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.

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。

Scheduling Step-Deteriorating Jobs on Parallel Machines by Mixed Integer Programming

Production scheduling has a major impact on the productivity of the manufacturing process. Recently, scheduling problems with deteriorating jobs have attracted increasing attentions from researchers. In many practical situations,it is found that some jobs fail to be processed prior to the pre-specified thresholds,and they often consume extra deteriorating time for successful accomplishment. Their processing times can be characterized by a step-wise function. Such kinds of jobs are called step-deteriorating jobs. In this paper,parallel machine scheduling problem with stepdeteriorating jobs( PMSD) is considered. Due to its intractability,four different mixed integer programming( MIP) models are formulated for solving the problem under consideration. The study aims to investigate the performance of these models and find promising optimization formulation to solve the largest possible problem instances. The proposed four models are solved by commercial software CPLEX. Moreover,the near-optimal solutions can be obtained by black-box local-search solver LocalS olver with the fourth one. The computational results show that the efficiencies of different MIP models depend on the distribution intervals of deteriorating thresholds, and the performance of LocalS olver is clearly better than that of CPLEX in terms of the quality of the solutions and the computational time.

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.

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.

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的应用服务器集群能耗与性能实时优化

在节能减排和激烈同行竞争的环境下,应用服务器集群的能耗与性能优化十分迫切.针对已有研究在性能指标和实时性方面的不足,提出一种集群能耗与性能实时优化方案.该方案结合采用线性加权法和主目标法优化集群功率与请求丢弃率这两个目标,将双目标优化转换成一个单目标约束优化.首先基于CPU频率等效连续调整模式下的服务器负载-功率模型,定义很少的变量将集群优化描述成混合整数二次规划问题,然后采用变量拆分和变量转换将其转化成混合整数线性规划(mixed integer linear programming,MILP)问题并引入特殊顺序集约束,最后采用Gurobi优化器求解该MILP.通过对CPU频率调整的进一步优化,大幅度减少了CPU频率的切换.多种场景下的测试表明,该方案的求解时间约在10 ms左右,特殊顺序集约束的引入使求解时间更为稳定,从而能够保证优化的实时进行.

基于MILP的GIFT积分区分器搜索及优化

Banik等提出的轻量级分组密码GIFT算法已经入选了NIST针对国际轻量级密码算法开展的标准化竞赛的最终轮。目前已有针对其的线性分析、差分分析等的相关研究,但针对GIFT的积分分析仍待进一步研究。针对GIFT在积分密码分析过程中可分路径表达冗余的问题,提出了基于混合整数线性规划模型的积分区分器搜索求解和优化算法。首先对GIFT算法创建MILP积分分析模型,利用可分性质分别对GIFT算法的线性层和非线性层进行刻画。对线性层利用传播规则进行表达;对非线性S盒在传播规则的基础上使用贪心算法对表达式进行精简优化,得到了15个不等式作为约束条件。经过MILP求解后,得到64个9轮积分区分器。在此基础上,针对基于贪心算法的MILP求解模型精确度不足问题,引入MILP模型对S盒的可分性质进行重新表达,设计基于MILP的约简算法对GIFT积分区分器搜索进行优化,并重新求解MILP模型,最高得到了3个13轮的积分区分器。因此,基于MILP的S盒新约简算法可以优化S盒可分性质的表达,有效增加对GIFT算法的积分区分器攻击轮数,提高积分攻击效果。

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.

基于多周期性MILP模型的新型配电系统拓扑辨识方法

在新兴低成本、非接触式的电流传感器的基础上,提出了基于多周期性混合整数线性优化的拓扑辨识方法。基于支路电流绝对值误差建立了拓扑辨识的混合整数非线性优化(MINLP)模型,采用线性化方法将MINLP模型转化为混合整数线性优化(MILP)模型,并通过多周期性测量数据建立多周期性优化模型,从而减小伪测量误差的影响。此外,证明了支路电流传感器优化配置条件,以确保拓扑辨识的准确性。在IEEE-33节点系统的仿真测试结果表明,所提出的拓扑辨识方法拓扑辨识精度高,随多周期性场景的增加,拓扑辨识精度逐渐增加,且受伪测量误差的影响比受支路电流测量误差更大。

Hybrid Continuous-Time MILP Model for Crude Oil Scheduling under the Influence of High Tides

Vessels,especially very large or ultra large crude carriers(VLCCs or ULCCs),often can only dock and leave the berth during high tide periods to prevent being stranded.Unfortunately,the current crude scheduling models do not take into account tidal conditions,which will seriously affect the feasibility of crude schedule.So we first focus on the docking and leaving operations under the tidal actions,and establish a new hybrid continuous-time mixed integer linear programming(MILP)model which incorporates global event based formulation and unit-specific event based formulation.Upon considering that the multiple blending of crude oil can easily cause the production fluctuating,there are some reasonable assumptions that storage tanks can only store pure crude,and charging tanks just can be refilled after being emptied,which helps us obtain a simple MILP model without composition discrepancy caused by crude blending.Two cases are used to demonstrate the efficacy of proposed scheduling model.The results show that the optimization schedule can minimize the demurrage of the vessels and the number of feeding changeovers of crude oil distillation units(CDUs).

