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Local edge metric dimensions via corona products and integer linear programming

COMPUTATIONAL & APPLIED MATHEMATICS 2024年第6期43卷 1-12页

作者： Amini, Fateme Henning, Michael A. Tavakoli, Mostafa Ferdowsi Univ Mashhad Fac Math Sci Dept Appl Math Mashhad 91775 Iran Univ Johannesburg Dept Math & Appl Math ZA-2006 Auckland Pk South Africa

Let G be a connected graph. The distance between two vertices u and v in G, denoted by dG(u, v), is the number of edges in a shortest path from u to v, while the distance between an edge e = xy and a vertex v in G is dG(e, v) = min{dG(x, v), dG(y, v)}. For an edge e. E(G) and a subset S of V( G), the representation of e with respect to S = {x1,..., xk} is the vector rG(e|S) = (d1,..., dk), where di = dG(e, xi) for i. [k]. If rG(e|S) = rG( f |S) for every two adjacent edges e and f of G, then S is called a local edge metric generator for G. The local edge metric dimension of G, denoted by edim (G), is the minimum cardinality among all local edge metric generators in G. For two non-trivial graphs G and H, we determine edim ( G H) in the edge corona product G H and we determine edim (G. H) in the corona product G H. We also formulate the problem of computing edim (G) as an integer linear programming model.

关键词： Metric dimension Local edge metric dimension Corona product Edge corona product integer linear programming

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Accurate Flow Decomposition via Robust integer linear programming

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2024年第6期21卷 1955-1964页

作者： Dias, Fernando H. C. Tomescu, Alexandru I. Aalto Univ Dept Math & Syst Anal Syst Anal Lab Espoo 02150 Finland Univ Helsinki Dept Comp Sci Helsinki 00100 Finland

Minimum flow decomposition (MFD) is a common problem across various fields of Computer Science, where a flow is decomposed into a minimum set of weighted paths. However, in Bioinformatics applications, such as RNA transcript or quasi-species assembly, the flow is erroneous since it is obtained from noisy read coverages. Typical generalizations of the MFD problem to handle errors are based on least-squares formulations or modelling the erroneous flow values as ranges. All of these are thus focused on error handling at the level of individual edges. In this paper, we interpret the flow decomposition problem as a robust optimization problem and lift error-handling from individual edges to solution paths. As such, we introduce a new minimum path-error flow decomposition problem, for which we give an integer linear programming formulation. Our experimental results reveal that our formulation can account for errors significantly better, by lowering the inaccuracy rate by 30-50% compared to previous error-handling formulations, with computational requirements that remain practical.

关键词： Bioinformatics Genomics RNA Splicing Assembly integer linear programming Sequential analysis Flow decomposition integer programming network flow uncertainty

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Tabu Search-Based Heuristic Solver for General integer linear programming Problems

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IEEE ACCESS 2024年 12卷 19059-19076页

作者： Koguma, Yuji Independent Researcher Kanagawa Japan

This paper presents a tabu search-based heuristic solver for general integer linear programming (ILP) problems as a dependable alternative to branch-and-bound (B&B) solvers. It aims to expand the range of ILP instances for which optimization practitioners can obtain reasonable solutions using either B&B or heuristic solvers. The challenge in developing such a heuristic solver is ensuring both good performance and versatility. The proposed solver addresses this difficulty by incorporating several performance-improving techniques for search behavior and computation speed while maintaining the versatility. These techniques include instance size reduction, neighborhood filtering, and accelerating solution evaluation. The proposed algorithm was implemented in C++17 and made available as an open-source solver that accepts ILP instances formulated for B&B solvers without modification. In numerical experiments with a 120-second time limit, the proposed solver found better feasible solutions than existing open-source B&B solvers for 17 out of the 82 feasible pure integer instances from MIPLIB 2017 Benchmark Set, including instances with over 100,000 variables. An ablation study verified that the incorporated techniques were essential for the performance.

关键词： Search problems Metaheuristics integer linear programming Indexes Behavioral sciences Heuristic algorithms Simulated annealing heuristics metaheuristics tabu search local search

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Sparse Array Design via integer linear programming

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2024年 72卷 4812-4826页

作者： Zhuang, Yangjingzhi Zhang, Xuejing He, Zishu Greco, Maria Sabrina Gini, Fulvio Univ Elect Sci & Technol China Dept Informat & Commun Engn Chengdu 611731 Peoples R China Univ Pisa Dept Informat Engn I-56122 Pisa Italy

In this paper, a design framework based on integer linear programming is proposed for optimizing sparse array structures. We resort to binary vectors to formulate the design problem for non-redundant arrays (NRA) and minimum-redundant arrays (MRA). The flexibility of the proposed framework allows for dynamic adjustment of constraints to meet various applicative requirements, e.g., to achieve desired array apertures and mitigate mutual coupling effects. The proposed framework is also extended to the design of high-order arrays associated by exploiting high-order cumulants. The effectiveness of the proposed sparse array design framework is investigated through extensive numerical analysis. A comparative analysis with closed-form solutions and integer linear programming-based array design methods confirms the superiority of the proposed design framework in terms of number of degrees of freedom (DOF) and direction of arrival (DOA) estimation accuracy.

