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10th International Symposium on Dependable Software Engineering: Theories, Tools and Applications, SETTA 2024

作者： Li, Yuchen Fu, Hongfei Long, Haowen Li, Guoqiang Shanghai Jiao Tong University Shanghai China

ISBN: (纸本)9789819606016

Invariant generation is a fundamental problem in program verification that targets the automated generation of invariants that capture the set of reachable program states. Modular operations that calculate the remainder of an integer variable against a divisor are common in programs, and therefore the generation of invariants with modular information is indispensible for proving the correctness of such programs. In this paper, we propose a novel approach for generating affine invariants with modular information via constraint solving. Our approach first transforms affine programs with modular operations into affine transition systems, and then applies existing approaches in Farkas’ Lemma to solve the invariants. Experimental results over a suite of benchmarks that involve complex modular operations show that our approach is time efficient and can generate tight or even accurate linear invariants with modular information. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： integer linear programming

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A Novel Superstructure-based Approach to Batch Process Scheduling Problems 10

A Novel Superstructure-based Approach to Batch Process Sched...

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10th International Conference on Control, Decision and Information Technologies (CoDIT)

作者： Bharucha, Aadil Misra, Shamik Gudi, Ravindra D.

ISBN: (纸本)9798350373981;9798350373974

In this work, a novel superstructure-based optimization framework is proposed for batch process scheduling problems. The framework uses a novel maximal flow unit network (m-FUN) representation of the batch processes for the scheduling. The m-FUN representation is developed based on the material flow in and around the processes and storage vessels. The proposed m-FUN framework results in a mixed integer linear programming (MILP) problem and is applied to optimize three case studies taken from the literature. The efficacy of the proposed framework is tested with multiple instances with increasing scheduling horizons and various objectives. The results of this study are compared with other popular solution methods available in the literature. The proposed framework attains the same objective, demonstrating its efficacy in rigorously representing the process nuances and characteristics. Inherent material flow representation in the proposed framework enables seamless incorporation of utility flows, which will be beneficial in integrating utility network design along with the batch scheduling problem.

关键词： integer linear programming

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MULTI-TRIP ALGORITHM FOR MULTI-DEPOT RURAL POSTMAN PROBLEM WITH RECHARGEABLE VEHICLES

MULTI-TRIP ALGORITHM FOR MULTI-DEPOT RURAL POSTMAN PROBLEM W...

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ASME 2024 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2024

作者： Sathyamurthy, Eashwar Azarm, Shapour Herrmann, Jeffrey W. Department of Mechanical Engineering University of Maryland College ParkMD20742 United States Department of Mechanical Engineering The Catholic University of America WashingtonDC20064 United States

ISBN: (纸本)9780791888339

Autonomous vehicles have emerged as transformative technologies with vast implications across various domains, including surveillance. However, they are constrained by battery limitations, which can hinder their usability and efficiency. Designing algorithms to efficiently utilize them optimizing their battery usage, is crucial to unlocking their full potential. This paper addresses this challenge by studying an extension of the rural postman problem with multiple depots and rechargeable and reusable vehicles that can make multiple trips but have limited battery capacity. It presents a new Mixed integer linear programming (MILP) formulation to find optimal solutions to the problem and proposes a new heuristic called the multi-trip (MT) algorithm. The paper describes the results of a study that tested the MT algorithm, other heuristics, and the MILP formulation on both benchmark instances and larger, real-world instances generated from road maps. Our results show that the MT algorithm found feasible solutions for every instance and produced better solutions than heuristics from the literature on 38 of the 39 instances that were tested. Due to its requirements for memory and computing time, the Gurobi optimizer used for solving the MILP formulation could not find optimal solutions for the largest instances that we tested. This research contributes to enhancing the efficiency and effectiveness of battery-operated unmanned by developing new heuristics to address the challenge of battery limitations. © 2024 by ASME.

关键词： integer linear programming

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Investigating inclusion of linear sensitivity factors in analytical frequency constrained unit commitment formulation 33

Investigating inclusion of linear sensitivity factors in ana...

