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Tire noise optimization problem: a mixed integer linear programming approach

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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Complete mixed integer linear programming formulations for modularity density based clustering

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DISCRETE OPTIMIZATION 2017年 25卷 141-158页

作者： Costa, Alberto Ng, Tsan Sheng Foo, Lin Xuan Natl Univ Singapore Singapore Singapore Swiss Fed Inst Technol Future Resilient Syst Zurich Switzerland Natl Univ Singapore Dept Ind & Syst Engn Singapore Singapore

Modularity density maximization is a clustering method that improves some issues of the commonly used modularity maximization approach. Recently, some mixed integer linear programming (MILP) reformulations have been proposed in the literature for the modularity density maximization problem, but they require as input the solution of a set of auxiliary binary Non-linear Programs (NLPs). These can become computationally challenging when the size of the instances grows. In this paper we propose and compare some explicit MILP reformulations of these auxiliary binary NLPs, so that the modularity density maximization problem can be completely expressed as MILP. The resolution time is reduced by a factor up to two order of magnitude with respect to the one obtained with the binary NLPs. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Clustering Modularity density mixed integer linear programming Reformulations

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

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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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A mixed integer linear programming solution for single hoist multi-degree cyclic scheduling with reentrance

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ENGINEERING OPTIMIZATION 2014年第5期46卷 704-723页

作者： Li, Xin Fung, Richard Y. K. City Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Hong Kong Peoples R China

This article considers single hoist multi-degree cyclic scheduling problems with reentrance. Time window constraints are also considered. Firstly, a mixed integer programming model is formulated for multi-degree cyclic hoist scheduling without reentrance, referred to as basic lines in this article. Two valid inequalities corresponding to this problem are also presented. Based on the model for basic lines, an extended mixed integer programming model is proposed for more complicated scheduling problems with reentrance. Phillips and Unger's benchmark instance and randomly generated instances are applied to test the model without reentrance, solved using the commercial software CPLEX. The efficiency of the model is analysed based on computational time. Moreover, an example is given to demonstrate the effectiveness of the model with reentrance.

关键词： hoist scheduling problems mixed integer linear programming multi-degree cycle reentrance robotic cells

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Experiences with mixed integer linear programming based approaches on short-term hydro scheduling

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IEEE TRANSACTIONS ON POWER SYSTEMS 2001年第4期16卷 743-749页

作者： Chang, GW Aganagic, M Waight, JG Medina, J Burton, T Reeves, S Christoforidis, M Natl Chung Cheng Univ Dept Elect Engn Chiayi 621 Taiwan Siemens Energy Management & Informat Syst Brooklyn Pk MN 55428 USA ECNZ So Generat Grp Twizel New Zealand Swiss Rail SBB Zollikofen Switzerland

This paper describes experiences with mixed integer linear programming (MILP) based approaches on the short-term hydro scheduling (STHS) function. The STHS is used to determine the optimal or near-optimal schedules for the dispatchable hydro units in a hydro-dominant system for a user-definable study period at each time step while respecting all system and hydraulic constraints. The problem can be modeled in detail for a hydro system that contains both conventional and pumped-storage units. Discrete and dynamic constraints such as unit startup/shutdown and minimum-up/minimum-down time limits are also included in the model for hydro unit commitment (HUC). The STHS problem is solved with a state-of-the-art package which includes an algebraic modeling language and a MILP solver. The usefulness of the proposed solution algorithm is illustrated by testing the problem with actual hydraulic system data. Numerical experiences show that the solution technique is computationally efficient, simple, and suit able for decision support of short-term hydro operations planning. In addition, the proposed approaches can be easily extended for scheduling applications In deregulated environment.

关键词： algebraic modeling language hydro unit commitment interior point method mixed integer linear programming short-term hydro scheduling

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Energy-saving optimization of application server clusters based on mixed integer linear programming

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JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING 2023年 171卷 111-129页

作者： Xiong, Zhi Zhao, Min Yuan, Ziyue Xu, Jianlong Cai, Lingru Shantou Univ Dept Comp Sci & Technol Shantou 515063 Peoples R China Shantou Univ Minist Educ Key Lab Intelligent Mfg Technol Shantou 515063 Peoples R China

The issue of how to dynamically optimize the deployment of an application server cluster according to the changing load to reduce energy consumption is an important problem that must be urgently solved. In this paper, we propose an energy-saving optimization strategy for application server clusters, whose optimization content includes the on/off state, CPU frequency, and load size of each server. Compared with existing research, our strategy is not only more accurate in power and load models but also considers the switching cost of servers to avoid server switching jitter. The strategy includes two schemes, which both formulate the cluster energy-saving optimization as a mixed integer linear programming (MILP) problem and then adopt a toolkit to solve the problem. One scheme defines variables for each server, and the resulting programming problem is called the MILP4PH problem. The other scheme defines variables for each server type, resulting in a programming problem called the MILP4GH problem. The experimental results reveal that for clusters with poor homogeneity, the MILP4PH problem has fewer variables and can be solved in real time, while for clusters with good homogeneity, the MILP4GH problem has fewer variables and can be solved in real time.(c) 2022 Elsevier Inc. All rights reserved.

