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动态规划 5

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Weibull分布杂波 1

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square-twist折纸 1

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A new approach for scheduling of multipurpose batch processes with unlimited intermediate storage policy

Nikolaos Rakovitis, Nan Zhang, Jie Li, Liping Zhang

《化学科学与工程前沿（英文）》 2019年第13卷第4期页码 784-802 doi: 10.1007/s11705-019-1858-4

摘要： The increasing demand of goods, the high competitiveness in the global marketplace as well as the need to minimize the ecological footprint lead multipurpose batch process industries to seek ways to maximize their productivity with a simultaneous reduction of raw materials and utility consumption and efficient use of processing units. Optimal scheduling of their processes can lead facilities towards this direction. Although a great number of mathematical models have been developed for such scheduling, they may still lead to large model sizes and computational time. In this work, we develop two novel mathematical models using the unit-specific event-based modelling approach in which consumption and production tasks related to the same states are allowed to take place at the same event points. The computational results demonstrate that both proposed mathematical models reduce the number of event points required. The proposed unit-specific event-based model is the most efficient since it both requires a smaller number of event points and significantly less computational time in most cases especially for those examples which are computationally expensive from existing models.

关键词： scheduling multipurpose batch processes simultaneous transfer mixed-integer linear programming

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Multi-objective optimization for the multi-mode finance-based project scheduling problem

Sameh Al-SHIHABI, Mohammad AlDURGAM

《工程管理前沿（英文）》 2020年第7卷第2期页码 223-237 doi: 10.1007/s42524-020-0097-1

摘要： The finance-based scheduling problem (FBSP) is about scheduling project activities without exceeding a credit line financing limit. The FBSP is extended to consider different execution modes that result in the multi-mode FBSP (MMFBSP). Unfortunately, researchers have abandoned the development of exact models to solve the FBSP and its extensions. Instead, researchers have heavily relied on the use of heuristics and meta-heuristics, which do not guarantee solution optimality. No exact models are available for contractors who look for optimal solutions to the multi-objective MMFBSP. CPLEX, which is an exact solver, has witnessed a significant decrease in its computation time. Moreover, its current version, CPLEX 12.9, solves multi-objective optimization problems. This study presents a mixed-integer linear programming model for the multi-objective MMFBSP. Using CPLEX 12.9, we discuss several techniques that researchers can use to optimize a multi-objective MMFBSP. We test our model by solving several problems from the literature. We also show how to solve multi-objective optimization problems by using CPLEX 12.9 and how computation time increases as problem size increases. The small increase in computation time compared with possible cost savings make exact models a must for practitioners. Moreover, the linear programming-relaxation of the model, which takes seconds, can provide an excellent lower bound.

关键词： multi-objective optimization finance-based scheduling multi-mode project scheduling mixed-integer linear programming CPLEX

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Benefit-based cost allocation for residentially distributed photovoltaic systems in China: A cooperative game theory approach

Xi LUO, Xiaojun LIU, Yanfeng LIU, Jiaping LIU, Yaxing WANG

《工程管理前沿（英文）》 2021年第8卷第2期页码 271-283 doi: 10.1007/s42524-019-0083-7

摘要： Distributed photovoltaic (PV) systems have constantly been the key to achieve a low-carbon economy in China. However, the development of Chinese distributed PV systems has failed to meet expectations because of their irrational profit and cost allocations. In this study, the methodology for calculating the levelized cost of energy (LCOE) for PV is thoroughly discussed to address this issue. A mixed-integer linear programming model is built to determine the optimal system operation strategy with a benefit analysis. An externality-corrected mathematical model based on Shapley value is established to allocate the cost of distributed PV systems in 15 Chinese cities between the government, utility grid and residents. Results show that (i) an inverse relationship exists between the LCOEs and solar radiation levels; (ii) the government and residents gain extra benefits from the utility grid through net metering policies, and the utility grid should be the highly subsidized participant; (iii) the percentage of cost assigned to the utility grid and government should increase with the expansion of battery bank to weaken the impact of demand response on increasing theoretical subsidies; and (iv) apart from the LCOE, the local residential electricity prices remarkably impact the subsidy calculation results.

