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Bridging mixed integer linear programming for truss topology optimization and additive manufacturing

OPTIMIZATION AND ENGINEERING 2021年第2期22卷 849-893页

作者： Reintjes, Christian Lorenz, Ulf Univ Siegen Chair Technol Management Unteres Schloss 3 D-57072 Siegen Germany

One crucial advantage of additive manufacturing regarding the optimization of lattice structures is that there is a reduction in manufacturing constraints compared to classical manufacturing methods. To make full use of these advantages and to exploit the resulting potential, it is necessary that lattice structures are designed using optimization. Against this backdrop, two mixed integer programs are developed in order to use the methods of mathematical optimization in the context of topology optimization on the basis of a fitted ground structure method. In addition, an algorithm driven product design process is presented to systematically combine the areas of mathematical optimization, computer aided design, finite element analysis and additive manufacturing. Our developed computer aided design tool serves as an interface between state-of-the-art mathematical solvers and computer aided design software and is used for the generation of design data based on optimization results. The first mixed integer program focuses on powder-based additive manufacturing, including a preprocessing that allows a multi-material topology optimization. The second mixed integer program generates support-free lattice structures for additive manufacturing processes usually depending on support structures, by considering geometry-based design rules for inclined and support-free cylinders and assumptions for location and orientation of parts within a build volume. The problem to strengthen a lattice structure by local thickening or beam addition or both, with the objective function to minimize costs, is modeled. In doing so, post-processing is excluded. An optimization of a static area load with a practice-oriented number of connection nodes and beams was manufactured using the powder-based additive manufacturing system EOS INT P760.

关键词： Technical operations research mixed integer linear programming Design for additive manufacturing Unstructured lattices Truss topology design Topology optimization

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Tire noise optimization problem: a mixed integer linear programming approach

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RAIRO-OPERATIONS RESEARCH 2021年第5期55卷 3073-3085页

作者： Becker, Matthias Ginoux, Nicolas Martin, Sebastien Roka, Zsuzsanna Leibniz Univ Hannover FG HCI Appelstr 9A D-30167 Hannover Germany Univ Lorraine CNRS IECL F-57000 Metz France Univ Lorraine Lab Concept Optimisat & Modelisat Syst LCOMS EA 7306 F-57000 Metz France

We present a mixed integer linear programming (MILP) approach in order to model the non-linear problem of minimizing the tire noise function. In a recent work, we proposed an exact solution for the Tire Noise Optimization Problem, dealing with an APproximation of the noise (TNOP-AP). Here we study the original non-linear problem modeling the EXact- or real-noise (TNOP-EX) and propose a new scheme to obtain a solution for the TNOP-EX. Relying on the solution for the TNOP-AP, we use a Branch&Cut framework and develop an exact algorithm to solve the TNOP-EX. We also take more industrial constraints into account. Finally, we compare our experimental results with those obtained by other methods.

关键词： mixed integer linear programming branch-and-cut tire shape optimization

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mixed integer linear programming formulations for the hydro production function in a unit-based short-term scheduling problem

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2021年 128卷 106747-106747页

作者： Guisandez, Ignacio Ignacio Perez-Diaz, Juan Univ Politecn Madrid Dept Hydraul Energy & Environm Engn Madrid 28040 Spain

The growing complexity of power system operation demands a greater performance of the modeling approaches, even for generation technologies already consolidated as hydroelectricity. Five mixed integer linear programming formulations for modeling the hydro production function (HPF) are compared: four based on previous references (the traditional method based on a single concave piecewise linear flow-power function, the rectangle method, the logarithmic independent branching 6-stencil method, and the quadrilateral method), and one firstly presented in the paper (the parallelogram method). The comparison is made in the context of daily and weekly hydro scheduling problems of a hypothetical three-plant system on different national day-ahead markets and using different levels of detail in the HPF discretization and time limits. The discussion of results is focused around the relative accuracy, effectiveness, and speed of the analyzed methods to solve the scheduling problems in order to aid in making the most appropriate choice depending on the time horizon. This discussion shows the logarithmic independent branching 6-stencil method as one of the most accurate, the parallelogram method as one of the most effective, and the traditional method based on a single concave piecewise linear flow-power function as the fastest one.

