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Optimising aircraft arrivals in terminal airspace by mixed integer linear programming model

AERONAUTICAL JOURNAL 2020年第1278期124卷 1129-1145页

作者： Cecen, R. K. Cetek, F. Aybek Anadolu Univ Eskisehir Turkey Eskisehir Tech Univ Eskisehir Turkey

Air traffic flow becomes denser and more complex within terminal manoeuvering areas (TMAs) due to rapid growth rates in demand. Effective TMA arrival management plays a key role in the improvement of airspace capacity, flight efficiency and air traffic controller performance. This study proposes a mixed integer linear programming model for aircraft landing problems with area navigation (RNAV) route structure using three conflict resolution and sequencing techniques together: flexible route allocation, airspeed reduction and vector manoeuver. A two-step mixed integer linear programming model was developed that minimises total conflict resolution time and then total airborne delay using lexicographic goal programming. Experimental results demonstrate that the model can obtain conflict-free and time optimal aircraft trajectories for RNAV route structures.

关键词： Air traffic flow management conflict-free arrival sequencing mixed integer linear programming goal programming extended terminal airspace

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mixed integer linear programming and constraint programming models for the online printing shop scheduling problem

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COMPUTERS & OPERATIONS RESEARCH 2020年 123卷

作者： Lunardi, Willian T. Birgin, Ernesto G. Laborie, Philippe Ronconi, Debora P. Voos, Holger Univ Luxembourg 29 John F Kennedy L-1855 Luxembourg Luxembourg Univ Sao Paulo Inst Math & Stat Dept Comp Sci Rua Matao 1010Cidade Univ BR-05508090 Sao Paulo SP Brazil IBM France 9 Rue VerdunBP 85 F-94253 Gentilly France Univ Sao Paulo Polytech Sch Dept Prod Engn Av Prof Luciano Cualberto 1380Cidade Univ BR-05508010 Sao Paulo SP Brazil

In this work, the online printing shop scheduling problem is considered. This challenging real problem, that appears in the nowadays printing industry, can be seen as a flexible job shop scheduling problem with sequence flexibility in which precedence constraints among operations of a job are given by an arbitrary directed acyclic graph. In addition, several complicating particularities such as periods of unavailability of the machines, resumable operations, sequence-dependent setup times, partial overlapping among operations with precedence constraints, release times, and fixed operations are also present in the addressed problem. In the present work, mixed integer linear programming and constraint programming models for the minimization of the makespan are presented. Modeling the problem is twofold. On the one hand, the problem is precisely defined. On the other hand, the capabilities and limitations of a commercial software for solving the models are analyzed. Extensive numerical experiments with small-, medium-, and large-sized instances are presented. Numerical experiments show that the commercial solver is able to optimally solve only a fraction of the small-sized instances when considering the mixed integer linear programming model;while all small-sized and a fraction of the mediumsized instances are optimally solved when considering the constraint programming formulation of the problem. Moreover, the commercial solver is able to deliver feasible solutions for the large-sized instances that are of the size of the instances that appear in practice. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Flexible job shop scheduling with sequence flexibility Resumable operations Unavailability of the machines Sequence-dependent setup time mixed integer linear programming Constraint programming

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Layout optimization of simplified trusses using mixed integer linear programming with runtime generation of constraints

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2020年第5期61卷 1977-1999页

作者： Fairclough, H. Gilbert, M. Univ Sheffield Dept Civil & Struct Engn Sir Frederick Mappin BldgMappin St Sheffield S1 3JD S Yorkshire England

Traditional truss layout optimization employing the ground structure method will often generate layouts that are too complex to fabricate in practice. To address this, mixed integer linear programming can be used to enforce buildability constraints, leading to simplified truss forms. Limits on the number of joints in the structure and/or the minimum angle between connected members can be imposed, with the joints arising from crossover of pairs of members accounted for. However, in layout optimization, the number of constraints arising from 'crossover joints' increases rapidly with problem size, along with computational expense. To address this, crossover constraints are here dynamically generated and added at runtime only as required (so-called lazy constraints);speedups of more than 20 times are observed whilst ensuring that there is no loss of solution quality. Also, results from the layout optimization step are shown to provide a suitable starting point for a non-linear geometry optimization step, enabling results to be obtained that are in agreement with literature solutions. It is also shown that symmetric problems may not have symmetric optimal solutions, and that multiple distinct and equally optimal solutions may be found.