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33rd Southern African Universities Power Engineering Conference, SAUPEC 2025

作者： Olasoji, Azeez O. Oyedokun, D.T.O. Rajabdorri, Mohammad Sierra-Aguillar, Juan E. University of Cape Town Department of Electrical Engineering Cape Town South Africa Iit ETSI-ICAI Universidad Pontificia Comillas Madrid Spain Universidad de Antioquia Department of Electrical Engineering Medellin Colombia

ISBN: (纸本)9798331535162

As power systems transition towards cleaner energy sources and reduce reliance on conventional generation sources, power systems become increasingly vulnerable to frequency instability following large disturbances due to lower inertia levels. To address this, frequency constraints are being integrated into unit commitment (UC) processes to ensure acceptable frequency deviations during contingencies. However, the inclusion of transmission constraints introduces significant computational complexity. This paper investigates an alternative approach to incorporating transmission line constraints into the analytical frequency-constrained UC (FCUC) problem, aiming to explore whether the computational burden can be reduced using linear sensitivity factors (LSFs) to represent transmission line parameters, aiming to improve computational efficiency. Findings obtained from the study indicate that LSF-based FCUC models offer comparable computational performance compared to DC-based FCUC models while showing reduced spillage under network congestions. These results highlight LSFs as a feasible approach for co-optimizing transmission and frequency constraints in low-inertia power systems, with further validations on larger networks recommended. © 2025 IEEE.

关键词： integer linear programming

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k-Prime Total Labeling of Union of Graphs

k-Prime Total Labeling of Union of Graphs

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International Conference on Computational Engineering, ICCE 2023

作者： Teresa Arockiamary, S. Vijayalakshmi, G. Affiliated to University of Madras Chennai India

ISBN: (纸本)9783031777639

For every positive integer k, a simple graph G of order p and size q is said to be k-prime total labeling if there exists a one-one and onto function g whose vertex and edge labels are from k to k+p+q-1 such that for any edge uv inE(G);g(u), g(v), g(uv) are comparatively prime in pairs. Such a graph is known as the k-prime total graph. In our present study, we analyze some class of union of graphs that admit k-prime total labeling for each positive integer k. … © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： integer linear programming

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Optimizing pushback design considering minimum mining width for open pit strategic planning

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ENGINEERING OPTIMIZATION 2022年第9期54卷 1494-1508页

作者： Nancel-Penard, Pierre Morales, Nelson Univ Chile Dept Min Engn DELPHOS Mine Planning Lab Santiago Chile Univ Chile Adv Min Technol Ctr Santiago Chile

Open pit mines contain ore to be extracted from the surface downwards to obtain a profit. This is achieved using large pieces of equipment with significant space requirements to extract the material from the surface. Unfortunately, the industry currently lacks a standard methodology for optimizing the designs of these spaces;current practice may lead to inconsistent, subjective and suboptimal results. Automatic design of practicable portions of the mines called pushbacks is a desirable tool for the mining industry. This article proposes a new approach based on an integer linear programming model (ILP) determining the volumes to be extracted to maximize profit while respecting geospatial and design constraints. Design constraints require that the minimum width be respected at the bottom of the mine and between successive pushbacks. The ILP is applied to three case studies to show that the model can generate practical solutions in minutes.

关键词： Minimum mining width pushback design mathematical modelling integer linear programming

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Chessboard Domination: Introduction of Some New Problems 20th

Chessboard Domination: Introduction of Some New Problems

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20th Combinatorial and Additive Number Theory, New York Number Theory Seminar, CANT 2022 and 21st Combinatorial and Additive Number Theory, New York Number Theory Seminar, CANT 2023

作者： Adhikari, S.D. Hegde, Shruti Molla, Md Ibrahim Department of Mathematics Ramakrishna Mission Vivekananda Educational and Research Institute Belur711202 India

ISBN: (纸本)9783031650635

For a positive integer n, considering the n×n chessboard, for a chess piece P, one is interested in the graph Pn by taking the squares of the chessboard as its vertices where two squares are adjacent if the piece P situated at one of the squares is able to move directly to the other. After recalling some known results and open questions on the domination number γ(Pn) for the square board Pn, we here introduce some new questions. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： integer linear programming

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Inside the Box: 0–1 linear programming Under Interval Uncertainty 4th

Inside the Box: 0–1 Linear Programming Under Interval Unce...

