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A low-carbon, fixed-tour scheduling problem with time windows in a time-dependent traffic environment

INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2023年第18期61卷 6177-6196页

作者： Zhang, Siyue Zhou, Shenghan Luo, Rui Zhao, Runze Xiao, Yiyong Xu, Yuchun Beihang Univ Sch Reliabil & Syst Engn Beijing 100191 Peoples R China Aston Univ Sch Engn & Appl Sci Birmingham England

Traffic congestion is a major concern in urban transportation in supply chain management. Road-based logistic companies can mitigate their Carbon dioxide (CO2) emissions effectively by optimising their operation. In this study, we observed a low-carbon, fixed-tour scheduling problem with time windows (LC-FTSP-TW) that is designed to consider the factors that can minimise the greenhouse-gas emissions of logistics systems. Through better planning of the delivery times, we delineated a system to control the schedules of two vehicle types: fossil-fuel-powered and electric-powered vehicles. We formulated the LC-FTSP-TW as a mixed-integer linear programming model that can take into consideration time-varying traffic conditions, customer time windows, and vehicle energy-consumption functions. The proposed model was observed to be convenient for practical use, as it could be solved directly using commercial optimisation toolboxes, such as CPLEX and Gurobi, with continuous optimal results. In addition, we developed an efficient dynamic programming algorithm for solving large-sized problems with discrete optimal results. Computational experiments were conducted on a group of test instances to verify the proposed model and algorithm, which demonstrated considerable reductions in CO2 emissions compared to non-optimised solutions for both the tested fossil-fuel-powered and electric-powered vehicles.

关键词： Dynamic programming green supply chain mixed integer linear programming carbon dioxide emissions optimisation

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Computationally Efficient Collision-Free Trajectory Planning of Satellite Swarms Under Unmodeled Orbital Perturbations

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2023年第8期46卷 1548-1563页

作者： Basu, Himadri Pedari, Yasaman Almassalkhi, Mads Ossareh, Hamid R. Univ Grenoble Alpes Grenoble Images Parole Signal Automat Lab CNRS F-38000 Grenoble France Univ Vermont Dept Elect & Biomed Engn Burlington VT 05405 USA

This paper studies the problem of collision-free trajectory planning for a satellite swarm reconfiguration under perturbations and modeling uncertainties in a low Earth orbit (LEO). Determining exact trajectory planning solutions is computationally heavy as they require solving a mixed-integer nonlinear program owing to i) nonlinear relative dynamic models of satellites, ii) fuel-optimal assignment of satellites on the final formation, and iii) nonconvex collision avoidance constraints. To address these, first, a suitable linear model for trajectory planning is identified by quantifying modeling accuracy associated with various models capturing LEO perturbations. The effects of any residual modeling errors in the path prediction are mitigated by shrinking-horizon model-predictive feedback control, which updates the control command based on the latest satellite measurements. Secondly, an optimal swarm configuration is efficiently computed by decoupling the target-assignment algorithm from the trajectory optimization problem. Based on the estimated fuel expenditure for each satellite-target pairing, the target-assignment algorithm selects a configuration with minimal fuel consumption. Lastly, to determine collision-free, fuel-optimal maneuvers, two novel trajectory planning approaches, namely, distributed and decentralized trajectory optimization, are presented. While the former iteratively searches for collision-free feasible paths to optimal terminal configuration, the latter computes a near-optimal configuration with collision-free paths.

关键词： Satellite Formation Flying Pontryagin's Maximum Principle mixed integer linear programming Energy Economics Feedback Control Adaptive Control Algorithm Aircraft Operations Planets Sun Synchronous Orbit Computational Fluid Dynamics

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Optimal operation of building microgrids - comparison with mixed-integer linear and continuous non-linear programming approaches

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COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING 2018年第2期37卷 603-616页

作者： Reinbold, Vincent Dinh, Van-Binh Tenfen, Daniel Delinchant, Benoit Saelens, Dirk Katholieke Univ Leuven Leuven Belgium Grenoble Univ Grenoble France Inst Fed Educ Ciencia & Tecnol Santa Catarina Florianopolis SC Brazil Grenoble Univ Grenoble Elect Engn Lab G2Elab Grenoble France