关键词： Hydro production function mixed integer linear programming Problem linearization Short-term hydro scheduling

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Global solutions of nonconvex standard quadratic programs via mixed integer linear programming reformulations

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JOURNAL OF GLOBAL OPTIMIZATION 2021年第2期81卷 293-321页

作者： Gondzio, Jacek Yildirim, E. Alper Univ Edinburgh Sch Math James Clerk Maxwell Bldg Edinburgh EH9 3FD Midlothian Scotland

A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We propose two alternative formulations. Our first formulation is based on casting a standard quadratic program as a linear program with complementarity constraints. We then employ binary variables to linearize the complementarity constraints. For the second formulation, we first derive an overestimating function of the objective function and establish its tightness at any global minimizer. We then linearize the overestimating function using binary variables and obtain our second formulation. For both formulations, we propose a set of valid inequalities. Our extensive computational results illustrate that the proposed mixed integer linear programming reformulations significantly outperform other global solution approaches. On larger instances, we usually observe improvements of several orders of magnitude.

关键词： Nonconvex optimization Quadratic programming mixed integer linear programming Global optimization

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New mixed integer linear programming models and an iterated local search for the clustered traveling salesman problem with relaxed priority rule

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2023年第1期46卷 1-1页

作者： Doan, Thanh Tan Bostel, Nathalie Ha, Minh Hoang Nguyen, Vu Hoang Vuong Univ Nantes CNRS LS2N F-44000 Nantes France Phenikaa Univ Fac Comp Sci ORLab Hanoi 12116 Vietnam VNU Univ Engn & Technol Fac Informat Technol ORLab Hanoi Vietnam

The Traveling Salesman Problem (TSP) is a well known problem in operations research with various studies and applications. In this paper, we address a variant of the TSP in which the customers are divided into several priority groups and the order of servicing groups can be flexibly changed with a rule called the d-relaxed priority rule. The problem is called the Clustered Traveling Salesman Problem with Relaxed Priority Rule (CTSP-d). We propose two new mixed integer linear programming (MILP) models for the CTSP-d and a metaheuristic based on Iterated Local Search (ILS) with operators designed for or adapted to the problem. The experimental results obtained on the benchmark instances show that two new models performs better than previous ones, and ILS also proves its performance with 13 new best known solutions found and significant stability compared to existing metaheuristics.

关键词： Traveling Salesman Problem d-relaxed priority rule mixed integer linear programming Iterated local search

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Improving the manufacturability of highly materially restricted topology-optimized designs with mixed integer linear programming

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ENGINEERING STRUCTURES 2023年第1期284卷

作者： Carstensen, Josephine, V Kim-Tackowiak, Hajin Liang, Mia Y. MIT Dept Civil & Environm Engn 77 Massachusetts Ave Cambridge MA 02139 USA

This paper presents a new free-form topology optimization framework for highly materially restricted design situations. Highly materially restricted design situations are herein defined as being limited significantly by the combined demands on material use and manufacturability. The new framework uses the ground structure approach with frame elements and casts the design problem as a mixed integer linear Program (MILP), ensuring a solution with a manufacturable discrete material distribution. This paper also presents an extension to hybrid mesh ground structures containing both frame and thin solid elements. In both cases, the user can easily tailor the resultant design to discrete fabrication requirements as e.g. relevant when using an extrusion -based Additive Manufacturing (AM) process that requires the design features to adhere to a discrete number of bead depositions. The new framework is numerically demonstrated on topology optimization benchmark examples. In addition, numerical and experimental comparisons are made to the conventional density-based topology optimization approach (with continuous density variables). When the design is highly restricted, the new MILP framework is in most tested cases found to generate solutions with improved numerical predictions on the compliance. For the experimentally validated case study, the numerical prediction is seen to significantly underestimate the experimentally observed performance gain. The experimental investigation additionally cements the high performance of density-based topology optimization in design situations with low levels of design restrictions. In these cases (6 out of 7 tested herein), the solutions generated with density-based topology optimization have comparable or preferable performance.

关键词： Topology optimization Manufacturability Additive Manufacturing Frame structures Hybrid mesh mixed integer linear programming

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mixed integer linear programming Models for Scheduling Elective Surgical Procedures 1

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20th International Conference on Computational Science and Its Applications (ICCSA)

作者： Hortencio, Hanna Pamplona Ronconi, Debora Pretti Univ Sao Paulo Dept Prod Engn EP USP Av Prof Almeida Prado 128Cidade Univ BR-05508900 Sao Paulo Brazil

ISBN: (数字)9783030588083

ISBN: (纸本)9783030588083;9783030588076

The problem of scheduling surgeries consists of allocating patients and resources to each surgical stage, considering the patient's needs, as well as sequencing and timing constraints. This problem is classified as NP-hard and has been widely discussed in the literature for the past 60 years. Nevertheless, many authors do not take into account the multiple stages and resources required to address the complex aspects of operating room management. The general goal of this paper is to propose a mathematical model to represent and solve this problem. Computational tests were also performed to compare the proposed model with a similar model from the literature, with a 64% average reduction in computational time.