关键词： Layout optimization Topology optimization Discrete optimization Truss optimization Multiple load-cases mixed integer linear programming

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Data-driven mixed-integer linear programming-based optimisation for efficient failure detection in large-scale distributed systems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第1期303卷 337-353页

作者： Er-Rahmadi, Btissam Ma, Tiejun Univ Southampton Southampton Business Sch Dept Decis Analyt & Risk Ctr Risk Res Bldg 2Univ Rd Southampton SO17 1BJ Hants England Univ Edinburgh Artificial Intelligence Applicat Inst Sch Informat Informat Forum Crichton St Edinburgh EH8 9AB Midlothian Scotland Edinburgh Res Ctr Huawei Technol R&D 2 Semple St Edinburgh EH3 8BL Midlothian Scotland

Failure detectors (FDs) are fundamental building blocks for distributed systems. An FD detects whether a process has crashed or not based on the reception of heartbeats' messages sent by this process over a communication channel. A key challenge of FDs is to tune their parameters to achieve optimal performance which satisfies the desired system requirements. This is challenging due to the complexities of large-scale networks. Existing FDs ignore such optimisation and adopt ad-hoc parameters. In this paper, we propose a new mixed integer linear programming (MILP) optimisation-based FD algorithm. We obtain the MILP formulation via piecewise linearisation relaxations. The MILP involves obtaining optimal FD parameters that meet the optimal trade-off between its performance metrics requirements, network conditions and system parameters. The MILP maximises our FD's accuracy under bounded failure detection time while considering network and system conditions as constraints. The MILP's solution represents optimised FD parameters that maximise FD's expected performance. To adapt to real-time network changes, our proposed MILP-based FD fits the probability distribution of heartbeats' inter-arrivals. To address our FD scalability challenge in large-scale systems where the MILP model needs to compute approximate optimal solutions quickly, we also propose a heuristic algorithm. To test our proposed approach, we adopt Amazon Cloud as a realistic testing environment and develop a simulator for robustness tests. Our results show consistent improvement of overall FD performance and scalability. To the best of our knowledge, this is the first attempt to combine the MILP-based optimisation modelling with FD to achieve performance guarantees.

关键词： Nonlinear programming mixed integer linear programming Distributed systems Failure detection Heartbeats

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New mixed-integer linear programming model for solving the multidimensional multi-way number partitioning problem

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COMPUTATIONAL & APPLIED MATHEMATICS 2022年第3期41卷 1-72页

作者： Nikolic, Bojan Djukanovic, Marko Matic, Dragan Univ Banja Luka Fac Nat Sci & Math Banja Luka Bosnia & Herceg TU Wien Inst Log & Computat Vienna Austria

The multidimensional multi-way number partitioning problem considers a set of n vectors of a fixed dimension m >= 2 as an input. The goal is to find partitioning of the set into k >= 2 subsets such that sums per each coordinate in each subset are as nearly equal as possible. The problem has applications in key encryption and multiprocessor scheduling. Prior to this paper, there has been only one mixed-integer model proposed in case of general k >= 2. In this paper, we propose a new mixed-integer programming model for the general case. The obtained results indicate that our model significantly outperforms the model from literature for larger values of k.

关键词： mixed integer linear programming Partitioning problems Mathematical modelling

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Exercise programming and Optimization for Untrained Individual using mixed integer linear programming

Exercise Programming and Optimization for Untrained Individu...

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International Conference on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment and Management (HNICEM)

作者： Arianna Elise C. Chua Nilo T. Bugtai Robert Kerwin C. Billones Department of Manufacturing Engineering and Management De La Salle University Manila Philippines

Maintaining physical fitness through sports or exercise plays a role in our overall health and well-being, from recovering from cardiovascular diseases to avoiding serious injury. Although sports and exercise are as much as social or recreational activities, not all activities would be equivalent in terms of required physical exertion to maintain cardiovascular health and muscle hypertrophy. Broad guidelines guide medical and sports training professionals to prescribe the correct amount of physical activity for a training session. However, prescribing based on real-life exertion and fitness goals is left entirely to the trainer's discretion. Furthermore, given that the restrictions of one's schedule may discourage some people from getting any physical activity whatsoever, finding an exercise program that satisfies minimum fitness requirements in the least amount of time may encourage more to be more active. This study presents an optimization of a high-intensity interval training program using mixed integer linear programming (MILP), which seeks to select workouts that provide efficient aerobic and muscular gains while minimizing the time needed to perform the program. The program was constrained to suit a high-intensity aerobic program while engaging five muscle groups proportionately. An eight-exercise program was created using MILP, performed at a high intensity while ordering muscle groups' utilization sizes in descending order.

关键词： Training Resistance Sequential analysis Schedules Muscles mixed integer linear programming Health and safety

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A mixed integer linear programming model for multi-sector planning using speed and heading changes

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COMPUTERS & OPERATIONS RESEARCH 2021年 128卷

作者： Hassan, Mohamed Ossama Saucier, Antoine Yacout, Soumaya Soumis, Francois Ecole Polytech Montreal 2900 Blvd Edouard Montpetit Montreal PQ H3T 1J4 Canada