PurposeThis paper aims to present two mathematical models to solve the Energy Management problem of a building microgrid (MG). In particular, it proposes a deterministic mixed integer linear programming (MILP) and non-linear programming (NLP) formulations. This paper focuses on the modelling process and the optimization performances for both approaches regarding optimal operation of near-zero energy buildings connected to an electric MG with a 24-h time horizon. Design/methodology/approachA general architecture of a MG is detailed, involving energy storage systems, distributed generation and a thermal reduced model of the grid-connected building. A continuous non-linear model is detailed along with linearizations for the mixed-integer liner formulation. Multi-physic, non-linear and non-convex phenomena are detailed, such as ventilation and air quality models. FindingsResults show that both approaches are relevant for solving the energy management problem of the building MG. Originality/valueIntroduction and modelling of the thermal loads within the MG. The resulting linear program handles the mutli-objective trade-off between discomfort and the cost of use taking into account air quality criterion. linearization and modelling of the ventilation system behaviour, which is generally non-linear and non-convex equality constraints, involving air quality model, heat transfer and ventilation power. Comparison of both MILP and NLP methods on a general use case provides a solution that can be interpreted for implementation.

关键词： Microgrid mixed integer linear programming Optimal operation Sequential quadratic programming

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A Kernel search algorithm for virtual machine consolidation problem in cloud computing

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JOURNAL OF SUPERCOMPUTING 2023年第17期79卷 19277-19296页

作者： Luo, Jiang-Yao Yuan, Jian-Hua Beijing Univ Posts & Telecommun Sch Sci Beijing 100876 Peoples R China Beijing Univ Posts & Telecommun Key Lab Math & Informat Networks Minist Educ Beijing Peoples R China

Virtual machine consolidation refers to the process of reallocating virtual machines across a set of target servers. It can be formulated as a mixed integer linear programming problem, which is known to be NP-hard. In this paper, we propose a kernel search (KS) heuristic algorithm based on hard variable fixing to quickly obtain high-quality solutions for large-scale virtual machine consolidation problems (VMCPs). Since existing variable fixing strategies in KS algorithms may result in some VMCP instances being infeasible, our proposed KS algorithm employs a more efficient strategy to choose a set of fixed variables based on their corresponding reduced costs. Our numerical results on VMCP instances demonstrate that our proposed KS algorithm significantly outperforms mixed integer linear programming solvers in terms of CPU time. Moreover, our proposed strategy of variable fixing improves the efficiency of the KS algorithm significantly, with negligible degradation in solution quality.

关键词： Kernel search Heuristic algorithm mixed integer linear programming Virtual machine consolidation Cloud computing

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On the minimum number of resources for a perfect schedule

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CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH 2023年第1期31卷 191-204页

作者： Benmansour, Rachid Braun, Oliver Inst Natl Stat & Econ Appl SI2M Lab Rabat Morocco Trier Univ Appl Sci Environm Campus Birkenfeld D-55768 Birkenfeld Germany

In the single-processor scheduling problem with time restrictions there is one main processor and B resources that are used to execute the jobs. A perfect schedule has no idle times or gaps on the main processor and the makespan is therefore equal to the sum of the processing times. In general, more resources result in smaller makespans, and as it is in practical applications often more economic not to mobilize resources that will be unnecessary and expensive, we investigate in this paper the problem to find the smallest number B of resources that make a perfect schedule possible. We show that the decision version of this problem is NP-complete, derive new structural properties of perfect schedules, and we describe a mixed integer linear programming (MIP) formulation to solve the problem. A large number of computational tests show that (for our randomly chosen problem instances) only B = 3 or B = 4 resources are sufficient for a perfect schedule.

