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arXiv 2024年

作者： Langeveld, Niels Ralston, David

Proper continued fractions are generalized continued fractions with positive integer numerators ai and integer denominators with bi ≥ ai. In this paper we study the strength of approximation of irrational numbers to their convergents and classify which pairs of integers p, q yield a convergent p/q to some irrational x. Notably, we reduce the problem to finding convergence only of index one and two. We completely classify the possible choices for convergents of odd index and provide a near-complete classification for even index. We furthermore propose a natural two-dimensional generalization of the classical Gauss map as a method for dynamically generating all possible expansions and establish ergodicity of this *** Codes 11J70, 37E05, 37A44 © 2024, CC BY.

关键词： integer linear programming

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TARGETED LEAST CARDINALITY CANDIDATE KEY FOR RELATIONAL DATABASES

arXiv

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arXiv 2024年

作者： Nakos, Vasileios Ngo, Hung Q. Tsourakakis, Charalampos E. University of Athens & RelationalAI Inc Greece RelationalAI Inc.

Functional dependencies (FDs) are a central theme in databases, playing a major role in the design of database schemas and the optimization of queries [41]. In this work, we introduce the targeted least cardinality candidate key problem (TCAND). This problem is defined over a set of functional dependencies F and a target variable set T ⊆ V, and it aims to find the smallest set X ⊆ V such that the FD X → T can be derived from F. The TCAND problem generalizes the well-known NP-hard problem of finding the least cardinality candidate key [36], which has been previously demonstrated to be at least as difficult as the set cover problem. We present an integer programming (IP) formulation for the TCAND problem, analogous to a layered set cover problem. We analyze its linear programming (LP) relaxation from two perspectives: we propose two approximation algorithms and investigate the integrality gap. Our findings indicate that the approximation upper bounds for our algorithms are not significantly improvable through LP rounding, a notable distinction from the standard Set Cover problem. Additionally, we discover that a generalization of the TCAND problem is equivalent to a variant of the Set Cover problem, named Red Blue Set Cover [10], which cannot be approximated within a sub-polynomial factor in polynomial time under plausible conjectures [14]. Despite the extensive history surrounding the issue of identifying the least cardinality candidate key, our research contributes new theoretical insights, novel algorithms, and demonstrates that the general TCAND problem poses complexities beyond those encountered in the Set Cover problem. © 2024, CC BY.

关键词： integer linear programming

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FINDING SQUARES IN A PRODUCT INVOLVING SQUARES

arXiv

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arXiv 2024年

作者： Ern, Thang Pang Department of Mathematics National University of Singapore 10 Lower Kent Ridge Road 119076 Singapore

We wish to discuss positive integer solutions to the Diophantine equation(formula presented) and state some possible extensions of the problem. Some methods in analytic number theory will be used to tackle this proble... 详细信息

关键词： integer linear programming

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Optimal PMU placement to ensure system observability under contingencies

Optimal PMU placement to ensure system observability under c...

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IEEE General Meeting Power& Energy Society

作者： Ranjana Sodhi S. C. Srivastava S. N. Singh Department of Electrical Engineering Indian Institute of Technology Kanpur India Mississippi State University USA

Optimal placement of Phasor Measurement Units (PMUs), to ensure complete observability of power system, should not only be decided at the base case operating conditions but also must consider the contingency cases. This paper presents a simple and effective method for optimal placement of PMUs considering critical contingencies. A voltage stability based contingency screening method has been utilized to select critical contingency cases. An integer linear programming (ILP) based algorithm for the PMU placement has been modified to determine optimal PMU locations under the system intact and the critical contingency cases. The proposed method is tested on the IEEE 14-bus system, New England 39-bus system and Northern Region Power Grid (NRPG) 246-bus Indian system and the test results have been compared with three more modified PMU placement methods viz. depth first search, direct spanning tree and direct N-1 spanning tree methods.

关键词： Phasor measurement units Observability Power system measurements Power system stability Power systems Jacobian matrices Voltage integer linear programming System testing Power system control

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Solving the Multi-Mode Resource-Constrained Project Scheduling Problem with SMT

Solving the Multi-Mode Resource-Constrained Project Scheduli...

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International Conference on Tools for Artificial Intelligence (ICTAI)

作者： Miquel Bofill Jordi Coll Josep Suy Mateu Villaret Departament d'Informàtica Matemàtica Aplicada i Estadística Universitat de Girona Spain

ISBN: (纸本)9781509044603

The Multi-Mode Resource-Constrained Project Scheduling Problem (MRCPSP) is a generalization of the well known Resource-Constrained Project Scheduling Problem (RCPSP). The most common exact approaches for solving this problem are based on branch-and-bound algorithms, mixed integer linear programming and Boolean satisfiability (SAT). In this paper, we present a new exact approach for solving this problem, using Satisfiability Modulo Theories (SMT). We provide two encodings into SMT and several reformulation and preprocessing techniques. The optimization algorithm that we propose uses an SMT solver as an oracle, and depending on its answer is able to update the encoding for the next optimization step. We report extensive performance experiments showing the utility of the proposed techniques and the good performance of our approach that allows us to close several open instances.

关键词： Schedules Encoding Silicon Optimization integer linear programming Search problems Upper bound

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Integrated User Matching and Pricing in Round-Trip Car-Sharing

Integrated User Matching and Pricing in Round-Trip Car-Shari...

