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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

A multi-objective mixed integer linear programming model for thesis defence scheduling

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第1期312卷 92-116页

作者： Almeida, Joao Santos, Daniel Figueira, Jose Rui Francisco, Alexandre P. Univ Lisbon CEGIST Inst Super Tecn Lisbon Portugal Univ Lisbon INESC ID Inst Super Tecn Lisbon Portugal

In this paper, we address the thesis defence scheduling problem, a critical academic scheduling management process, which has been overshadowed in the literature by its counterparts, course timetabling and exam scheduling. Specifically, we address the single defence assignment type of thesis defence schedul-ing problems, where each committee is assigned to a single defence, scheduled for a specific day, hour and room. We formulate a multi-objective mixed-integer linear programming model, which aims to be applicable to a broader set of cases than other single defence assignment models present in the literature, which have a focus on the characteristics of their universities. For such a purpose, we introduce a dif-ferent decision variable, propose constraint formulations that are not regulation and policy specific, and cover and offer new takes on the more common objectives seen in the literature. We also include new objective functions based on our experience with the problem at our university and by applying knowl-edge from other academic scheduling problems. We also propose a two-stage solution approach. The first stage is employed to find the number of schedulable defences, enabling the optimisation of instances with unschedulable defences. The second stage is an implementation of the augmented & epsilon;-constraint method, which allows for the search of a set of different and non-dominated solutions while skipping redundant iterations. The methodology is tested for case-studies from our university, significantly outperforming the solutions found by human schedulers. A novel instance generator for thesis scheduling problems is presented. Its main benefit is the generation of the availability of committee members and rooms in availability and unavailability blocks, resembling their real-world counterparts. A set of 96 randomly generated instances of varying sizes is solved and analysed regarding their relative computational performance, the number of schedulable de

关键词： Timetabling Education integer programming Multiple objective programming Scheduling

An integer programming Approach for Angular Coverage under Uncertainty

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An Integer Programming Approach for Angular Coverage under U...

IEEE Conference on Decision and Control

作者： Yuntian Zhang Chen Chen Shuxin Ding Fang Deng National Key Lab of Autonomous Intelligent Unmanned Systems Beijing Institute of Technology Beijing China China Academy of Railway Sciences Corporation Limited Signal and Communication Research Institute Beijing China Traffic Management Laboratory for High-Speed Railway National Engineering Research Center of System Technology for High-Speed Railway and Urban Rail Transit Beijing China Beijing Institute of Technology Chongqing Innovation Center Chongqing China

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

This paper investigates angular coverage under uncertainty (ACU). A compact integer programming (IP) formulation is developed to model the angular field-of-view (FoV) of sensors and probabilistic coverage under uncertainty. The IP formulation minimizes the weighted non-coverage probability over the target set as well as considering the practical colocation and budget constraints. Recognizing the non-linearity, non-convexity, and non-separability of ACU, we first introduce the reformulation-linearisation technique (RLT) to obtain a tractable mixed-integer linear programming model which provides a tight lower bound for the original problem. Further, we exploit the structure of the mathematical model and customize a branch-and-cut (B&C) algorithm to solve the derived problem exactly. We show that the solution for the derived problem can also solve the original problem based on the bounding scheme. Computational experiments on a series of problem instances ranging from moderate to large size scaling up to 4,000 dimensional decision variables reveal the effectiveness and efficiency of the proposed exact approach.

关键词： integer programming Lower bound Uncertainty Probabilistic logic Mathematical models Distance measurement Sensors Mixed integer linear programming Computational efficiency IP networks

Optimal Single-Item Replenishment Scheme and Pricing Strategy for Vegetable Category Based on LSTM Time-Series Prediction Mixed integer programming Model

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Optimal Single-Item Replenishment Scheme and Pricing Strateg...

