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mixed-integer linear programming approach for global discrete sizing optimization of frame structures

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2018年第2期57卷 579-593页

作者： Van Mellaert, R. Mela, K. Tiainen, T. Heinisuo, M. Lombaert, G. Schevenels, M. Katholieke Univ Leuven Dept Architecture Fac Engn Sci Kasteelpk Arenberg 1 Box 2431 B-3001 Leuven Belgium Tampere Univ Technol Dept Civil Engn Tampere Finland Katholieke Univ Leuven Dept Civil Engn Fac Engn Sci Leuven Belgium

This paper focuses on discrete sizing optimization of frame structures using commercial profile catalogs. The optimization problem is formulated as a mixed-integer linear programming (MILP) problem by including the equations of structural analysis as constraints. The internal forces of the members are taken as continuous state variables. Binary variables are used for choosing the member profiles from a catalog. Both the displacement and stress constraints are formulated such that for each member limit values can be imposed at predefined locations along the member. A valuable feature of the formulation, lacking in most contemporary approaches, is that global optimality of the solution is guaranteed by solving the MILP using branch-and-bound techniques. The method is applied to three design problems: a portal frame, a two-story frame with three load cases and a multiple-bay multiple-story frame. Performance profiles are determined to compare the MILP reformulation method with a genetic algorithm.

关键词： Global optimization Discrete optimization Sizing optimization Frame structures mixed-integer linear programming

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Optimal Multi-Scenario, Multi-Objective Allocation of Fault Indicators in Electrical Distribution Systems Using a mixed-integer linear programming Model

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IEEE TRANSACTIONS ON SMART GRID 2019年第4期10卷 4508-4519页

作者： Acosta, Jhair S. Lopez, Juan Camilo Rider, Marcos J. Univ Estadual Campinas Dept Syst & Energy Sch Elect & Comp Engn BR-13083852 Campinas SP Brazil

In this paper, a mixed-integer nonlinear programming (MINLP) model for the optimal multiscenario allocation of fault indicators (FIs) in electrical distribution systems (EDS) is presented. The original MINLP model is linearized to obtain an equivalent mixed-integer linear programming (MILP) model. The proposed MILP formulation is a precise, flexible, and scalable optimization model whose optimal solution is guaranteed by commercial solvers. In order to improve the practicality and scope of the proposed method, different demand levels, topologies, and N - 1 contingencies are included as scenarios within the proposed model. The flexibility of the model is also emphasized by adding a custom noncontinuous interruption cost function. The objective function minimizes the average cost of energy not supplied and the present value of the overall investments made over a discrete planning horizon. Since the proposed model is convex, other conflicting objectives can be considered using a simple step-by-step approach to construct the optimal Pareto front. In order to demonstrate the efficiency and scalability of the proposed method, two different EDS are tested: a 69-node RBTS4 benchmark and a real Brazilian distribution system. Results show the efficiency of the proposed method to improve the overall reliability of the system even when few FIs are installed.

关键词： Allocation of fault indicators electrical distribution systems energy not supplied mixed-integer linear programming multi-scenario multi-objective optimization

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mixed-integer linear programming and constraint programming formulations for solving resource availability cost problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第2期266卷 472-486页

作者： Kreter, Stefan Schutt, Andreas Stuckey, Peter J. Zimmermann, Juergen Tech Univ Clausthal Inst Management & Econ Operat Res Grp Julius Albert Str 2 D-38678 Clausthal Zellerfeld Germany CSIRO Decis Sci Data61 Canberra ACT Australia Univ Melbourne Dept Comp & Informat Syst Melbourne Vic 3010 Australia

We consider the resource availability cost problem and two extensions through general temporal constraints and calendar constraints. With general temporal constraints minimum and maximum time lags between the activities can be ensured. Calendar constraints are used to model breaks in the availability of a resource, e.g., weekends or public holidays of resource types that equal staff. Especially if long-term and capital-intensive projects are under consideration, resource availability cost problems should be applied because in such projects it is more important to minimize the cost than, e.g., the project duration. We present mixed-integer linear programming (MILP) formulations as well as constraint programming (CP) models for the three problems. In a performance study we compare the results of the MILP formulations solved by CPLEX and the CP models solved by the lazy clause generation solver CHUFFED on benchmark instances from literature and also introduce new benchmarks. Our CP models close all open instances for resource availability cost problems from the literature. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Project scheduling Resource availability cost problem General temporal constraints and calendars Lazy clause generation mixed-integer linear programming

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Solution for short-term hydrothermal scheduling with a logarithmic size mixed-integer linear programming formulation

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ENERGY 2019年 171卷 770-784页

作者： Jian, Jinbao Pan, Shanshan Yang, Linfeng Guangxi Univ Coll Elect Engn Nanning 530004 Peoples R China Guangxi Univ Nationalities Coll Sci Nanning 530006 Peoples R China Guangxi Univ Coll Comp Elect & Informat Nanning 530004 Peoples R China