关键词： solar photovoltaic cost allocation cooperative game theory Shapley value mixed-integer linear programming levelized cost of energy

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基于网络图拓扑结构的MILP模型求解智能制造系统中的工艺规划问题 Article

刘齐浩, 李新宇, 高亮

《工程（英文）》 2021年第7卷第6期页码 807-817 doi: 10.1016/j.eng.2021.04.011

摘要：从工艺网络图的拓扑结构出发，本文提出了一个全新的混合整数线性规划（mixedinteger linear programming, MILP）数学模型，并通过三种优先关系矩阵讨论了网络图中工序的优先关系

关键词：智能工艺规划工艺网路图混合整数线性规划 CPLEX

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Energy systems engineering: methodologies and applications

Pei LIU, Efstratios N. PISTIKOPOULOS, Zheng LI

《能源前沿（英文）》 2010年第4卷第2期页码 131-142 doi: 10.1007/s11708-010-0035-8

摘要： Energy systems are the major contributor to ever-increasing primary energy consumption and consequent greenhouse gas emissions. To tackle these critical problems, planning and design of energy systems needs to be improved towards a more efficient, cost-effective, and environmentally benign direction. However, although there are many technical choices available, they are often developed separately by their own technical communities and driven by their specific interest, thus methods and experience obtained in planning and design of a certain type of energy systems are usually not applicable to other types of energy systems. Energy systems engineering provides a generic methodological framework to facilitate the planning and design of energy systems and to produce integrated solutions to real-life complex energy problems via a systematic approach.In this paper, we present an overview of key methodologies of energy systems engineering, covering superstructure based modelling, mixed-integer programming, multi-objective optimization, optimization under uncertainty, and life-cycle assessment. Applications of these methodologies in polygeneration energy systems design, hydrogen infrastructure planning, and design of energy systems in commercial buildings are provided to demonstrate the capability of these methodologies.

关键词： energy systems engineering superstructure mixed-integer programming multi-objective optimization optimization under uncertainty life-cycle assessment

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Product decomposition strategy for optimization of supply chain planning

Braulio BRUNAUD, Maria Paz OCHOA, Ignacio E. GROSSMANN

《工程管理前沿（英文）》 2018年第5卷第4期页码 466-478 doi: 10.15302/J-FEM-2018059

摘要：

Optimization of large-scale supply chain planning models requires the application of decomposition strategies to reduce the computational expense. Two major options are to use either spatial or temporal Lagrangean decomposition. In this paper, to further reduce the computational expense a novel decomposition scheme by products is presented. The decomposition is based on a reformulation of knapsack constraints in the problem. The new approach allows for simultaneous decomposition by products and by time periods, enabling the generation of a large number of subproblems, that can be solved by using parallel computing. The case study shows that the proposed product decomposition exhibits similar performance as the temporal decomposition, and that selecting different orders of products and aggregating the linking constraints can improve the efficiency of the algorithm.

关键词： supply chain planning Lagrangean decomposition mixed-integer programming

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使用数据驱动模型优化抗体纯化策略 Article

刘松崧, Lazaros G. Papageorgiou

《工程（英文）》 2019年第5卷第6期页码 1077-1092 doi: 10.1016/j.eng.2019.10.011

摘要：

本工作致力于抗体片段纯化过程的多尺度优化。优化了生产过程中的色谱决策，包括色谱柱的数量及其大小，每批的循环数以及操作流速。使用基于微型实验数据的制造规模模拟数据集，建立了以负载质量、流速和柱床高度为输入的色谱通量数据驱动模型。与其他方法相比，分段线性回归建模方法具有简单、预测精度高的优点。提出了两种混合整数非线性规划（MINLP）模型，结合数据驱动模型，以最小化每克抗体纯化过程的总成本。然后，使用线性化技术和多参数分解将这些MINLP模型重新构造为混合整数线性规划（MILP）模型。研究了两个具有不同色谱柱尺寸替代品的工业相关案例，以证明所提出模型的适用性。

关键词：抗体纯化多尺度优化抗原结合片段混合整数规划数据驱动模型分段线性回归

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Robust energy-efficient train speed profile optimization in a scenario-based position–time–speed network

《工程管理前沿（英文）》 2021年第8卷第4期页码 595-614 doi: 10.1007/s42524-021-0173-1

摘要： Train speed profile optimization is an efficient approach to reducing energy consumption in urban rail transit systems. Different from most existing studies that assume deterministic parameters as model inputs, this paper proposes a robust energy-efficient train speed profile optimization approach by considering the uncertainty of train modeling parameters. Specifically, we first construct a scenario-based position–time–speed (PTS) network by considering resistance parameters as discrete scenario-based random variables. Then, a percentile reliability model is proposed to generate a robust train speed profile, by which the scenario-based energy consumption is less than the model objective value at

α

confidence level. To solve the model efficiently, we present several algorithms to eliminate the infeasible nodes and arcs in the PTS network and propose a model reformulation strategy to transform the original model into an equivalent linear programming model. Lastly, on the basis of our field test data collected in Beijing metro Yizhuang line, a series of experiments are conducted to verify the effectiveness of the model and analyze the influences of parameter uncertainties on the generated train speed profile.

