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Drawing and Labeling High-Quality Metro Maps by mixed-integer programming

IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2011年第5期17卷 626-641页

作者： Noellenburg, Martin Wolff, Alexander KIT Inst Theoret Informat D-76131 Karlsruhe Germany Univ Wurzburg Lehrstuhl Informat 1 D-97074 Wurzburg Germany

Metro maps are schematic diagrams of public transport networks that serve as visual aids for route planning and navigation tasks. It is a challenging problem in network visualization to automatically draw appealing metro maps. There are two aspects to this problem that depend on each other: the layout problem of finding station and link coordinates and the labeling problem of placing nonoverlapping station labels. In this paper, we present a new integral approach that solves the combined layout and labeling problem (each of which, independently, is known to be NP-hard) using mixed-integer programming (MIP). We identify seven design rules used in most real-world metro maps. We split these rules into hard and soft constraints and translate them into an MIP model. Our MIP formulation finds a metro map that satisfies all hard constraints (if such a drawing exists) and minimizes a weighted sum of costs that correspond to the soft constraints. We have implemented the MIP model and present a case study and the results of an expert assessment to evaluate the performance of our approach in comparison to both manually designed official maps and results of previous layout methods.

关键词： Network visualization graph drawing graph labeling metro map octilinear layout mixed-integer programming

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New Product Introduction Against a Predator: A Bilevel mixed-integer programming Approach

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NAVAL RESEARCH LOGISTICS 2009年第8期56卷 714-729页

作者： Smith, J. Cole Lim, Churlzu Alptekinoglu, Aydin Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA Univ N Carolina Syst Engn & Engn Management Program Charlotte NC 28223 USA So Methodist Univ Edwin L Cox Sch Business Dallas TX 75275 USA

We consider a scenario with two firms determining which products to develop and introduce to the market. In this problem, there exists a finite set of potential products and market segments. Each market segment has a preference list of products and will buy its most preferred product among those available. The firms play a Stackelberg game in which the leader firm first introduces a set of products, and the follower responds with its own set of products. The leader's goal is to maximize its profit subject to a product introduction budget, assuming that the follower will attempt to minimize the leader's profit using a budget of its own. We formulate this problem as a multistage integer program amenable to decomposition techniques. Using this formulation, we develop three variations of an exact mathematical programming method for solving the multistage problem, along with a family of heuristic procedures for estimating the follower solution. The efficacy of our approaches is demonstrated on randomly generated test instances. This article contributes to the operations research literature a multistage algorithm that directly addresses difficulties posed by degeneracy, and contributes to the product variety literature an exact optimization algorithm for a novel competitive product introduction problem. (C) 2009 Wiley Periodicals, Inc. Naval Research Logistics 56: 714-729, 2009

关键词： mixed-integer programming product introduction Stackelberg game

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A Reliability-Based Network Reconfiguration Model in Distribution System with DGs and ESSs Using mixed-integer programming

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ENERGIES 2020年第5期13卷 1219页

作者： Guo, Shanghua Lin, Jian Zhao, Yuming Wang, Longjun Wang, Gang Liu, Guowei South China Univ Technol Sch Elect Power Engn Guangzhou 510640 Peoples R China Shenzhen Power Supply Co Ltd Shenzhen 518001 Peoples R China

Widely used distribution generations (DGs) and energy storage systems (ESSs) enable a distribution system to have a more flexible fault reconfiguration capability. In order to enhance the service reliability and the benefit of distribution networks with DGs and ESSs, this paper proposes a novel distribution system reconfiguration (DSR) model including DGs and ESSs. Meanwhile, the impact of sectionalizing switches and tie switches on reliability is considered. The concept of "boundary switch" is introduced for quantifying the customer interruption duration. The DSR model is presented to minimize the sum of the customer interruption cost, the operation cost of switches, and the depreciation cost of DGs and ESSs. Furthermore, the proposed model is converted into a mixed-integer linear programming, which can be efficiently solved by commercial solvers. Finally, the validity and efficiency of the proposed DSR model are verified by a modified IEEE 33-bus system and a modified PG&E69-bus network. The obtained results indicate the advantages of DGs and ESSs in reducing outage time, and suggest that the types and locations of SSs have great effects on the resulting benefit of DGs and ESSs.

关键词： distribution system reconfiguration distribution generation energy storage system switch customer interruption duration mixed-integer programming

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A mixed-integer programming approach to the parallel replacement problem under technological change

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2016年第3期54卷 680-695页

作者： Bueyuektahtakin, I. Esra Hartman, Joseph C. Wichita State Univ Dept Ind & Mfg Engn Wichita KS USA Univ Massachusetts Coll Engn Lowell MA USA

The parallel replacement problem under economies of scale (PRES) determines minimum cost replacement policies for each asset in a group of assets that operate in parallel and are subject to fixed and variable purchase costs. We study the mixed-integer programming formulation of PRES under technological change by incorporating capacity gains into the model such that newer, technologically advanced assets have higher capacity than assets purchased earlier. We provide optimal solution characteristics and insights about the economics of the problem and derive associated cutting planes for optimising the problem. Computational experiments illustrate that the inequalities are quite effective in solving PRES under technological change instances.

