷 345-365页

作者： Martin, Mateus Usberti, Fabio Luiz Lyra, Christiano Fluminense Fed Univ UFF Dept Prod Engn BR-25650050 Petropolis RJ Brazil Fed Univ Sao Paulo UNIFESP Inst Sci & Technol BR-12247014 Sao Jose Dos Campos SP Brazil Univ Estadual Campinas Inst Comp UNICAMP BR-13083852 Campinas SP Brazil Univ Estadual Campinas Sch Elect & Comp Engn UNICAMP BR-13083852 Campinas SP Brazil

Power distribution networks should strive for reliable delivery of energy. In this paper, we support this endeavor by addressing the Maintenance Resources Allocation Problem (MRAP). This problem consists of scheduling preventive maintenance plans on the equipment of distribution networks for a planning horizon, seeking the best trade-offs between system reliability and maintenance budgets. We propose a novel integer linear programming (ILP) formulation to effectively model and solve the MRAP for a single distribution network. The formulation also enables flexibility to suit new developments, such as different reliability metrics and smart-grid innovations. Then we develop a straightforward ILP formulation to address the MRAP for several distribution networks which takes the advantages of exchanging maintenance information between local agents and upper management. Using a general-purpose ILP solver, we performed computational experiments to assess the performance of the proposed approaches. Optimal maintenance trade-offs were achieved with the new formulations for real-scale distribution networks within short running times. To the best of our knowledge, this is the first time that the MRAP is optimally solved using ILP, for single or multiple distribution networks.

关键词： Maintenance Reliability Power distribution networks integer linear programming Multicriteria optimization

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An optimization protocol for MRI examination resource allocation based on demand forecasting and linear programming

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SCIENTIFIC REPORTS 2025年第1期15卷 1-13页

作者： Zhou, Zhongbin Zhou, Hanyu Qiao, Yuanyuan Gao, Zihan Yang, Ying 6th Med Ctr PLA Gen Hosp Beijing 100048 Peoples R China China Unicom Beijing Branch Beijing 100006 Peoples R China

The accessibility of medical services in Mainland China had been on the rise, leading to a surge in the number of Magnetic Resonance Imaging (MRI) scans. This increase had caused substantial delays in MRI examination queues at large hospitals. With MRI equipment and exams being costly, over-purchasing machines could lead to underutilization of resources. It was, therefore, crucial to devise a comprehensive method that could shorten patient wait times and optimize the use of medical resources within hospitals. The research had utilized daily MRI examination application data from a hospital covering the period from July 1, 2017, to November 30, 2022. The Autoregressive Integrated Moving Average (ARIMA) model and the AutoRegressive Integrated Moving Average with exogenous (ARIMAX) model were developed using SAS (version 9.3) software. Moreover, Non-AutoRegressive (NAR) and Non-AutoRegressive with exogenous (NARX) models were built using MATLAB (version R2015b) to forecast future MRI examination demands. Integrating the ARIMAX model with the NARX model, an ARIMAX-NARX model had been *** predictive accuracy of these models was then assessed and compared. Based on the prediction outcomes, an integer linear programming model was employed to calculate the optimal number of MRI examinations per machine per day, targeting cost reduction. An optimization flowchart for MRI examination resource allocation was developed by integrating critical process components, thus streamlining and systematizing the optimization process to improve efficiency. Analysis of the data revealed a weekly cyclical trend in MRI examination applications. Among the ARIMA, ARIMAX, NAR, NARX, ARIMAX-NARX models evaluated for their predictive skills, the NARX model emerged as the most accurate for forecasting. An integer linear programming (ILP) model was utilized to plan the number of examinations for each MRI machine, effectively reducing costs. An optimization flowchart was developed to integ

关键词： MRI ARIMA model NAR model integer linear programming Optimization protocol

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An integer programming Approach for Scheduling a Professional Sports League

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American Journal of Computational Mathematics 2024年第4期14卷 401-423页