关键词： Sensor arrays Antenna arrays Mutual coupling Vectors Sensors Redundancy Apertures Non-redundant array minimum-redundant array sparse array design integer linear programming

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Designing unit Ising models for logic gate simulation through integer linear programming

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INTERNATIONAL JOURNAL OF PARALLEL EMERGENT AND DISTRIBUTED SYSTEMS 2025年第2期40卷 116-136页

作者： Tsukiyama, Shunsuke Nakano, Koji Parque, Victor Ito, Yasuaki Kato, Takumi Kawamata, Yuya Ii, Kaiki Hiroshima Univ Grad Sch Adv Sci & Engn Kagamiyama 1-4-1 Higashihiroshima Hiroshima 7398527 Japan NTT DATA Grp Corp Res & Dev Headquarters Koto ku Tokyo Japan

Ising models minimizing a quadratic objective function with spin variables of either $ {-}1 $ -1 or $ +1 $ +1 are instrumental in tackling combinatorial optimization problems by programmable Quantum Annealers. This paper introduces unit Ising models, where non-zero coefficients are restricted to $ {-}1 $ -1 or $ +1 $ +1. Due to the limited resolution of quantum annealers, unit Ising models are more suitable for quantum annealers. A fixed unit Ising model for logic circuits could lead to Application-Specific Unit Quantum Annealers (ASUQAs) for inverse function computation, similar to ASICs. Our findings suggest a powerful new method for compromising the RSA cryptosystem by leveraging ASUQAs for factorization.

关键词： Quantum computing one-way function factorization application specific hardware integer linear programming

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An integer linear programming model for multi document summarization of learning materials using phrase embedding technique

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INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2024年第6期15卷 2772-2785页

作者： Iyyappan, K. Sakkaravarthy Balasundaram, S. R. Natl Inst Technol Dept Comp Applicat Tiruchirappalli Tamilnadu India

Automatic text summarization (ATS) plays a vital role in condensing original text documents while preserving the most crucial information. Its benefits extend to various domains, including e-Learning systems, where educational content can be summarized to facilitate easier access and comprehension. Multi-document summarization (MDS) techniques enable the creation of concise summaries from groups of related text documents. Leveraging MDS for summarizing learning materials opens new avenues, offering students and teachers reference summaries for enhanced learning experiences. This paper introduces a concept-based integer linear programming model for summarizing learning materials, leveraging a phrase embedding technique. Phrases are treated as fundamental and significant semantic building blocks of sentences, facilitating the comprehension and summarization of documents. Embedding techniques are employed to semantically identify related phrases, eliminate redundancy, and enhance coherence through vector representations. Summaries are generated using the ILP technique, selecting key sentences and reducing redundancy with phrase vectors. The paper proposes sentence reordering techniques based on phrases and sentences to further enhance coherence. The resulting summaries are automatically evaluated using ROUGE metrics, demonstrating the superior performance of the proposed approach compared to various benchmark and baseline methods on both the DUC 2004 benchmark dataset and the newly created educational dataset, EduSumm.

关键词： E-learning Multi document summarization Phrase embeddings integer linear programming

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A symbiosis between population based incremental learning and LP-relaxation based parallel genetic algorithm for solving integer linear programming models

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COMPUTING 2023年第5期105卷 1121-1139页

作者： Fallah, Mohammad K. Fazlali, Mahmood Daneshtalab, Masoud GC Shahid Beheshti Univ Fac Math Sci Dept Data & Comp Sci Tehran Iran Malardalen Univ Intelligent Future Technol Vasteras Sweden

Solving integer linear programming (ILP) models generally lies in the category of NP-hard problems and finding the optimal answer for large models is a computational challenge. Genetic algorithms are a family of metaheuristic algorithms capable of adjusting and redesigning parameters and operations according to the characteristics of ILP models. On the other hand, still the genetic algorithm performs a lot of operations to solve large models, and parallel processing is a suitable technique to tackle this problem. This paper introduces an LP-Relaxation based parallel genetic algorithm that uses a population-based incremental learning technique to presents an expandable solver for large ILP models derived from a behavioral synthesis of digital circuits. In the proposed algorithm, each chromosome provides a state subspace of possible solutions, and each generation is produced based on a probability vector as well as elitism. Our experiments verify the efficiency of the proposed algorithm on multicore platforms, as it outperformed four previous genetic algorithms for solving mixed integer programming problems. The proposed genetic algorithm solved 20 ILP models include up to 5183 int / binary decision variables in less than 20 min using four 16-core AMD Opteron 6386 SE processors. Also, the results indicate that for models with more than 4000 variables, the speedup and the efficiency of the proposed parallel genetic algorithm on 60 CPU cores is more than 18X and 30%, respectively.