Short-term hydrothermal scheduling issue is usually hard to tackle on account of its highly non-convex and non-differentiable characteristics. A popular strategy for handling these difficulties is to reformulate the issue by various linearization techniques. However, in this process, a fairly large number of continuous/binary variables and constraints will be introduced, which may result in a heavy computational burden. In this study, a logarithmic size mixed-integer linear programming formulation is presented for this issue, that is, only a logarithmic size of binary variables and constraints will be required to piecewise linearize the nonlinear functions. Based on such a formulation, a global optimum is therefore can be solved efficiently. To remove the linearization errors and cope with the network loss, a derivable nonlinear programming formulation is derived. By optimizing this formulation via the powerful interior point method, where the previous global solution of mixed-integer linear programming formulation is used as the starting point, a promising feasible solution is consequently attained. Numerical results show that the presented logarithmic size mixed-integer linear programming formulation is more efficient than the generalized one and when it is incorporated into the solution procedure, the proposed methodology is competitive with currently state-of-the-art approaches. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Short-term hydrothermal scheduling Piecewise linearize Logarithmic size mixed-integer linear programming Non-linear programming

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mixed-integer linear programming method for multi-degree and multi-hoist cyclic scheduling with time windows

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ENGINEERING OPTIMIZATION 2018年第11期50卷 1978-1995页

作者： Mao, Yong-nian Tang, Qiu-hua Li, Zi-xiang Zhang, Li-ping Wuhan Univ Sci & Technol Key Lab Met Equipment & Control Technol Wuhan Hubei Peoples R China Wuhan Univ Sci & Technol Hubei Key Lab Mech Transmiss & Mfg Engn Wuhan Hubei Peoples R China

Multi-degree cyclic hoist scheduling and multi-hoist cyclic scheduling are both capable of improving the throughput in an automatic electroplating line. However, previous research on integrated multi-degree and multi-hoist cyclic scheduling is rather limited. This article develops an optimal mixed-integer linear programming model for the integrated multi-degree and multi-hoist cyclic scheduling with time window constraints. This model permits overlap on hoist coverage ranges, and it proposes new formulations to avoid hoist collisions, by which time window constraints and tank capacity constraints are also formulated. A set of available benchmark instances and newly generated instances are solved using the CPLEX solver to test the performance of the proposed method. Computational results demonstrate that the proposed method outperforms the zone partition heuristic without overlapping, and the throughputs are improved by a significant margin using the proposed method, especially for large-size instances.

关键词： Multi-degree cyclic scheduling multi-hoist scheduling mixed-integer linear programming time windows

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Two-stage design optimization based on artificial immune system and mixed-integer linear programming for energy supply networks

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ENERGY 2019年 170卷 1228-1248页

作者： Wakui, Tetsuya Hashiguchi, Moe Sawada, Kento Yokoyama, Ryohei Osaka Prefecture Univ Dept Mech Engn Naka Ku 1-1 Gakuen Cho Sakai Osaka 5998531 Japan

A two-stage optimization approach based on an artificial immune system (AIS) and mixed-integer linear programming (MILP) was developed to efficiently solve large-scale structural design problems of energy supply networks and obtain multiple and diverse design candidates. By focusing on a hierarchical relationship between design and operation variables, a structural design problem, formulated using MILP, is decomposed into an upper-level design problem and a lower-level operation problem. The upper-level design problem is solved using an AIS, in which multiple and diverse sets of suboptimal solutions are searched in a short computation time. In the lower-level optimization, design variables are fixed at the values searched in the upper-level optimization and operation variables are optimized using MILP. Moreover, the lower-level optimization for multiple sets of design variables is separately conducted using parallel computing. The developed approach was applied to the structural design of an energy supply network, consisting of candidates of cogeneration units and heat pump water heating units under power and heat interchange, for a housing complex with four dwellings. The diversity and energy-saving performance of multiple design candidates were analyzed. The computational efficiency was also demonstrated in comparison to the results obtained using only a commercial MILP solver. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Energy supply network Microgrid Structural design Two-stage optimization Artificial immune system mixed-integer linear programming

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Alternative mixed integer linear programming Optimization for Joint Job Scheduling and Data Allocation in Grid Computing

arXiv

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arXiv 2025年

作者： Feng, Shengyu Kim, Jaehyung Yang, Yiming Boudreau, Joseph Chowdhury, Tasnuva Hoisie, Adolfy Khan, Raees Kilic, Ozgur O. Klasky, Scott Korchuganova, Tatiana Nilsson, Paul Outschoorn, Verena Ingrid Martinez Park, David K. Podhorszki, Norbert Ren, Yihui Suter, Frederic Vatsavai, Sairam Sri Yang, Wei Yoo, Shinjae Maeno, Tadashi Klimentov, Alexei Carnegie Mellon University PittsburghPA United States Yonsei University Seoul Korea Republic of University of Pittsburgh PittsburghPA United States Brookhaven National Laboratory UptonNY United States Oak Ridge National Laboratory Oak RidgeTN United States University of Massachusetts Amherst AmherstMA United States SLAC National Accelerator Laboratory Menlo ParkCA United States

