Short-Term Scheduling of Combined Cycle Units Using Mixed Integer Linear Programming Solution

Combined cycle plants (CCs) are broadly used all over the world. The inclusion of CCs into the optimal resource scheduling causes difficulties because they can be operated in different operating configuration modes based on the number of combustion and steam turbines. In this paper a model CCs based on a mixed integer linear programming approach to be included into an optimal short term resource optimization problem is presented. The proposed method allows modeling of CCs in different modes of operation taking into account the non convex operating costs for the different combined cycle mode of operation.

A mixed integer linear programming approach for municipal solid waste management

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Combining Geographic Information Systems for Transportation and Mixed Integer Linear Programming in Facility Location-Allocation Problems

In this study, we aimed to assess the solution quality for location-allocation problems from facilities generated by the software TransCAD®?, a Geographic Information System for Transportation (GIS-T). Such facilities were obtained after using two routines together: Facility Location and Transportation Problem, when compared with optimal solutions from exact mathematical models, based on Mixed Integer Linear Programming (MILP), developed externally for the GIS. The models were applied to three simulations: the first one proposes opening factories and customer allocation in the state of Sao Paulo, Brazil;the second involves a wholesaler and a study of location and allocation of distribution centres for retail customers;and the third one involves the location of day-care centers and allocation of demand (0 - 3 years old children). The results showed that when considering facility capacity, the MILP optimising model presents results up to 37% better than the GIS and proposes different locations to open new facilities.

The Linear Formulation of Thermal Unit Commitment Problem with Uncertainties through a Computational Mixed Integer

The solar and wind renewable energy is developing very rapidly to fulfill the energy gap. This specific increasing share of renewable energy is a reaction to the ecological trepidations to conciliate economics with security due to the new challenges in power system supply. In solar and wind renewable energy, the only partially predictable is the output with very low controllability which creates unit commitment problems in thermal units. In this research paper, a different linear formulation via mixed integer is presented that only requires “binary variables” and restraints concerning earlier stated models. The framework of this model allows precisely the costs of time-dependent startup & intertemporal limitations, for example, minimum up & down times and a ramping limit. To solve the unit commitment problem efficiently, a commercially available linear programming of mixed-integer is applied for sizeable practical scale. The results of the simulation are shown in conclusions.

Detection of gross errors using mixed integer optimization approach in process industry

A novel mixed integer linear programming (NMILP) model for detection of gross errors is presented in this paper. Yamamura et al.(1988) designed a model for detection of gross errors and data reconciliation based on Akaike information cri- terion (AIC). But much computational cost is needed due to its combinational nature. A mixed integer linear programming (MILP) approach was performed to reduce the computational cost and enhance the robustness. But it loses the super performance of maximum likelihood estimation. To reduce the computational cost and have the merit of maximum likelihood estimation, the simultaneous data reconciliation method in an MILP framework is decomposed and replaced by an NMILP subproblem and a quadratic programming (QP) or a least squares estimation (LSE) subproblem. Simulation result of an industrial case shows the high efficiency of the method.

Integer Programming Formulations for Maximum Lifetime Broadcasting Problems in Wireless Sensor Networks

Approaches based on integer linear programming have been recently proposed for topology optimization in wireless sensor networks. They are, however, based on over-theoretical, unrealistic models. Our aim is to show that it is possible to accommodate realistic models for energy consumption and communication protocols into integer linear programming. We analyze the maximum lifetime broadcasting topology problem and we present realistic models that are also shown to provide efficient and practical solving tools. We present a strategy to substantially speed up the convergence of the solving process of our algorithm. This strategy introduces a practical drawback, however, in the characteristics of the optimal solutions retrieved. A method to overcome this drawback is discussed. Computational experiments are reported.

Optimal configuration of distributed power flow controller to enhance system loadability via mixed integer linear programming

The increase of energy consumption has caused power systems to operate close to the limit of their capacity.The distributed power flow controller(DPFC),as a new member of distributed flexible AC transmission systems,is introduced to remove this barrier.This paper proposes an optimal DPFC configuration method to enhance system loadability considering economic performance based on mixed integer linear programming.The conflicting behavior of system loadability and DPFC investment is analyzed and optimal solutions are calculated.Thereafter,the fuzzy decision-making method is implemented for determining the most preferred solution.In the most preferred solution obtained,the investment of DPFCs is minimized to find the optimal number,locations and set points.Simulation results on the IEEERTS79 system demonstrate that the proposed method is effective and reasonable.

A Green Mixed Integer Linear Programming Model for Optimization of Byproduct Gases in Iron and Steel Industry

Byproduct gas is an important secondary energy in iron and steel industry, and its optimization is vital to cost reduction. With the development of iron and steel industry to be more eco-friendly, it is necessary to construct an integrated optimized system, taking economics, energy consumption and environment into consideration. Therefore, the environmental cost caused by pollutants discharge should be factored in total cost when optimizing byproduct gas distribution. A green mixed integer linear programming （MILP） model for the optimization of byproduct gases was established to reduce total cost, including both operation cost and environmental cost. The operation cost included penalty for gas deviation, costs of fuel and water consumption, holder booster trip penalty, and so forth; while the environmental cost consisted of penalties for both direct and indirect pollutants discharge. Case study showed that the proposed model brought an optimum solution and 2.2% of the total cost could be reduced compared with previous one.