关键词： integer linear programming LP-relaxation Genetic algorithm Incremental learning

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New ?-constraint methods for multi-objective integer linear programming: A Pareto front representation approach

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第1期306卷 286-307页

作者： Mesquita-Cunha, Mariana Figueira, Jose Rui Barbosa-Povoa, Ana Paula Univ Lisbon Inst Super Tecn CEGIST Ctr Management Studies Lisbon Portugal

Dealing with multi-objective problems by using generation methods has some interesting advantages since it provides the decision-maker with the complete information about the set of non-dominated cri-terion vectors (Pareto front) and a clear overview of the different trade-offs of the problem. However, providing many solutions to the decision-maker may also be overwhelming. As an alternative approach, showing a representative set of the Pareto front may be advantageous. Choosing such a representative set is by itself also a multi-objective problem that must consider the number of alternatives to present, the uniformity, and/or the coverage of the representation, to guarantee its quality. This paper proposes three algorithms for the representation problem for multi-objective integer linear programming problems with two or more objective functions, each one of them dealing with each dimension of the problem (cardi-nality, coverage, and uniformity). Such algorithms are all based on the epsilon-constraint approach. In addition, the paper also presents strategies to overcome poor estimations of the Pareto front bounds. The algo-rithms were tested on the ability to efficiently generate the whole Pareto front or a representation of it. The uniformity and cardinality algorithms proved to be very efficient both on binary and on integer problems, being amongst the best in the literature. Both coverage and uniformity algorithms provide good quality representations on their targeted objective, while the cardinality algorithm appears to be the most flexible, privileging uniformity for lower cardinality representations and coverage on higher cardinality.(c) 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://***/licenses/by-nc-nd/4.0/ )

关键词： Multiple objective programming integer linear programming Generation methods Representation methods

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integer linear programming Reformulations for the linear Ordering Problem 5th

Integer Linear Programming Reformulations for the Linear Ord...

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4th International Conference on Optimization and Learning (OLA)

作者： Dupin, Nicolas Univ Angers LERIA SFR MATHSTIC F-49000 Angers France

ISBN: (纸本)9783031220388;9783031220395

This article studies the linear ordering problem, with applications in social choice theory and databases for biological datasets. integer linear programming (ILP) formulations are available for linear ordering and some extensions. ILP reformulations are proposed, showing relations with the Asymmetric Travel Salesman Problem. If a strictly tighter ILP formulation is found, numerical results justify the quality of the reference formulation for the problem in the Branch&Bound convergence. The quality of the continuous relaxation allows to design rounding heuristics, it offers perspectives to design matheuristics.

关键词： Optimization integer linear programming linear ordering Median of permutations Consensus ranking Polyhedral analysis

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Analysis of Authorization Constraints via integer linear programming

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2023年第3期35卷 2258-2271页

作者： Yang, Benyuan Hu, Hesuan Xidian Univ Sch Electromech Engn Xian 710071 Shaanxi Peoples R China Nanyang Technol Univ Coll Engn Sch Comp Sci & Engn Singapore 639798 Singapore Xi An Jiao Tong Univ State Key Lab Mfg Syst Engn Xian 710054 Shaanxi Peoples R China

This paper focuses on constraint verification and violation resolution for Petri nets (PNs) modeling of role-based access control (RBAC) policy. Checking the satisfiability of authorization constraints imposes a major challenge when the number of states of a target system is large. To overcome this difficulty, we provide three necessary and sufficient conditions to check three different constraints, namely Separation of Duties (SoDs), Binding of Duties (BoDs), and Constraints of Cardinality (CoCs). The proposed results are based on the solutions of integer linear programming problems (ILPs). By relying on an ILP formulation that does not require the explicit computation of the net reachability set, the proposed approach is particularly well suited for large-size PNs. When the given system does not satisfy a considered constraint, the objective is to propose a suitable violation resolution strategy to correctly enforce the given constraint. In this paper, enforcement of control places and administration of RBAC are presented to solve the SoD, BoD, and CoC violations. All violations can be corrected in a once for all manner while simultaneously ensuring the satisfaction of all other constraints. The comparison between our approach and the existing ones is given to illustrate the effectiveness and efficiency of ours.

关键词： Authorization Blacklisting Mathematical models Petri nets integer linear programming Optimization Monitoring Role-based access control authorization constraints integer linear programming

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