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.

Randomized MILP framework for Securing Virtual Machines from Malware Attacks

Cloud computing involves remote server deployments with public net-work infrastructures that allow clients to access computational resources.Virtual Machines(VMs)are supplied on requests and launched without interactions from service providers.Intruders can target these servers and establish malicious con-nections on VMs for carrying out attacks on other clustered VMs.The existing system has issues with execution time and false-positive rates.Hence,the overall system performance is degraded considerably.The proposed approach is designed to eliminate Cross-VM side attacks and VM escape and hide the server’s position so that the opponent cannot track the target server beyond a certain point.Every request is passed from source to destination via one broadcast domain to confuse the opponent and avoid them from tracking the server’s position.Allocation of SECURITY Resources accepts a safety game in a simple format as input andfinds the best coverage vector for the opponent using a Stackelberg Equilibrium(SSE)technique.A Mixed Integer Linear Programming(MILP)framework is used in the algorithm.The VM challenge is reduced by afirewall-based controlling mechanism combining behavior-based detection and signature-based virus detection.The pro-posed method is focused on detecting malware attacks effectively and providing better security for the VMs.Finally,the experimental results indicate that the pro-posed security method is efficient.It consumes minimum execution time,better false positive rate,accuracy,and memory usage than the conventional approach.

基于MILP的PICO算法差分和线性区分器的搜索

PICO算法是由Bansod等人在2016年提出的一种基于替换和排列的SPN网络的轻量级分组密码.目前针对PICO算法抵抗差分和线性分析的能力还有待进一步评估.本文基于MILP模型,首先利用不等式组对各组件的差分特征和线性掩码的传播规律进行了精细的刻画,其次针对密码算法的结构特点及S盒特性,对该模型进行了优化,缩小了搜索空间,并提出了针对PICO算法有效的两步搜索算法.最后利用该算法,搜索到了3条新的概率为2−63的21轮差分区分器,并首次搜索到了3条相关度为2−30的20轮线性区分器,为当前公开发表的最长线性区分器.

电力系统混合整数线性规划问题的运筹决策关键技术综述与展望

机组组合、检修计划、拓扑运行优化、电力系统规划等电力系统混合整数线性规划(MILP)问题旨在实现电力资源的最佳配置,应用广泛,其精准性与高效性直接影响了电力系统的安全性与经济性。随着“双碳”目标的提出,新型电力系统MILP问题模型复杂度更高、计算效率要求更严格,对当前运筹决策技术提出了更严峻的挑战。然而,现有依赖于国外进口求解器的电力系统运筹决策技术面临“组合爆炸”,且求解器依赖进口面临“卡脖子”困境,亟须实现技术突破。为此,该文系统地梳理了电力系统MILP问题的运筹决策技术,以及近年来通用MILP问题的最新进展,并展望了电力系统MILP问题运筹决策关键技术未来的研究方向,旨在为我国相关研究工作提供参考和思路。

考虑节点度紧致化的最优主动解列模型

为解决主动解列模型的连通性和解列模型趋于复杂化导致计算效率下降的问题,本文提出了考虑节点度紧致化的主动解列模型。首先基于单商品流的思想,提出保证孤岛连通性的解析约束;再结合主动解列自身特点和复杂网络中度的概念,提出一种模型紧致化方法以压缩混合整数规划模型的可行域;最后以切负荷与最小潮流中断之和最小为目标求取最优的解列断面。所提模型能保证孤岛内的连通性并且能够较快地求解大型系统的解列问题。3个测试系统的仿真实验表明了该模型的有效性和快速性。

分支定界搜索信息深度引导的电-气互联系统调度决策加速求解方法

电-气互联系统调度决策问题旨在实现天然气系统和电力系统中可调节资源的最佳配置,其精准性与高效性直接影响电-气互联系统运行的安全性与经济性。为描述可调节资源离散状态、非线性运行特性等物理性质,电-气互联系统调度决策问题中含有规模庞大的离散决策变量,模型复杂度高,使得现有依赖于商业混合整数线性规划(MILP)求解器的电力系统运筹优化技术面临“组合爆炸”的计算负担。为此,该文提出一种分支定界搜索信息深度引导的电-气互联系统调度决策加速求解方法。所提方法利用分支定界初始搜索阶段的信息构建小规模辅助MILP模型,并内嵌于分支定界搜索过程,引导剪除更多冗余搜索空间,在不损失最优性的前提下加速收敛。基于RTS-GMLC电力系统和天然气系统不同负荷水平及线性分段数下的30个算例仿真结果说明,相比于直接使用商业MILP求解器,所提方法在不损失最优性的前提下可实现平均4.20倍的加速,验证了所提方法的有效性。