Multi-objective optimization for electric water heater using mixed integer linear programming

Due to the capacity of thermal storage,electric water heater(EWH)is one of the best candidates for demand response programs.However,few attentions are given to the modeling and optimization of EWHs with thermostatically-controlled automatic water mixer(TCAWM).In this paper,differential thermodynamic model is established for EWHs with TCAWM and a piecewise linear approximation method is performed for the nonlinear thermodynamic model.The multi-objective optimization model is established by introducing an index reflecting the comfort degree of users,so that the optimal energy usage of the EWH can be obtained by mixed integer linear programming.Testing examples verify the effectiveness of the proposed method.

A mixed-integer linear programming approach for robust state estimation

In this paper,a mixed integer linear programming(MILP)formulation for robust state estimation(RSE)is proposed.By using the exactly linearized measurement equations instead of the original nonlinear ones,the existingmixed integer nonlinear programming formulation for RSE is converted to a MILP problem.The proposed approach not only guarantees to find the global optimum,but also does not have convergence problems.Simulation results on a rudimentary 3-bus system and several IEEE standard test systems fully illustrate that the proposed methodology is effective with high efficiency.

Reserve Constrained Dynamic Economic Dispatch with Valve-point Effect:A Two-stage Mixed Integer Linear Programming Approach

This paper proposes a deterministic two-stage mixed integer linear programming(TSMILP)approach to solve the reserve constrained dynamic economic dispatch(DED)problem considering valve-point effect(VPE).In stage one,the nonsmooth cost function and the transmission loss are piecewise linearized and consequently the DED problem is formulated as a mixed integer linear programming(MILP)problem,which can be solved by commercial solvers.In stage two,based on the solution obtained in stage one,a range compression technique is proposed to make a further exploitation in the subspace of the whole solution domain.Due to the linear approximation of the transmission loss,the solution obtained in stage two dose not strictly satisfies the power balance constraint.Hence,a forward procedure is employed to eliminate the error.The simulation results on four test systems show that TSMILP makes satisfactory performances,in comparison with the existing methods.

A Linear Mixed Integer Programming Model for N-Vehicle Exploration Problem

Finding the accurate solution for N-vehicle exploration problem is NP-hard in strong sense.In this paper,authors build a linear mixed integer programming model for N-vehicle exploration problem based on its properties.The model is then proved equivalent to the original problem.Given the model,one can apply the already existed methods and algorithms for mixed integer linear programming on N-vehicle exploration problem,which helps to enrich methods for solving N-vehicle exploration problem.

耦合调峰与通航需求的梯级水电站群短期多目标优化调度的MILP方法

电网调峰任务与河道通航需求间的矛盾是水电航运梯级调度时所面临的突出问题,区间回水的顶托作用增大了该问题的复杂性。建立考虑回水影响的梯级水电站群短期多目标优化调度的混合整数线性规划模型,模型以剩余负荷平均距与下游尾水位平均距最小为目标,在将非线性约束通过函数聚合后,利用六面体栅格化技术与第二类特殊有序集约束方法实现该约束的线性化。利用法线边界交叉方法对模型进行求解。算例结果表明,所提方法可以充分计及回水顶托的影响,兼顾调峰与通航需求,高效求解多目标调度问题并获得较理想的结果。

基于FT-MILP算法的大规模水电中长期优化调度研究

随着国内水利事业的快速发展,水电系统规模不断扩大,已有的模型设计通用性不强,优化调度维数灾问题日益凸显。为此,采用森林结构(FT)描述水电站群拓扑结构,利用混合整数线性规划算法(MILP)对模型中非线性函数进行分段线性插值处理,构建了基于FT-MILP算法的大规模水电系统中长期优化调度模型。以我国四川地区大型水电基地277座水电站为例,将所提FT-MILP算法与传统POA算法进行优化调度计算,并将优化调度结果与实际运行结果相比。结果表明,在丰、平、枯水年,大规模水电场景下,FT-MILP算法的水库群总发电量分别为传统POA算法的99.27%、99.14%、99.55%,计算效率约为传统POA算法的20倍,丰枯电量比分别由实际运行的2.26∶1、2.13∶1、1.98∶1减少为1.79∶1、1.70∶1、1.62∶1。因此FT-MILP算法在牺牲少量理论发电效益的同时,大幅缩短了计算耗时,且优化了丰枯出力结构,对于研究我国巨大规模的水电优化调度问题有一定的借鉴意义。