关键词： Minimizing the number of resources Perfect schedule Single-processor scheduling mixed integer linear programming

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Feasibility Jump: an LP-free Lagrangian MIP heuristic

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MATHEMATICAL programming COMPUTATION 2023年第2期15卷 365-388页

作者： Luteberget, Bjornar Sartor, Giorgio SINTEF Forskningsveien 1 N-0373 Oslo Norway

We present Feasibility Jump (FJ), a primal heuristic for mixed-integer linear programs (MIP) using stochastic guided local search over a Lagrangian relaxation. The method is incomplete: it does not necessarily produce solutions to all feasible problems, the solutions it produces are not in general optimal, and it cannot detect infeasibility. It does, however, very quickly produce feasible solutions to many hard MIP problem instances. Starting from any variable assignment, Feasibility Jump repeatedly selects a variable and sets its value to minimize a weighted sum of constraint violations. These weights (which correspond to the Lagrangian multipliers) are adjusted for constraints that remain violated in local minima. Contrary to many other primal heuristics, Feasibility Jump does not require a solution of the continuous relaxation, which can be time-consuming for some problems. We compare FJ against FICO Xpress Solver 8.14 and we show that this heuristic is effective on a range of problems from the MIPLIB 2017 benchmark set, significantly improving the average time to find a first feasible solution. We also show that providing these quick solutions to Xpress produces a modest reduction in the average time to optimality in the same benchmark set. Our entry based on FJ to the MIP 2022 Computational Competition (which challenged participants to write LP-free MIP heuristics) won 1st place. Moreover, an implementation of Feasibility Jump now runs by default on FICO Xpress Solver 9.0, where similar results to the ones presented here could be observed.

关键词： mixed integer linear programming Metaheuristics Lagrangian relaxation Guided local search Primal heuristics

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Scheduling Lockdowns Under Conditions of Pandemic Uncertainty

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IEEE ACCESS 2023年 11卷 118689-118697页

作者： Kaplan, Radoslaw Ksiazek, Roger Gdowska, Katarzyna Lebkowski, Piotr AGH Univ Krakow Fac Management PL-30059 Krakow Poland

The objective of our work was to develop a tool to support the process of making strategic decisions about the COVID-19 pandemic by optimizing suppression intervention schedules. We focus mainly on hard lockdowns that have the effect of containing the spread of the virus and, consequently, minimizing the number of infections and keeping the incidence of COVID-19 at low levels. Properly implemented restrictions can reduce the likelihood of infection and thus push the pandemic back. On the contrary, lifting restrictions results in a sharp increase in likelihood of infection and the development of a pandemic. The model proposed in this paper indicates the optimal moments to implement full lockdown, accounting for both the costs of lockdown and the costs of not applying lockdown.

关键词： Pandemics COVID-19 Viruses (medical) Predictive models Costs Uncertainty Distribution functions Decision making mixed integer linear programming Strategic planning decision making lockdown scheduling mixed integer programming strategic management

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Virtual Target Selection for a Multiple-Pursuer-Multiple-Evader Scenario

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JOURNAL OF AEROSPACE INFORMATION SYSTEMS 2025年第5期22卷 391-400页

作者： Weintraub, Isaac E. Von Moll, Alexander Casbeer, David W. Manyam, Satyanarayana G. Air Force Res Lab Control Sci Ctr Wright Patterson AFB OH 45433 USA InfoSciTex Corp 4027 Col Glenn Hwy Dayton OH 45431 USA

This paper considers an N-pursuer-M-evader scenario involving L virtual targets. The virtual targets serve as an intermediary target for the pursuers, allowing the pursuers to delay their final assignment to the evaders. However, upon reaching the virtual target, the pursuers must decide which evader to capture. It is assumed that there are more pursuers than evaders and that the pursuers are faster than the evaders. The objective is two-part: first, assign each pursuer to a virtual target and evader such that the pursuer team's energy is minimized, and, second, choose the virtual targets' locations for this minimization problem. The approach taken is to consider the Apollonius geometry between each pursuer's virtual target location and each evader. Using the constructed Apollonius circles, the pursuer's travel distance and maneuver at a virtual target are obtained. These metrics serve as a gauge for the total energy required to capture a particular evader and are used to solve the joint virtual target selection and pursuer-evader assignment problem. This paper provides a mathematical definition of this problem, the solution approach taken, and an example. Following the example, a Monte Carlo analysis is performed, demonstrating the efficacy of the algorithm and its suitability for real-time applications.