Interactive Intelligent Systems and Techniques (IIST), International Conference on

作者： Zhikun Huang Zhijie Huang Wenjian Wu Yufei Huang School of Information Management Jiangxi University of Finance and Economics Jiangxi China

ISBN: (数字)9798350374421

ISBN: (纸本)9798350374438

The replenishment and pricing of superstore vegetables is an important part of daily life, and the merchants' prediction and optimisation scheme for the future has gradually become an important issue in production and life. This paper focuses on the problem of total replenishment and pricing strategy of superstores, predicts and analyses the results based on LSTM time-series prediction, and finally gives the optimal total replenishment and pricing strategy of superstores in different scenarios. Firstly, the data are preprocessed to filter out the types of products available for sale from 24-30 June 2023 Meanwhile, based on the LSTM time-series prediction model, the basic relationship between short-term sales quantity and pricing is predicted. Then, under the premise of trying to meet the market demand for each category of vegetable goods, a mixed integer programming model aimed at maximising the benefits of the business dynasty is established, the 0-1 variable is introduced to constrain the selection of single products, and multiple constraints are established on the number of single products, the order quantity of single products, and the demand for each type of goods, which is solved to produce a profit of 1098.360 yuan on 1 July. Finally, based on a simple model perturbation, it is judged that the scheme is more reasonable and the result is superior, and finally gives the optimal single-item replenishment scheme and pricing strategy.

关键词： integer programming Analytical models Perturbation methods Pricing Production Predictive models Data models Forecasting Long short term memory Business

Large Language Model Watermark Stealing With Mixed integer programming

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arXiv 2024年

作者： Zhang, Zhaoxi Zhang, Xiaomei Zhang, Yanjun Zhang, Leo Yu Chen, Chao Hu, Shengshan Gill, Asif Pan, Shirui University of Technology Sydney Australia Griffith University Australia Royal Melbourne Institute of Technology Australia Huazhong University of Science and Technology China

The Large Language Model (LLM) watermark is a newly emerging technique that shows promise in addressing concerns surrounding LLM copyright, monitoring AI-generated text, and preventing its misuse. The LLM watermark scheme commonly includes generating secret keys to partition the vocabulary into green and red lists, applying a perturbation to the logits of tokens in the green list to increase their sampling likelihood, thus facilitating watermark detection to identify AI-generated text if the proportion of green tokens exceeds a threshold. However, recent research indicates that watermarking methods using numerous keys are susceptible to removal attacks, such as token editing, synonym substitution, and paraphrasing, with robustness declining as the number of keys increases. Therefore, the state-of-the-art watermark schemes that employ fewer or single keys have been demonstrated to be more robust against text editing and paraphrasing. In this paper, we propose a novel green list stealing attack against the state-of-the-art LLM watermark scheme and systematically examine its vulnerability to this attack. We formalize the attack as a mixed integer programming problem with constraints. We evaluate our attack under a comprehensive threat model, including an extreme scenario where the attacker has no prior knowledge, lacks access to the watermark detector API, and possesses no information about the LLM's parameter settings or watermark injection/detection scheme. Extensive experiments on LLMs, such as OPT and LLaMA, demonstrate that our attack can successfully steal the green list and remove the watermark across all settings. © 2024, CC BY-NC-SA.

关键词： integer programming

Polynomial Time Algorithms for integer programming and Unbounded Subset Sum in the Total Regime

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arXiv 2024年

作者： Aggarwal, Divesh Joux, Antoine Santha, Miklos Węgrzycki, Karol Centre for Quantum Technologies Department of Computer Science NUS Singapore CISPA Helmholtz Center for Information Security Germany Centre for Quantum Technologies National University of Singapore Singapore Saarland University Max Planck Institute for Informatics Saarbrücken Germany

The Unbounded Subset Sum (Unbounded Subset Sum) problem is an NP-hard computational problem where the goal is to decide whether there exist non-negative integers x1, . . ., xn such that x1a1 + . . . + xnan = b, where ... 详细信息

关键词： integer programming

An integer programming Approach for Quick-Commerce Assortment Planning

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arXiv 2024年

作者： Chen, Yajing He, Taotao Rong, Ying Wang, Yunlong Antai College of Economics and Management Shanghai Jiao Tong University Shanghai200030 China