The Multi-Sector Planning (MSP) concept, adopted in both the SESAR and NextGen projects, promotes the control of aircraft and resolution of conflicts over a medium time horizon to reduce and balance con-troller workload. In the context of MSP, we propose a first formulation of the complexity resolution prob-lem that allows trajectory modifications using both speed and heading changes assuming exact knowledge of aircraft positions. This model is also the first to have the capacity to ensure workload bal-ancing among sectors in a Multi-Sector Area (MSA). The number of crossing conflicts in a sector is used as a measure of controller workload. This problem is formulated as a mixed integer linear programming model that allows obtaining optimal solutions. This model ensures neighbor trajectory recovery and min-imal delays. This model was tested on a set of conflict detection and resolution benchmark test problems with up to 300 simultaneous conflicts. Conflict-free solutions were obtained in less than 1.4 s. The model was also tested on several distinct sets of randomly generated problems with an MSA of four sectors and up to 150 aircraft. The number of crossing conflicts was reduced by more than 99% with a computation time smaller than four seconds. It was found that it is beneficial to allow the use of both speed and head-ing changes in high traffic situations. It was also found that considering workload balancing allows the minimization of the total workload in the MSA while preventing overloading some sectors. (c) 2020 Elsevier Ltd. All rights reserved.

关键词： Multi-sector planning Air traffic control Conflict detection and resolution Workload balancing mixed integer linear programming

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mixed integer linear programming Model for Scheduling Burn-in Ovens to Minimize Total Weighted Earliness/Lateness

Mixed Integer Linear Programming Model for Scheduling Burn-i...

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Recent Advances and Innovations in Engineering (ICRAIE)

作者： Dhaval Jayendrakumar Pujara Muthu Mathirajan Indian Institute of Science Bengaluru India

ISBN: (数字)9781728188676

ISBN: (纸本)9781728188683

This study deals with scheduling of Burn-in Oven (BO), a Batch Processing Machine (BPM) in the testing stage of Semiconductor Manufacturing (SM) process. We consider a new problem configuration, close to real-life machining environment, wherein multiple BOs having different capacity are employed parallelly to process the variety of jobs. Jobs have non-agreeable release date & due date, non-identical processing time and non-identical job size. An early completion of job at BO is penalized with earliness penalty whereas late completion of job at BO causes a lateness penalty. In the current Just in Time (JIT) manufacturing scenario, an organization aims to minimize both the penalties (cost). Hence, this study aims to minimize the total weighted earliness/lateness of the jobs. We propose a mixed integer linear programming (MILP) model for dynamic scheduling of (a) single, and (b) multiple BOs. Each of the proposed MILP are validated by developing a suitable numerical example.

关键词： Job shop scheduling Ovens Computational modeling Dynamic scheduling Numerical models mixed integer linear programming Manufacturing

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Optimizing the Hyperparameters of a mixed integer linear programming Solver to Speed up Electric Vehicle Charging Control 1

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23rd European International Conference on the Applications of Evolutionary Computation (EvoApplications) Held as Part of EvoStar Conference

作者： Ishihara, Takahiro Limmer, Steffen Tokyo Inst Technol Grad Sch Engn Dept Syst & Control Tokyo 1528552 Japan Honda Res Inst Europe GmbH D-63073 Offenbach Germany

ISBN: (数字)9783030437220

ISBN: (纸本)9783030437213;9783030437220

Optimization of charging profiles for controlled charging of electric vehicles is commonly done via mixed integer linear programming. The runtime of the optimization can represent an issue for the practical use. However, by tuning the parameter setting of the employed solver, it is possible to speed up the optimization process. The present work evaluates two popular hyperparameter tuning tools - irace (iterated racing) and SMAC (sequential model-based algorithm configuration) - for the optimization of parameters of the SCIP (Solving Constraint integer Programs) solver with the objective to speed up the solving process for four common variants of the electric vehicle charging scheduling problem. Based on the results, the most important solver parameters are identified. It is shown that by tuning a very limited number of parameters, speed-ups of 60% and more can be achieved.

关键词： Hyperparameter optimization SMAC irace mixed integer linear programming SCIP Electric vehicles

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Multi-UAV Routing with Priority using mixed integer linear programming 20

Multi-UAV Routing with Priority using Mixed Integer Linear P...

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20th International Conference on Control, Automation and Systems (ICCAS)

作者： Hong, Youkyung Jung, Sunggoo Kim, Suseong Cha, Jihun Elect & Telecommun Res Inst Daejeon 34129 South Korea

ISBN: (纸本)9788993215199

This study proposes a new mission planning method to perform routing with multiple quadrotors. Unlike conventional routing missions, this study considers the specialized routing mission for quadrotors where there is a visit priority between nodes, and there is a task to be performed at the node. One of our contributions is that a multi-layered hierarchical architecture is designed for mission planning itself at the top level, and for interworking with path planning and flight control required at the lower levels. In mission planning, to determine the optimal pair between agents and visiting nodes and the optimal order of nodes, the optimization problem is designed and solved based on mixed-integer linear programming. Furthermore, we evaluate our method by performing MATLAB and Gazebo co-simulation in a ROS environment.

关键词： Unmanned Aerial Vehicle Task Assignment Routing mixed integer linear programming

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