关键词： technological change cutting planes parallel equipment replacement US Postal Service (USPS) fleet management case optimization mixed-integer programming

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An improved mixed-integer programming approach for bi-objective parallel machine scheduling and location

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COMPUTERS & INDUSTRIAL ENGINEERING 2022年 174卷

作者： Wu, Peng Wang, Yun Cheng, Junheng Li, Yantong Fuzhou Univ Sch Econ & Management Fuzhou Peoples R China Fujian Normal Univ Sch Econ Fuzhou Peoples R China Dalian Maritime Univ Sch Maritime Econ & Management Dalian Peoples R China

This paper investigates a new bi-objective parallel machine scheduling and location problem: selecting locations for available machines, assigning jobs to these located machines for processing, and sequencing the assigned jobs on each machine to optimize the location cost and makespan, simultaneously. For the challenging NPhard problem, we first develop a novel bi-objective mixed-integer linear programming (MILP) model with fewer integer variables compared with the state-of-the-art one. Then, several valid inequalities are proposed to tighten it further. We develop an epsilon-constraint based on the fuzzy-logic method to solve the bi-objective model. Computational results for benchmark instances show that the proposed approach obtains more Pareto-optimal solutions compared with the state-of-the-art one and is more than 15 times faster than it. Valid inequalities can reduce average computation time by more than 90%.

关键词： Parallel machine scheduling and location Bi-objective optimization mixed-integer programming Valid inequalities

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Utilizing dependence among variables in evolutionary algorithms for mixed-integer programming: A case study on multi-objective constrained portfolio optimization

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SWARM AND EVOLUTIONARY COMPUTATION 2021年 66卷 100928-100928页

作者： Chen, Yi Zhou, Aimin Das, Swagatam East China Normal Univ Shanghai Key Lab Multidimens Informat Proc 3663 North Zhongshan Rd Shanghai 200062 Peoples R China East China Normal Univ Dept Comp Sci & Technol 3663 North Zhongshan Rd Shanghai 200062 Peoples R China Indian Stat Inst Elect & Commun Sci Unit 203 BT Rd Kolkata 700108 India

mixed-integer Non-Linear programming (MINLP) is not rare in real-world applications such as portfolio invest-ment. It has brought great challenges to optimization methods due to the complicated search space that has both continuous and discrete variables. This paper considers the multi-objective constrained portfolio optimization problems that can be formulated as MINLP problems. Since each continuous variable is dependent to a discrete variable, we propose a Compressed Coding Scheme (CCS), which encodes the dependent variables into a contin-uous one. In this manner, we can reuse some existing search operators and the dependence among variables will be utilized while the algorithm is optimizing the compressed variables. CCS actually bridges the gap between the portfolio optimization problems and the existing optimizers, such as Multi-Objective Evolutionary Algorithms (MOEAs). The new approach is applied to two benchmark suites, involving the number of assets from 31 to 2235. The experimental results indicate that CCS is not only efficient but also robust for dealing with the multi-objective constrained portfolio optimization problems.

关键词： Evolutionary computations mixed-integer programming Coding scheme Multi-objective constrained portfolio optimization

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Stochastic mixed-integer programming for a spare parts inventory management problem

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COMPUTERS & OPERATIONS RESEARCH 2022年 138卷 105568-105568页

作者： Johannsmann, Leonie M. Craparo, Emily M. Dieken, Thor L. Fugenschuh, Armin R. Seitner, Bjoern O. Helmut Schmidt Univ Univ Fed Armed Forces Hamburg Holstenhofweg 85 D-22043 Hamburg Germany Naval Postgrad Sch Operat Res Dept 1411 Cunningham Rd Monterey CA 93943 USA Logistikzentrum Bundeswehr Anton Dohrn Weg 59 D-26389 Wilhelmshaven Germany Brandenburg Univ Technol Cottbus Senftenberg Pl Deutsch Einheit 1 D-03046 Cottbus Germany

The German Armed Forces provide an operation contingent to support the North Atlantic Treaty Organization (NATO) Response Force (NRF). To fulfill a mission, the NRF operates a number of technical systems, mostly vehicles. Each system is composed of several parts which might fail over time, and it can only be used again in the mission if all broken parts are replaced. For short deployments (e.g., one month), the NRF troops bring with them a tightly constrained "warehouse"of spare parts. To ensure an optimal use of the space, we present a two-stage stochastic programming model where in the first stage spare parts are chosen, then failures occur at random, and in the second stage the parts are assigned to the broken systems. We carry out a scenario-based approach, where the failures are simulated by a Monte-Carlo approach. We demonstrate that the resulting mixed-integer linear program can be solved using standard numerical solvers. Using real-world input data provided by the German Armed Forces and simulated data, we analyze the sensitivity of the solutions with respect to the size of the warehouse, the service level, and the number of scenarios, and compare our approach with simpler, doctrine based warehousing strategies.