关键词： Application server cluster Energy-saving optimization mixed integer linear programming Switching jitter Homogeneity

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Time-Optimal Coordination of Flexible Manufacturing Systems Using Deterministic Finite Automata and mixed integer linear programming

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DISCRETE EVENT DYNAMIC SYSTEMS-THEORY AND APPLICATIONS 2009年第3期19卷 287-315页

作者： Kobetski, Avenir Fabian, Martin Chalmers Univ Technol Dept Signals & Syst S-41296 Gothenburg Sweden

Automation and flexibility are often mentioned as key concepts in modern production industry. To increase the level of flexibility, deterministic finite automata (DFA) can be used to model, specify and verify the production systems. Often, it is also desirable to optimize some production criteria, such as for example the cycle time of a manufacturing cell. In this paper, a method for automatic conversion from DFA to a mixed integer linear programming (MILP) formulation is first presented. This conversion is developed for a number of DFA structures that have shown to be useful in practical applications. Special attention is paid to reducing the search region explored by the MILP solver. Second, a conversion from the MILP solution to a DFA supervisor is described. This allows to combine the advantages of DFA modeling with the efficiency of MILP and supervisory control theory to automatically generate time-optimal, collision-free and non-blocking working schedules for flexible manufacturing systems.

关键词： Discrete event systems Scheduling mixed integer linear programming Collision avoidance Deadlock avoidance

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Robust Automated Mass Spectra Interpretation and Chemical Formula Calculation Using mixed integer linear programming

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ANALYTICAL CHEMISTRY 2013年第20期85卷 9777-9784页

作者： Baran, Richard Northen, Trent R. Lawrence Berkeley Natl Lab Div Life Sci Berkeley CA 94720 USA

Untargeted metabolite profiling using liquid chromatography and mass spectrometry coupled via electrospray ionization is a powerful tool for the discovery of novel natural products, metabolic capabilities, and biomarkers. However, the elucidation of the identities of uncharacterized metabolites from spectral features remains challenging. A critical step in the metabolite identification workflow is the assignment of redundant spectral features (adducts, fragments, multimers) and calculation of the underlying chemical formula. Inspection of the data by experts using computational tools solving partial problems (e.g., chemical formula calculation for individual ions) can be performed to disambiguate alternative solutions and provide reliable results. However, manual curation is tedious and not readily scalable or standardized. Here we describe an automated procedure for the robust automated mass spectra interpretation and chemical formula calculation using mixed integer linear programming optimization (RAMSI). Chemical rules among related ions are expressed as linear constraints and both the spectra interpretation and chemical formula calculation are performed in a single optimization step. This approach is unbiased in that it does not require predefined sets of neutral losses and positive and negative polarity spectra can be combined in a single optimization. The procedure was evaluated with 30 experimental mass spectra and was found to effectively identify the protonated or deprotonated molecule ([M + H](+) or [M - H](-)) while being robust to the presence of background ions. RAMSI provides a much-needed standardized tool for interpreting ions for subsequent identification in untargeted metabolomics workflows.

关键词： CHEMICAL formulas linear programming METABOLITES ELECTROSPRAY ionization mass spectrometry IONS mixed integer linear programming MASS spectrometry PROTON transfer reactions

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Optimal scheduling in a yogurt production line based on mixed integer linear programming

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JOURNAL OF FOOD ENGINEERING 2007年第2期80卷 445-453页

作者： Doganis, Philip Sarimveis, Haralambos Natl Tech Univ Athens Sch Chem Engn Athens 17580 Greece

A mixed integer linear programming (MILP) model is proposed in this paper that targets the optimal production scheduling in a single yogurt production line. The model takes into account all the standard constraints encountered in production scheduling (material balances, inventory limitations, machinery capacity, labor shifts and manpower restrictions). Furthermore, it considers special features that characterize yogurt production, which are limitations in production sequencing mainly due to different fat contents and flavors of various products and sequence-dependent setup times and costs. The objective function that is minimized considers all major sources of variable cost that depend on the production schedule, i.e. changeover cost, inventory cost and labor cost. The model is applied to a yogurt production line of a major dairy industry and the results are presented and discussed. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： production scheduling yogurt production mixed integer linear programming sequence-dependent setups

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Spillways Scheduling for Flood Control of Three Gorges Reservoir Using mixed integer linear programming Model

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MATHEMATICAL PROBLEMS IN ENGINEERING 2014年第1期2014卷 1-9页

作者： Feng, Maoyuan Liu, Pan Wuhan Univ State Key Lab Water Resources & Hydropower Engn S Wuhan 430072 Peoples R China Hubei Prov Collaborat Innovat Ctr Water Resources Wuhan 430072 Peoples R China

This study proposes a mixed integer linear programming (MILP) model to optimize the spillways scheduling for reservoir flood control. Unlike the conventional reservoir operation model, the proposed MILP model specifies the spillways status (including the number of spillways to be open and the degree of the spillway opened) instead of reservoir release, since the release is actually controlled by using the spillway. The piecewise linear approximation is used to formulate the relationship between the reservoir storage and water release for a spillway, which should be open/closed with a status depicted by a binary variable. The control order and symmetry rules of spillways are described and incorporated into the constraints for meeting the practical demand. Thus, a MILP model is set up to minimize the maximum reservoir storage. The General Algebraic Modeling System (GAMS) and IBM ILOG CPLEX Optimization Studio (CPLEX) software are used to find the optimal solution for the proposed MILP model. The China's Three Gorges Reservoir, whose spillways are of five types with the total number of 80, is selected as the case study. It is shown that the proposed model decreases the flood risk compared with the conventional operation and makes the operation more practical by specifying the spillways status directly.

关键词： SPILLWAYS SCHEDULING FLOOD control GORGES mixed integer linear programming FLOOD risk

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