In this paper, we explore the challenge of assortment planning in the context of quick-commerce, a rapidly-growing business model that aims to deliver time-sensitive products. In order to achieve quick delivery to satisfy the immediate demands of online customers in close proximity, personalized online assortments need to be included in brick-and-mortar store offerings. With the presence of this physical linkage requirement and distinct multinomial logit (MNL) choice models for online consumer segments, the firm seeks to maximize overall revenue by selecting an optimal assortment of products for local stores and by tailoring a personalized assortment for each online consumer segment. We refer to this problem as quick-commerce assortment planning (QAP). We employ an integer programming approach to solve this NP-hard problem to global optimality. Specifically, we propose convexification techniques to handle its combinatorial and nonconvex nature. We capture the consumer choice of each online segment using a convex hull representation. By exploiting the geometry behind Luce’s choice axiom, we provide a compact polyhedral characterization of the convex hull under various operational constraints that are not totally-unimodular. Furthermore, we conduct a polyhedral study on the relation between assortment decisions for products to offer and choice probabilities of products under the MNL model. Our methodology, coupled with a modified choice probability ordered separation algorithm, yields formulations that provide a significant computational advantage over existing methods. Through comprehensive numerical studies, we emphasize the significance of aligning offline and online assortment decisions and underscore the perils associated with inaccurately specifying customer behavior models. Finally, we use the geometry insights from our polyhedral results to develop a polynomial time randomized algorithm for solving a variant of QAP. © 2024, CC BY-NC-SA.

关键词： integer programming

Multilevel Facility Location Optimization: A Novel integer programming Formulation and Approaches to Heuristic Solutions

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arXiv 2024年

作者： Alidaee, Bahram Wang, Haibo School of Business Administration The University of Mississippi UniversityMS38677 United States A.R. Sánchez Jr. School of Business Texas A&M International University LaredoTX78045 United States

We attack the 4-level facility location problem (4L-FLP), a critical component in supply chains. Foundational tasks here involve selecting markets, plants, warehouses, and distribution centers to maximize profits while considering related constraints. Based on a variation of the quadratic assignment problem, we propose a novel integer programming formula that significantly reduces the variables. Our model incorporates several realistic features, including transportation costs and upper bounds on facilities at each level. It accounts for one-time fixed costs associated with selecting each facility. To solve this complex problem, we develop and experimentally test two solution procedures: a multi-start greedy heuristic and a multi-start tabu search. We conduct extensive sensitivity analyses on the results to assess the reliability of proposed algorithms. This study contributes to improved solution methods for large-scale 4L-FLPs, providing a valuable tool for supply chain maturity. © 2024, CC BY.

关键词： integer programming

Mixed integer programming Algorithm in the Optimization of Air Traffic Control Flight Scheduling

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Mixed Integer Programming Algorithm in the Optimization of A...

Computers, Information Processing and Advanced Education (CIPAE), 2020 International Conference on

作者： Fangjun Wu Air Traffic Control and Navigation School Air Force Engineering University Xi'an Shaanxi China

ISBN: (数字)9798331527662

ISBN: (纸本)9798331527679

With the rapid development of the global aviation industry, the sharp increase in the number of flights has put forward higher requirements for air traffic management, especially in ensuring flight punctuality and aviation safety. This study focuses on flight scheduling problems in air traffic control, using the Mixed integer programming (MIP) algorithm to optimize scheduling strategies. Specifically, the article constructed a mathematical model that includes multiple constraints such as airport capacity, flight time windows, and flight connectivity, and iteratively solved the problem to find the optimal or approximately optimal scheduling solution. This method not only improves the efficiency of scheduling, but also enhances the flexibility and practicality of scheduling schemes, providing an effective tool for aviation control departments to reduce flight delays, improve airspace utilization efficiency, and passenger satisfaction. In sunny and cloudy weather, the accuracy of the algorithm can reach 97% or above, indicating that the algorithm can accurately schedule flights under normal conditions. The research results of this article can provide theoretical basis and technical support for the modernization of China's aviation control construction. The research results of this article can to some extent enrich the basic theory of flight scheduling and provide new ideas and methods for solving practical problems.

关键词： integer programming Job shop scheduling Accuracy Processor scheduling Computational modeling Optimal scheduling Airports Computational efficiency Air traffic control Meteorology