关键词： robust train speed profile percentile reliability model scenario-based position–time–speed network mixed-integer programming

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基于车联网的信号灯协同控制 Article

李婉, 班学钢

《工程（英文）》 2020年第6卷第12期页码 1463-1472 doi: 10.1016/j.eng.2020.10.009

摘要：

本文提出了一个基于车联网（CV）环境的交通主干道信号灯协同控制的模型及其求解方法。首先，我们将信号优化与协同控制问题归结为一个混合整数非线性规划（MINLP）。通过考虑单个车辆轨迹的最小油耗和行程时间求解最优相位持续时间和相位差。由于模型的复杂性，我们将问题分解为两个层次：使用动态规划（DP）优化相位持续时间的交叉路口层，以及用于优化所有交叉路口相位差的干道交通层。同时，我们开发了一种基于预测的方法以求解上述双层优化模型。在各种场景下，我们利用交通模拟对模型进行了测试。与传统的感应信号灯协同控制相比，求解MINLP和双层优化模型生成的信号时序规划可以合理地提升交通信号灯控制性能和路网的服务水平。在高密度的交通流量的环境中并考虑不同车辆类型时，与感应信号灯相比，上述双层优化模型的求解法使路网总成本降低了3.8%，MINLP的应用使系统总成本降低了5.9%。这也表明对于交通密度相对较高的干道交通来说，本文提出的协同控制方案效果显著。而仿真结果也表明对于同时拥有主要道路和次要道路的交叉路口而言，面向主要道路进行的协同控制对次要道路上的车辆几乎没有影响。

关键词：车联网交通信号灯协同控制动态规划双层优化混合整数非线性规划

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不确定条件下采用精确参数规划的非线性模型过程操作

Vassilis M. Charitopoulos,Lazaros G. Papageorgiou,Vivek Dua

《工程（英文）》 2017年第3卷第2期页码 202-213 doi: 10.1016/J.ENG.2017.02.008

摘要：

本文提出了新的两(多) 参数规划(mp-P) 启发算法以求解混合整数非线性规划(MINLP) 问题，并着重说明了算法在过程综合问题中的应用。对于因对数项导致的非线性，开发了针对确定性问题的参数算法(p-MINLP)。关键之处是通过将二进制变量和(或) 不确定参数作为符号参数重新生成和求解一阶Karush Kuhn Tucker(KKT) 系统的解析表达式。为此，采用了符号处理和求解技术。为了证明所提出的算法的适用性和有效性，对两个过程综合案例研究进行了验证，相应的结果经最新的数值MINLP 求解器验证是有效的。对于p-MINLP，给出了不确定参数的显函数表示的最优解。

关键词：参数规划不确定性过程综合混合整数非线性规划符号操作

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An interval joint-probabilistic programming method for solid waste management: a case study for the city

Yi XU, Shunze WU, Hongkuan ZANG, Guiguang HOU

《环境科学与工程前沿（英文）》 2014年第8卷第2期页码 239-255 doi: 10.1007/s11783-013-0536-x

摘要： Currently, environmental protection and resources conservation continue to be challenges faced by solid-waste managers in China. These challenges are being further compounded by rapid socioeconomic development and population growth associated with increased waste generation rates and decreased waste disposal capacities. In response to these challenges, an interval joint-probabilistic mixed-integer programming (IJMP) method is developed for supporting long-term planning of waste management activities in the city of Tianjin, which is one of the largest municipalities in the northern part of China. In the IJMP, joint probabilistic constraints are introduced into an interval-parameter mixed-integer programming framework, such that uncertainties presented in terms of interval values and random variables can be reflected. Moreover, a number of violation levels for the waste-management-capacity constraints are examined, which can facilitate in-depth analyses of tradeoffs among economic objective and system-failure risk. The results indicate that reasonable solutions have been generated. They are valuable for supporting the adjustment of the city’s existing waste-management practices and the long-term planning of the city’s waste-management facilities.