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International Conference on Intelligent Transportation

作者： Avalpreet Singh Brar Rong Su Gioele Zardini Jaskaranveer Kaur Continental Automotive Singapore School of Electrical and Electronic Engineering Nanyang Technological University Singapore Laboratory for Information and Decision Systems Massachusetts Institute of Technology Cambridge MA USA

ISBN: (数字)9798331505929

ISBN: (纸本)9798331505936

Traditional round-trip car rental systems mandate users to return vehicles to their point of origin, limiting the system's adaptability to meet diverse mobility demands. This constraint often leads to fleet under-utilization and incurs high parking costs for idle vehicles. To address this inefficiency, we propose a N-user matching algorithm which is designed to facilitate one-way trips within the round-trip rental framework. Our algorithm addresses the joint problem of optimal pricing and user matching through a Two-Stage integer linear programming (ILP)-based formulation. In the first stage, optimal rental prices are determined by setting a risk factor that governs the likelihood of matching a set of N-user. The second stage involves maximizing expected profit through a novel ILP-based user-matching formulation. Testing our algorithm on real-world scenarios demonstrates an approximate 35 % increase in demand fulfillment. Additionally, we assess the model's robustness under uncertainty by varying factors such as the risk factor (probability of user's ride acceptance at the offered price), cost factor (rental cost-to-fare ratio), and maximum chain length.

关键词： Costs Uncertainty Limiting Shared transport Pricing integer linear programming Robustness Data models Intelligent transportation systems Testing

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Optimal Installation of Electric Vehicle Charging Stations Using Fleet-vehicles Data

Optimal Installation of Electric Vehicle Charging Stations U...

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IEEE Power and Energy Society General Meeting

作者： Jeeyung Kim Sangjae Bae Dining Lborory Indusri Engineering Seou Nion UniversiyDeren of Civi nd Environen Engineering Universiy of Ciforni Berkeey

ISBN: (数字)9781728155081

ISBN: (纸本)9781728155081;9781728155098

The Electric Vehicle has became viable option not only for individual drivers but also for the industries or government-affiliated organizations who own fleet vehicles. Before replacement of vehicles, construction of electric vehicle supply equipment (EVSE) has to be preceded. In order to establish optimal EVSE configuration, not only the locations but also the number of charging stations should be decided. Besides, as various types of chargers provide significantly different charging rates, what kind of chargers will be installed should also be taken into consideration. The optimal deployment of EV charging stations should both meet the charging demand and minimize the total cost including installation and operation at the same time. We formulate the problem as optimization framework utilizing fleet-vehicles mobility data, and present solutions based on integer linear programming. We propose a robust methodology which provides the location and the number of type of EVSE and validate our methodology by comparing costs and the ratio of covered trips, which provides practical comparison for fleet organizations.

关键词： Organizations Charging stations integer linear programming Electric vehicle charging Optimization Petroleum Vehicles

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MINLP algorithms mixed with constraint programming

MINLP algorithms mixed with constraint programming

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World Congress on Intelligent Control and Automation (WCICA)

作者： Longhua Ma Liyan Zhang Jixin Qian National Laboratory of Industrial Control Technology Institute of Systems Engineering University of Zhejiang Hangzhou China

ISBN: (纸本)0780382730

This paper advanced mixed integer nonlinear programming (MINLP) algorithms mixed with constraint programming (CP) to solve industrial process hybrid model mixed with logical rule. CP methods have proved to be successful in solving highly constrained discrete optimization and feasibility problems. It can effectively solve hybrid model mixed with logical rule by integrating CP, nonlinear programming and mixed integer linear programming. Computational results demonstrated this algorithm.

关键词： Logic programming integer linear programming Industrial control Laboratories Systems engineering and theory Electrical equipment industry Constraint optimization Mixed integer linear programming

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Solving Real Life Nurse Rostering Problem in a Local Hospital Based on Spreadsheet 20

Solving Real Life Nurse Rostering Problem in a Local Hospita...

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Proceedings of the 2020 4th International Conference on Electronic Information Technology and Computer Engineering

作者： Ziran Zheng Xiaoju Gong Business School Shandong Normal University Jinan Shandong China School of Nursing Shandong Provincial Hospital Jinan Shandong China

ISBN: (纸本)9781450387811

Nurse rostering problem(NPR) is a complex optimization problem that appears in health care institutions. Even though a number of algorithms have been proposed to solve the problem, in real-life settings, software tools capable of generating high quality nurse rostering is still unavailable due to various reasons. To solve this issue in a local hospital, we implement a nurse rostering system in Excel that helps managers in charge to build rosters. The problem is modeled by an integer linear programming formulation and a variable neighborhood search algorithm is adopted to solve the optimization problem. Important issues like continuity and fairness are also addressed in the model. Data sets derived from real life settings and randomly generated instances are used to test the solver compared with commercial integer programming solver. Results indicate that the spreadsheet based rostering tool is capable of finding high quality solutions for all instances within acceptable time limits.

关键词： Nursing rostering integer linear programming Excel variable neighborhood search

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Product mix planning in semiconductor foundry manufacturing

Product mix planning in semiconductor foundry manufacturing

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Semiconductor Manufacturing Technology Workshop

作者： Y-C Chou Industrial Engineering National Taiwan University Taipei Taiwan

ISBN: (纸本)0780363744

Since a semiconductor foundry plant manufactures a wide range of memory and logic products using the make-to-order business model, the product mix is an important production decision. This paper first describes the characteristics of the product mix planning problem in foundry manufacturing that are attributable to the long flow time and queuing network behaviors. The issues of time bucket selection, mix optimization and bottleneck-based planning are next addressed. A decision software system based on integer linear programming techniques and a heuristic procedure have been implemented for mix planning. It was determined that the suitable time bucket of planning is either one week or one month and the lead-time offset factor should be included in the logic of workload calculation. This paper also presents various facets of product mix decisions and how they should be integrated with operations management.

关键词： Semiconductor device manufacture Capacity planning Foundries Logic Production integer linear programming Portfolios Process planning Cost accounting Aggregates

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