作者： Vardges Melkonian Department of Mathematics Ohio University Athens OH USA

This paper gives integer linear programming (ILP) models for scheduling the League Phase of one of the most popular professional club competitions in the world, UEFA Champion’s League. There are 36 teams in the competition, but each team plays only 8 other teams in the League Phase. Thus, the difficulty or ease of a team’s opponents, known as strength of schedule (SOS), compared to other teams will be different. Our main ILP model aims to minimize the maximum difference between SOS of any two teams, thus making the schedule as fair as possible. We also give a model for creating a timetable of all the matchups obtained by the first model. The models were implemented and tested using optimization software AMPL. Our main model obtained a schedule with a difference 0.4 between the highest and the lowest SOS, while that difference is 19 for the actual 2024-2025 competition. Thus, our model returns a schedule that is significantly fairer compared to the actual competition.

关键词： Sport Scheduling Optimization Modeling integer linear programming

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A survey of some operations research and data sciences applications developed in the last 20 years at Argentinian and Chilean Universities

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ANNALS OF OPERATIONS RESEARCH 2024年 1-23页

作者： Duran, Guillermo Univ Buenos Aires Fac Ciencias Exactas & Nat Inst Calculo RA-C1428EGA Buenos Aires Argentina Univ Buenos Aires Fac Ciencias Exactas & Nat Dept Matemat RA-C1428EGA Buenos Aires Argentina Consejo Nacl Invest Cient & Tecn RA-C1425FQB Buenos Aires Argentina Univ Chile Fac Ciencias Fis & Matemat Dept Ingn Ind Santiago Chile

A survey is presented of a series of projects designed and implemented over the past 20 years by operations research and data sciences teams based at the University of Buenos Aires and the University of Chile. The projects were undertaken at the request of entities in both the public and private sectors and addressed problems in logistics and transport, production planning, efficient allocation of human resources, shift scheduling, tender auction management, public health and education, among other areas. In each case, a summary is given of the mathematical techniques used, the models and algorithms developed, and the results and impacts obtained. The principal difficulties encountered and the factors behind the projects' success are also discussed.

关键词： OR applications Data sciences Public administration Salmon farming Hydrocarbons integer linear programming Heuristics

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Exact methods for the Oven Scheduling Problem

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CONSTRAINTS 2023年第2期28卷 320-361页

作者： Lackner, Marie-Louise Mrkvicka, Christoph Musliu, Nysret Walkiewicz, Daniel Winter, Felix TU Wien DBAI Christian Doppler Lab Artificial Intelligence & Op Favoritenstr 9 A-1040 Vienna Austria MCP GmbH Canovagasse 7 A-1010 Vienna Austria

The Oven Scheduling Problem (OSP) is a new parallel batch scheduling problem that arises in the area of electronic component manufacturing. Jobs need to be scheduled to one of several ovens and may be processed simultaneously in one batch if they have compatible requirements. The scheduling of jobs must respect several constraints concerning eligibility and availability of ovens, release dates of jobs, setup times between batches as well as oven capacities. Running the ovens is highly energy-intensive and thus the main objective, besides finishing jobs on time, is to minimize the cumulative batch processing time across all ovens. This objective distinguishes the OSP from other batch processing problems which typically minimize objectives related to makespan, tardiness or lateness. We propose to solve this NP-hard scheduling problem using exact techniques and present two different modelling approaches, one based on batch positions and another on representative jobs for batches. These models are formulated as constraint programming (CP) and integer linear programming (ILP) models and implemented both in the solver-independent modeling language MiniZinc and using interval variables in CP Optimizer. An extensive experimental evaluation of our solution methods is performed on a diverse set of problem instances. We evaluate the performance of several state-of-the-art solvers on the different models and on three variants of the objective function that reflect different real-life scenarios. We show that our models can find feasible solutions for instances of realistic size, many of those being provably optimal or nearly optimal solutions.

关键词： Oven Scheduling Problem Parallel batch processing Constraint programming integer linear programming

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