This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To tackle the nonlinearity in the constraint, we alternatively fix a subset of decision variables and optimize the remaining ones via mixed integer linear programming (MILP). We solve the MILP problem at each iteration via an off-the-shelf MILP solver. Our experimental results show that our method significantly outperforms existing heuristic methods, employing either independent optimization or joint optimization strategies. We have also verified the generalization ability of our method over grid environments with various sizes and its high robustness to the algorithm hyper-parameters. Copyright © 2025, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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PAAMP: Polytopic Action-Set And Motion Planning for Long Horizon Dynamic Motion Planning via mixed integer linear programming

arXiv

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arXiv 2024年

作者： Jaitly, Akshay Farzan, Siavash Robotics Engineering Department Worcester Polytechnic Institute WorcesterMA01609 United States Electrical Engineering Department California Polytechnic State University San Luis ObispoCA93407 United States

— Optimization methods for long-horizon, dynamically feasible motion planning in robotics tackle challenging non-convex and discontinuous optimization problems. Traditional methods often falter due to the nonlinear characteristics of these problems. We introduce a technique that utilizes learned representations of the system, known as Polytopic Action Sets, to efficiently compute long-horizon trajectories. By employing a suitable sequence of Polytopic Action Sets, we transform the long-horizon dynamically feasible motion planning problem into a linear Program. This reformulation enables us to address motion planning as a mixed integer linear Program (MILP). We demonstrate the effectiveness of a Polytopic Action-Set and Motion Planning (PAAMP) approach by identifying swing-up motions for a torque-constrained pendulum as fast as 0.75 milliseconds. This approach is well-suited for solving complex motion planning and long-horizon Constraint Satisfaction Problems (CSPs) in dynamic and underactuated systems such as legged and aerial robots. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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mixed integer linear programming for Active Contact Selection in Deep Brain Stimulation

arXiv

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arXiv 2025年

作者： Frigge, Anna Franziska Medvedev, Alexander The Division of Systems and Control Department of Information Technology Uppsala University Uppsala Sweden

Deep brain stimulation (DBS) programming remains a complex and time-consuming process, requiring manual selection of stimulation parameters to achieve therapeutic effects while minimizing adverse side-effects. This study explores mathematical optimization for DBS programming, using functional subdivisions of the subthalamic nucleus (STN) to define the desired activation profile. A mixed integer linear programming (MILP) framework is presented allowing for dissimilar current distribution across active contacts. MILP is compared to a linear programming (LP) approach in terms of computational efficiency and activation accuracy. Results from ten Parkinson’s disease patients treated with DBS show that while MILP better matches the predefined stimulation target activation profile, LP solutions more closely resemble clinically applied settings, suggesting the profile may not fully capture clinically relevant patterns. Additionally, MILP’s limitations are discussed, including its reliance on precisely defined target regions and its computational burden for larger target sets. © 2025, CC BY-NC-SA.

关键词： mixed-integer linear programming

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Solving the Lexicographic Multi-Objective mixed-integer linear programming Problem using branch-and-bound and grossone methodology

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COMMUNICATIONS IN NONlinear SCIENCE AND NUMERICAL SIMULATION 2020年 84卷 105177-105177页

作者： Cococcioni, Marco Cudazzo, Alessandro Pappalardo, Massimo Sergeyev, Yaroslav D. Univ Pisa Pisa Italy Univ Calabria Arcavacata Di Rende Italy Lobachevsky State Univ Nizhni Novgorod Nizhnii Novgorod Russia

In the previous work (see [1]) the authors have shown how to solve a Lexicographic Multi-Objective linear programming (LMOLP) problem using the Grossone methodology described in [2]. That algorithm, called GrossSimplex, was a generalization of the well-known simplex algorithm, able to deal numerically with infinitesimal/infinite quantities. The aim of this work is to provide an algorithm able to solve a similar problem, with the addition of the constraint that some of the decision variables have to be integer. We have called this problem LMOMILP (Lexicographic Multi-Objective mixed-integer linear programming). This new problem is solved by introducing the GrossBB algorithm, which is a generalization of the Branch-and-Bound (BB) algorithm. The new method is able to deal with lower-bound and upper-bound estimates which involve infinite and infinitesimal numbers (namely, Grossone-based numbers). After providing theoretical conditions for its correctness, it is shown how the new method can be coupled with the GrossSimplex algorithm described in [1], to solve the original LMOMILP problem. To illustrate how the proposed algorithm finds the optimal solution, a series of LMOMILP benchmarks having a known solution is introduced. In particular, it is shown that the GrossBB combined with the GrossSimplex is able solve the proposed LMOMILP test problems with up to 200 objectives. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Multi-objective optimization Lexicographic optimization mixed-integer linear programming Numerical infinitesimals Grossone methodology

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