关键词： interval analysis mixed integer joint probabilistic constraint planning uncertainty waste management

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Cutting CO emissions through demand side regulation: Implications from multi-regional input–output linearprogramming model

《工程管理前沿（英文）》页码 452-461 doi: 10.1007/s42524-022-0209-1

摘要： This study combines multi-regional input–output (MRIO) model with linear programming (LP) model to explore economic structure adjustment strategies for the reduction of carbon dioxide (CO₂) emissions. A particular feature of this study is the identification of the optimal regulation sequence of final products in various regions to reduce CO₂ emissions with the minimum loss in gross domestic product (GDP). By using China’s MRIO tables 2017 with 28 regions and 42 economic sectors, results show that reduction in final demand leads to simultaneous reductions in GDP and CO₂ emissions. Nevertheless, certain demand side regulation strategy can be adopted to lower CO₂ emissions at the smallest loss of economic growth. Several key final products, such as metallurgy, nonmetal, metal, and chemical products, should first be regulated to reduce CO₂ emissions at the minimum loss in GDP. Most of these key products concentrate in the coastal developed regions in China. The proposed MRIO–LP model considers the inter-relationship among various sectors and regions, and can aid policy makers in designing effective policy for industrial structure adjustment at the regional level to achieve the national environmental and economic targets.

关键词： CO₂ emissions demand side regulation multi-regional input–output model linear programming model

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Optimal placement of PMUs for the smart grid implementation in Indian power grid—A case study

Pathirikkat GOPAKUMAR, G. Surya CHANDRA, M. Jaya Bharata REDDY, Dusmata Kumar MOHANTA

《能源前沿（英文）》 2013年第7卷第3期页码 358-372 doi: 10.1007/s11708-013-0257-7

摘要： Efficient utilization of energy resources is essential for a developing country like India. The concept of smart grid (SG) can provide a highly reliable power system with optimized utilization of available resources. The present Indian power grid requires revolutionary changes to meet the growing demands and to make the grid smarter and reliable. One of the important requirements for SG is the instantaneous monitoring of the voltage, current and power flows at all buses in the grid. The traditional monitoring system cannot satisfy this requirement since they are based on nonlinear power flow equations. Synchro-phasor-measurement devices like phasor measurement units (PMUs) can measure the phasor values of voltages at installed buses. Consequently, the currents passing through all branches connected to that bus can be computed. Since the voltage phasor values at the neighboring buses of a bus containing the PMU can be estimated using Ohm’s law, it is redundant to install PMUs at all the buses in a power grid for its complete observability. This paper proposes the optimal geographical locations for the PMUs in southern region Indian power grid for the implementation of SG, using Integer Linear Programming. The proposed optimal geographical locations for PMU placement can be a stepping stone for the implementation of SG in India.

关键词： phasor measurement units (PMUs) smart grid (SG) southern region Indian power grid (SRIPG) integer linear programming (ILP)

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工程网络计划的LR型模糊系数线性规划方法

高朋,冯俊文

《中国工程科学》 2009年第11卷第2期页码 70-74

摘要：

工程网络计划的基础是对各工序持续时间的估计，而导致工序工期不确定性的因素不仅具有随机性，通常也具有模糊性。文章提出一种具有LR型模糊数的线性规划模型，解决了工程网络计划的时间参数估计和关键路径识别问题，并通过引入λ截集来充分描述决策者在不同情形下对工序工期估计的可信程度。最后给出一实例详细说明了该方法的应用过程及有效性。

关键词：工程网络计划模糊线性规划工序

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A refined risk explicit interval linear programming approach for optimal watershed load reduction with

Pingjian YANG,Feifei DONG,Yong LIU,Rui ZOU,Xing CHEN,Huaicheng GUO

《环境科学与工程前沿（英文）》 2016年第10卷第1期页码 129-140 doi: 10.1007/s11783-014-0683-8

摘要： To enhance the effectiveness of watershed load reduction decision making, the Risk Explicit Interval Linear Programming (REILP) approach was developed in previous studies to address decision risks and system returns. However, REILP lacks the capability to analyze the tradeoff between risks in the objective function and constraints. Therefore, a refined REILP model is proposed in this study to further enhance the decision support capability of the REILP approach for optimal watershed load reduction. By introducing a tradeoff factor ( ) into the total risk function, the refined REILP can lead to different compromises between risks associated with the objective functions and the constraints. The proposed model was illustrated using a case study that deals with uncertainty-based optimal load reduction decision making for Lake Qionghai Watershed, China. A risk tradeoff curve with different values of was presented to decision makers as a more flexible platform to support decision formulation. The results of the standard and refined REILP model were compared under 11 aspiration levels. The results demonstrate that, by applying the refined REILP, it is possible to obtain solutions that preserve the same constraint risk as that in the standard REILP but with lower objective risk, which can provide more effective guidance for decision makers.

关键词： refined risk explicit interval linear programming decision making objective-constraint uncertainty tradeoff aspiration level Lake Qionghai Watershed