分组密码复杂线性层可分性传播的MILP刻画方法

混合整数线性规划(MILP)作为一种自动化搜索工具,被广泛地应用于搜索分组密码的差分、线性、积分等密码性质.提出一种基于动态选取策略构建MILP模型的新技术,该技术在不同的条件下采用不同的约束不等式刻画密码性质的传播.具体地,从可分性出发根据输入可分性汉明重量的不同,分别采用不同的方法构建线性层可分性传播的MILP模型.最后,将该技术应用于搜索uBlock和Saturnin算法的积分区分器.实验结果表明:对于uBlock128算法,该技术可以搜索到比之前最优区分器多32个平衡比特的8轮积分区分器.除此之外,搜索到uBlock128和uBlock256算法比之前最优区分器更长一轮的9和10轮积分区分器.对于Saturnin256算法,同样搜索到比之前最优区分器更长一轮的9轮积分区分器.

基于MILP的轻量级密码算法ACE与SPIX的线性分析

研究了轻量级密码算法ACE与SPIX的线性性质.给出了环型与门组合结构精确的混合整数线性规划下的线性性质刻画,并将算法ACE与SPIX的非线性操作转化为环型与门组合.基于此构建了ACE置换与SLISCP置换的混合整数线性规划下的线性模型,求解模型得到了2至4步ACE置换与2至5步SLISCP置换最优的线性迹.证明了7步、12步ACE置换分别达到了128比特与320比特的安全目标,7步、13步SLISCP置换分别达到了128比特与256比特的安全目标.对于任意步数的ACE置换与SLISCP置换,认证加密算法ACE-AE-128与SPIX均能够抵抗明文处理阶段的线性区分攻击.

基于MILP对轻量级密码算法FBC-128的差分分析

FBC(Feistel-based Block Cipher)是入围全国密码算法设计竞赛第二轮的轻量级分组密码.由于它具备算法结构简洁、安全性高及软硬件实现性能卓越等优点,备受业界广泛关注.FBC密码算法的数据分组长度和密钥长度至少为128比特,记为FBC-128.目前对FBC-128算法差分攻击的最好结果是12轮,时间复杂度为293.41次加密,数据复杂度为2122个选择明文对.然而,FBC算法是否存在更长的差分区分器,能否对其进行更高轮数的密钥恢复攻击仍有待解决.本文基于混合整数线性规划(MILP)的自动化搜索方法,提出了“分段统计法”来求解FBC-128的差分特征.实验测试结果表明:FBC-128存在15轮差分区分器,其概率为2-121.然后将其向后扩展1轮,对16轮FBC-128算法发起密钥恢复攻击,其数据复杂度为2121个选择明文数据量,时间复杂度为292.68次加密.与已有结果相比,差分区分器和密钥恢复攻击都提升了4轮,并且所需的数据复杂度和时间复杂度更低.

SAILFISH-I、ASD算法基于MILP的积分分析

SAILFISH-I、ASD算法是近些年提出的基于Feistel和SPN结构的轻量级分组密码。根据密码的结构特点,分别构造了基于比特的混合整数线性规划(MILP)可分性质模型,并使用求解器Gurobi对MILP模型求解。本文首次得到SAILFISH-I算法的8、9、10轮积分区分器,ASD算法的7、8、9轮积分区分器。在SAILFISH-I的9轮积分区分器的基础上,向后扩展3轮,进行12轮积分攻击,攻击的数据复杂度约为2^(59.58)个选择明文,时间复杂度约为2^(109.99)次12轮加密,存储复杂度约为2^(57)个储存单元。在ASD的8轮积分区分器的基础上向后扩展2轮,进行10轮积分攻击,攻击的数据复杂度约为2^(57.39)个选择明文,时间复杂度约为2^(70.07)次10轮加密,存储复杂度约为2^(20)个储存单元。

基于MILP的多无人机对敌防空火力压制

建立了基于混合整数线性规划(Mixed Integer LinearProgram,MILP)的多无人机编队对敌防空火力压制协同任务分配模型,以0-1决策变量表征无人机—任务指派关系,引入连续时间决策变量来表示任务的执行时间,并通过对决策变量之间的线性等式和不等式的数学描述,建立无人机之间和无人机执行任务之间合理的协同约束关系。采用商用软件CPLEX对模型求解,仿真验证了模型的合理性。

求解带有阻塞限制的HFSP的MILP模型与改进回溯搜索算法

针对带有阻塞限制的不相关并行机混合流水车间调度问题,以最小化最长完工时间为目标,依据不同的建模思想,建立了求解该问题的4个混合整数线性规划(MILP)模型;鉴于混合整数线性规划不适合求解中大规模问题,提出了一种改进的回溯搜索算法以求解中大规模问题,在该算法中,引入了轮盘赌选择策略以及变邻域搜索算法,以提高算法的收敛速度以及局部搜索能力。最后,对所提MILP模型以及算法进行了对比分析,通过对具体实例的求解验证了所提MILP模型以及算法的有效性及优越性。