关键词： Scheduling Surgery mixed integer linear programming Multiple resources Multiple stages

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Portfolio optimization in district heating: Merit order or mixed integer linear programming?

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ENERGY 2023年 265卷

作者： Gonzalez-Salazar, Miguel Klossek, Julia Dubucq, Pascal Punde, Thomas Vattenfall Warme Berlin AG Berlin Germany

Long-term portfolio optimization is commonly used to find the most cost-effective design and operation of a district heating system, subject to technical, financial, and environmental restrictions. Optimizing a district heating system is not trivial and demands high accuracy and high computational speed. However, existing methods addressing this problem offer one or the other but not both at the same time. The state-of-the-art method for portfolio optimization is mixed integer linear programming (MILP), which is extensively used in industry and academia but can be computing and resource-intensive for large portfolio models. This limitation has motivated the development of various options to reduce the computation time while maintaining the ac-curacy to a large extent. An alternative method to MILP is the merit order (MO) method, which has been used especially for power generation applications due to its simplicity and faster computation but somewhat reduced accuracy. The aim of this paper is to investigate the potential advantages and disadvantages of MO models compared to MILP models in the context of optimizing the portfolio of assets supplying a district heating network. As a study case, we analyze a large portion of the district heating network in Berlin. Four MO model variants with different levels of complexity are proposed and compared to a reference MILP model. Results suggest that MO models variants including heat storage and describing CHP plants with significant detail have the potential to reduce calculation time by nearly three orders of magnitude compared to the reference MILP model, without significantly sacrificing accuracy. In fact, differences in heat generation and net present value (NPV) between the most accurate MO model and the reference MILP model account for +/- 4% and-6%, respectively. Moreover, results show that combining MO and MILP models is advantageous and offers high computational speed and at the same time high accuracy, especially wh

关键词： District heating Portfolio optimization mixed integer linear programming Marginal costs Merit order

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Task and Motion Planning of Fetch-and-Carry Including Push-Aside Action Using mixed integer linear programming

Task and Motion Planning of Fetch-and-Carry Including Push-A...

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IEEE/SICE International Symposium on System Integration

作者： Yusuke Kuribayashi Sotaro Sowa Keisuke Takeshita Kimitoshi Yamazaki Graduate School of Engineering Shinshu University Nagano Japan Toyota Motor Cooperation Faculty of Engineering Shinshu University Nagano Japan

ISBN: (数字)9798331531614

ISBN: (纸本)9798331531621

This paper describes a method for solving task planning and motion planning problems simultaneously. We target a fetch-and-carry of a small item by a single-arm mobile manipulator and introduce a method that can generate a sequence of actions and motions required for each action, even in environments with narrow open spaces such as corridors. In addition, to deal with a case where another object is already placed at the target location, we introduce a push-aside action and extend the previous method to include this action. As our method is formulated using mixed integer linear programming (MILP), the calculation time is relatively short, irrespective of the complexity of the target problem. To verify the efficiency of the proposed method, we performed a quantitative evaluation through simulation and conducted experiments on an actual mobile manipulator to verify feasibility of the methods.

关键词： System integration Manipulators Planning mixed integer linear programming Complexity theory

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Fast Topology Identification of AC / DC Hybrid Distribution Network Based on mixed integer linear programming

Fast Topology Identification of AC / DC Hybrid Distribution ...

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Cyber-Energy Systems and Intelligent Energy (ICCSIE), International Conference on

作者： Shiyao Hu Xichun Feng Xiaofan Kang Yuntao Ju Jing Jiang Economic and Technical Research Institute State Grid Hebei Electric Power Co. Ltd Shijiazhuang China School of Electrical and Control Engineering North China University of Technology Beijing China State Grid Economic and Technological Research Institute Co. Ltd Beijing China

ISBN: (数字)9798350373318

ISBN: (纸本)9798350373325

Topology identification is crucial for advanced analysis such as state estimation in hybrid AC/DC distribution networks. Traditional topology identification methods based on data statistics lack accuracy, and optimization-based methods exhibit low efficiency. To address these issues, a topology identification method based on mixed-integer linear programming is proposed. Initially, the normalized Lagrange multiplier is utilized to identify suspicious measurements, forming a set of suspicious measurements to reduce the number of integer variables to be determined. Subsequently, a linearization method for network constraints in hybrid AC/DC distribution networks is introduced to transform the topology identification problem into a mixed-integer linear programming model. The simulation results demonstrate that by constructing a set of suspicious measurements and linearizing network constraints, the efficiency of solving the problem is significantly improved while ensuring the accuracy of identification.

关键词： Accuracy Network topology Simulation Measurement uncertainty Distribution networks Transforms Time measurement Topology mixed integer linear programming State estimation

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