关键词： mixed integer linear programming Optimal Control Theory Optimization Algorithm Weapon Target Assignment Monte Carlo Analysis Guidance, Navigation, and Control Systems Missile Defense

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Phase ambiguity resolution and mixed pixel detection in EDM with multiple modulation wavelengths

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ISPRS JOURNAL OF PHOTOGRAMMETRY AND REMOTE SENSING 2023年第1期198卷 255-271页

作者： Butt, Jemil Avers Salido-Monzu, David Wieser, Andreas Swiss Fed Inst Technol Inst Geodesy & Photogrammetry Stefano Franscini Pl 5 CH-8093 Zurich Switzerland Atlas Optimizat GmbH Naglerwiesenstr 50 CH-8049 Zurich Switzerland

Distance measurement based on the accumulated phase of intensity-modulated continuous-wave lasers is an established approach for pointwise geometry acquisition in uncontrolled conditions, enabling some of the most accurate Lidar/laser-scanning solutions. Inherently affected by cycle ambiguities due to the modulo 2 pi phase observations, several modulation wavelengths are typically used in practical implementations to extend the measurement range. One of the main limitations of these systems arises from their inability to decouple mixed signals affected by different delays. This is especially relevant when the laser beam illuminates simultaneously two or more surfaces at significantly different distances, producing mixed-pixel measurements in which the estimated distance does not reliably correspond to any of the involved scatterers. Algorithms for detection and filtering of mixed pixels within point-cloud data have been proposed based on analyzing consistency across local neighborhoods. The resolution of multiple scatterers on individual measurements, however, has not been yet reported nor is provided by undisclosed commercial implementations. In this work, we analyze the problem of signal mixing in multi-wavelength phase-based distance estimation, and propose an algorithm for joint phase ambiguity resolution and mixed pixel detection based on mixed integer linear programming. We first analyze theoretically the performance limits of the proposed solution, demonstrating unbiasedness in the presence of noise and robustness in the presence of multiple scatterers. In addition, we investigate empirically the impact of noise, mixed measurements and choice of modulation wavelengths on the performance of the proposed algorithm. The results demonstrate the capacity of the presented approach, given an adequate wavelength selection, to provide unambiguous distance estimates under realistic noise conditions and to identify measurements affected by mixed pixels while approximati

关键词： Electro-optical distance measurement (EDM) Phase measurement Ambiguity resolution mixed pixel mixed integer linear programming

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A mathematical programming approach for resource allocation of data analysis workflows on heterogeneous clusters

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JOURNAL OF SUPERCOMPUTING 2023年第17期79卷 19019-19048页

作者： Mohammadi, Somayeh PourKarimi, Latif Droop, Felix De Mecquenem, Ninon Leser, Ulf Reinert, Knut Freie Univ Dept Math & Comp Sci Berlin Germany Razi Univ Dept Math & Comp Sci Kermanshah Iran Humboldt Univ Dept Math & Comp Sci Berlin Germany

Scientific communities are motivated to schedule their large-scale data analysis workflows in heterogeneous cluster environments because of privacy and financial issues. In such environments containing considerably diverse resources, efficient resource allocation approaches are essential for reaching high performance. Accordingly, this research addresses the scheduling problem of workflows with bag-of-task form to minimize total runtime (makespan). To this aim, we develop a mixed-integer linear programming model (MILP). The proposed model contains binary decision variables determining which tasks should be assigned to which nodes. Also, it contains linear constraints to fulfill the tasks requirements such as memory and scheduling policy. Comparative results show that our approach outperforms related approaches in most cases. As part of the post-optimality analysis, some secondary preferences are imposed on the proposed model to obtain the most preferred optimal solution. We analyze the relaxation of the makespan in the hope of significantly reducing the number of consumed nodes.

关键词： Heterogeneous cluster environments Scheduling Data analysis workflow mixed integer linear programming Makespan minimization Post-optimality analysis

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