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4th International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2023

作者： Garajová, Elif Hladík, Milan Charles University Faculty of Mathematics and Physics Department of Applied Mathematics Malostranské nám. 2/25 Prague118 00 Czech Republic Prague University of Economics and Business Faculty of Informatics and Statistics Department of Econometrics nám. W. Churchilla 1938/4 Prague130 67 Czech Republic

ISBN: (纸本)9783031812408

Many practical optimization problems require models that are able to reflect uncertainty or inexactness inherently present in the data. Interval linear programming provides a model for handling uncertain optimization problems, in which one assumes that only lower and upper bounds on the input data are available and the data can be independently perturbed within the intervals determined by the given bounds. Apart from the linear programming models with continuous variables, which have been explored by various authors, intervals also often arise in discrete optimization problems. We adopt the model of integer linear programming with binary variables, in which the constraint matrix, objective vector and right-hand-side vector are affected by interval uncertainty. For this model, only a few works investigating its properties can be found in the literature. In this paper, we discuss the main concepts of feasibility and optimality in the model and discuss their properties. Namely, we address the problem of computing the set and the range of optimal values and characterizing weak optimality of solutions. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： integer linear programming

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Optimal Placement of Phasor Measurement Unit System on the Hungarian Transmission Network 9

Optimal Placement of Phasor Measurement Unit System on the H...

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9th International Youth Conference on Energy (IYCE)

作者： Galo, Andras Farkas, Csaba Gregus, Zoltan Budapest Univ Technol & Econ Dept Elect Power Engn Budapest Hungary MAVIR Ltd Operat Secur Dev Dept Budapest Hungary MAVIR Ltd Secondary Syst Serv Budapest Hungary

ISBN: (纸本)9798350372397;9798350372380

Traditional Supervisory Control and Data Acquisition (SCADA) systems face significant challenges in accurately measuring dynamic changes in power systems, owing to their limited sampling rates and lack of time synchronization. Phasor Measurement Units (PMUs), with their high sampling rates (30-60 Hz) and GPS synchronization, offer a superior alternative for real-time monitoring and simplified state estimation. This study introduces a novel optimization algorithm designed to determine the optimal placement of PMUs in the Hungarian transmission network. The algorithm employs mixed-integer linear programming implemented using Python and MATLAB to achieve comprehensive network observability with minimal PMU deployment. The Hungarian network graph was constructed from data provided in the Union for the Coordination of Transmission of Electricity (UCTE) data exchange format, and the placement algorithm was applied. The results indicate that full network observability can be achieved by placing the PMUs at approximately one-third of the buses. Furthermore, the algorithm provides a strategic sequence for PMU placement, ensuring maximum information capture with each additional PMU while prioritizing critical buses such as those connected to major power plants and cross-border transmission lines. This method is scalable and can be adapted for any power network provided in the UCTE data exchange format.

关键词： PMU Phasor Measurement Unit optimal placement Hungarian transmission system integer linear programming UCTE data exchange format

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Variable and constraint reduction techniques for the temporal bin packing problem with fire-ups

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OPTIMIZATION LETTERS 2022年第8期16卷 2333-2358页

作者： Martinovic, John Strasdat, Nico Valerio de Carvalho, Jose Furini, Fabio Tech Univ Dresden Inst Numer Math Dresden Germany Univ Minho Dept Producao & Sistemas Braga Portugal Sapienza Univ Rome Dept Comp Control & Management Engn Antonio Ruber Rome Italy

The aim of this letter is to design and computationally test several improvements for the compact integer linear programming (ILP) formulations of the temporal bin packing problem with fire-ups (TBPP-FU). This problem is a challenging generalization of the classical bin packing problem in which the items, interpreted as jobs of given weight, are active only during an associated time window. The TBPP-FU objective function asks for the minimization of the weighted sum of the number of bins, viewed as servers of given capacity, to execute all the jobs and the total number of fire-ups. The fire-ups count the number of times the servers are activated due to the presence of assigned active jobs. Our contributions are effective procedures to reduce the number of variables and constraints of the ILP formulations proposed in the literature as well as the introduction of new valid inequalities. By extensive computational tests we show that substantial improvements can be achieved and several instances from the literature can be solved to proven optimality for the first time.

关键词： Cutting and packing Temporal bin packing problem Fire-ups integer linear programming

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