关键词： Logistics Warehouse management Spare parts management Uncertainty Scenario generation mixed-integer programming Two-stage stochastic optimization Operations research

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Fast Non-Parametric Learning to Accelerate mixed-integer programming for Hybrid Model Predictive Control ⁎

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IFAC-PapersOnLine 2020年第2期53卷 5239-5245页

作者： Jia-Jie Zhu Georg Martius Empirical Inference Department Max Planck Institute for Intelligent Systems Tübingen Germany Autonomous Learning Group Max Planck Institute for Intelligent Systems Tübingen Germany

Today’s fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that exact optimal control law can be computed, e.g., by mixed-integer programming (MIP) under piecewise-affine (PWA) system models. Despite the elegant theory, online solving hybrid MPC is still out of reach for many applications. We aim to speed up MIP by combining geometric insights from hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start techniques. Following a line of work in approximate explicit MPC, the proposed learning-control algorithm, LNMS, gains computational advantage over MIP at little cost and is straightforward for practitioners to implement.

关键词： Model Predictive Control of Hybrid System Machine Learning Learning for Control Nonparametric learning mixed-integer programming

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Reinforcement learning and mixed-integer programming for power plant scheduling in low carbon systems: Comparison and hybridisation

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APPLIED ENERGY 2023年第1期349卷

作者： O'Malley, Cormac de Mars, Patrick Badesa, Luis Strbac, Goran Imperial Coll London London SW7 2AZ England UCL Gower St London WC1E 6BT England Tech Univ Madrid UPM Ronda Valencia 3 Madrid 28012 Spain

Decarbonisation is driving dramatic growth in renewable power generation. This increases uncertainty in the load to be served by power plants and makes their efficient scheduling, known as the unit commitment (UC) problem, more difficult. UC is solved in practice by mixed-integer programming (MIP) methods;however, there is growing interest in emerging data-driven methods including reinforcement learning (RL). In this paper, we extensively test two MIP (deterministic and stochastic) and two RL (model-free and with lookahead) scheduling methods over a large set of test days and problem sizes, for the first time comparing the state-of-the-art of these two approaches on a level playing field. We find that deterministic and stochastic MIP consistently produce lower-cost UC schedules than RL, exhibiting better reliability and scalability with problem size. Average operating costs of RL are more than 2 times larger than stochastic MIP for a 50-generator test case, while the cost is 13 times larger in the worst instance. However, the key strength of RL is the ability to produce solutions practically instantly, irrespective of problem size. We leverage this advantage to produce various initial solutions for warm starting concurrent stochastic MIP solves. By producing several near-optimal solutions simultaneously and then evaluating them using Monte Carlo methods, the differences between the true cost function and the discrete approximation required to formulate the MIP are exploited. The resulting hybrid technique outperforms both the RL and MIP methods individually, reducing total operating costs by 0.3% on average.

关键词： Unit commitment Reinforcement learning mixed-integer programming Renewable power uncertainty

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A general mixed-integer programming framework for efficient modeling, integration and optimization of thermodynamic cycle-based energy systems

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ENERGY CONVERSION AND MANAGEMENT 2021年 250卷 114905-114905页

作者： Liang, Yingzong Hui, Chi Wai Luo, Xianglong Chen, Jianyong Yang, Zhi Chen, Ying Guangdong Univ Technol Sch Mat & Energy Guangzhou Peoples R China Guangdong Univ Technol Guangdong Prov Key Lab Funct Soft Matter Guangzhou Peoples R China Hong Kong Univ Sci & Technol Dept Chem & Biol Engn Clear Water Bay Hong Kong Peoples R China

Thermodynamic cycles are imperative systems for energy conversion, and optimization has been an important tool to improve their thermo-economic benefits. However, off-the-shelf software is often limited by long computational time, inflexibility for modeling and numerical difficulties. Here, we present an equation-based optimization framework featuring: (1) an inclusive modeling structure applicable to various thermodynamic cycles design problems;(2) versatile thermodynamic properties estimation for different working fluids;(3) capability of working fluids optimization with complex composition;(4) an efficient formulation method to model potential phase change of streams in simple/complicated heat exchangers;(5) a systematic optimization strategy to improve solution efficiency. The framework is formulated as mixed-integer nonlinear programming models, and its performance is demonstrated by two thermodynamic cycle optimization problems and one system design problem, including a supercritical CO2 Brayton cycle, cryogenic cycle (PRICO), and concentrated solar power (CSP) system. The Brayton cycle case serves as an illustrative example to show thermodynamic cycle design combining the consideration of stream properties calculation, unit operations, and flowsheet optimization. The PRICO example shows the efficacy of the proposed framework in simultaneously optimizing flowsheet and working fluids composition with complex heat exchangers and stream phase unknown a priori. The CSP case demonstrates that the framework can be extended to system optimization problems with high accuracy multiparameter equation of state. Results prove that the framework is efficient and effective in solving thermodynamic cycle and related energy systems optimization problems.

关键词： Thermodynamic cycle Heat integration mixed-integer programming

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