随机中断情境下的离散型设施选址问题研究

针对传统的供应链设施选址模型大多是基于静态背景下的确定性选址问题研究,而较少考虑中断风险因素的情况,基于随机中断情境,建立了混合整数规划模型表述的设施可靠性选址问题模型,采用拉格朗日松弛算法进行求解。通过构建的算例,求解了问题模型的最优解并验证了该算法的求解性能。     

约束求解与优化技术的结合

提出了将混合约束问题转化为混合整数规划问题的方法.用约束求解方法及混合整数规划方法共同求解混合约束问题可以令二者相互借鉴,从而促进二者求解技术的进一步发展.同时,由混合约束问题转化而来的混合整数规划问题也可作为求解混合整数规划问题的测试问题（benchmarks）.     

利用混合整数规划的卫星操作规划问题研究

对于成像卫星的操作规划,如何高效求解其规划问题模型是一个十分关键的问题。针对基于规划域定义语言(PDDL)表示的成像卫星操作规划问题的求解,采用将基于命题式的PDDL语言描述的模型转化为多值变量模型的方法,建立了基于混合整数规划的问题求解模型,从而可以方便地采用混合整数规划的已有求解器进行求解,提高了问题的求解效率。对关键技术进行了分析,并设计了问题求解流程。仿真实验结果证明该方法是可行和适用的。     

连锁门店选址与配送中心选择联合决策的f-MIGP模型

建立了连锁门店选址和配送中心选择联合决策问题的模糊多目标混合整数规划模型．针对该模型的特殊结构。提出一种适用的求解策略：首先确定每个模糊目标的隶属度函数;然后将模糊多目标混合整数规划模型转化为等价的清晰多目标混合整数规划模型,通过最大最小算子求出目标值;最后借助于两阶段算法,求出问题的最优解．通过应用算例进一步说明了该模型的有效性和可行性．     

考虑学习效应的单人作业车间调度算法

单人负责多台机器的单一工序作业车间场景中,工人由于重复操作机器而产生学习效应.针对考虑依赖工件位置学习效应的单人单工序作业车间最小化最大完工时间的调度问题,建立一种混合整数规划模型.为解决该问题,设计一个考虑学习效应的贪婪算子,利用该算子构造两种贪婪算法,并提出一种基于贪婪的模拟退火算法.为衡量混合整数规划模型、贪婪算法和基于贪婪的模拟退火算法的性能,设计两种规模问题的数据实验.通过实验得出:现代混合整数规划模型求解器可以解决机器数量和工件总数量乘积小于75的小规模问题;基于贪婪的模拟退火算法求解此问题具有有效性,适用于各种规模的问题;间隔插入贪婪算法解决此问题速度较快,效果良好,可以应用于需要快速求解的场景.     

一类混杂系统建模和优化控制的研究

为解决混杂系统优化控制的计算复杂性问题,针对结合逻辑规则的工业过程混杂模型,采用结合约束程序的混合整数非线性规划算法,求解这种混杂模型的优化控制。计算实例表明,通过混杂建模方法,可以充分利用工业对象的机理模型以及操作工经验或专家经验,建立系统的更精确模型;结合约束程序混合整数非线性规划算法可以较迅速地求解混杂模型优化控制问题,从而使该方法可以用于工业过程实时控制中。     

一类非线性系统最大可控不变集求解

针对非线性系统线性化在状态约束下最优鲁棒控制求解问题,提出了一种基于混合系统的非线性系统最大鲁棒控制不变集的方法.对于一类非线性系统通过平衡点线性化的方法转化为多模态的混合系统,并进行了混合逻辑动态模型(MLD)的建模,在不变集基本理论的基础上,通过多参数规划的混合整数规划(MIQP)的方法迭代求解最大可控不变集,并求得不变集内的最优控制器,解决系统的状态约束问题.通过一个非线性系统的实例进行建模、仿真,证明了本方法的可行性.     

一种求解混合整数规划的混合进化算法

提出一种基于正交试验设计的混合进化算法,用于求解混合整数规划问题.进化算法中采用一种混合启发式的变异算子,将正交试验设计作为杂交算子.为了增加种群的多样性,引入一种迁移算子.仿真实验结果表明,与已有的一些算法相比,所提出的求解混合整数规划的混合进化算法能快速收敛到问题的最优解,并且算法的计算量小,解的精度高.     

具有联合椭圆不确定集与概率约束的鲁棒投资组合选择

针对参数在一个联合椭圆不确定集中变化的情形,建立了一个具有概率约束的鲁棒投资组合模型,并将其转化为可由内点算法求解的含线性矩阵不等式(LMI)约束的凸规划问题.应用实际交易数据对所提出的模型进行数值实验和比较,结果表明此模型能够获得具有更好财富增长率的投资策略,并能有效地分散最优投资组合的风险.     

信号灯控制的多阶段决策模型及其前向动态规划算法

为研究路口交通信号灯的实时最优控制问题,提出一种以最小化等待时间为目标的多阶段决策模型.该模型利用最短绿灯和红灯时间的结构特征,通过合理选择系统状态和控制变量压缩了模型规模,进而提出了前向动态规划算法以高效得到最优解.数值实验显示,对比于固定时长的周期性控制可以节省路口车辆的等待时间;对比基于混合整数规划的求解方法,可以提高求解效率,满足实时控制的要求.     

基于混合整数规划的智能车横纵向一体化滚动优化决策

本文针对智能车辆的行为决策问题, 设计了基于混合整数规划的智能车横纵向一体化滚动优化决策方法. 该方法首先将纵向车速表示为非整数, 将期望车道表示为整数控制量, 建立了混合整数智能车决策简化模型; 然后, 设计了横纵向一体化滚动优化决策方法, 决策出纵向车速和换道动作, 根据系统输出与非线性约束的时域关系证明 了优化问题的递归可行性并通过遗传算法求解非线性混合整数规划优化问题. 基于车辆动力学仿真软件veDYNA 和Simulink进行了联合仿真, 并在红旗E-HS3智能车上开展了实车试验, 结果表明, 本文提出的基于混合整数规划的 智能车横纵向一体化决策方法能够实现超车、避障、跟车、停车和弯道工况下的行为决策.     

A genetic algorithm for solving the two-dimensional assortment problem

Assortment problems arise in various industries such as the steel, paper, textiles and transportation industries. Two-dimensional assortment problems involve finding the best way of placing a set of rectangles within another rectangle whose area is minimized. Such problems are nonlinear and combinatorial. Current mixed integer programming models give optimal solutions, but the computation times are unacceptable. This study proposes a genetic algorithm that incorporates a novel random packing process and an encoding scheme for solving the assortment problem. Numerical examples indicate that the proposed genetic algorithm is considerably more efficient and effective than a fast integer programming model. Errors with respect to the optimal solutions are low such that numerous practical industrial cutting problems can be solved efficiently using the proposed method.     

A MIXED INTEGER DYNAMIC PROGRAMMING APPROACH TO A CLASS OF OPTIMAL CONTROL PROBLEMS IN HYBRID SYSTEMS

An optimal control problem for hybrid systems is formulated based on hybrid machine models. A practical approach to solving the problem, suitable for a class of hybrid systems, is presented. This approach consists of transforming the hybrid machine model into a dynamic programming model. Transition costs, in this latter model, are computed using mixed integer programs formulated based on the structure of the original hybrid machine. It is shown that the optimal solution for this dynamic program corresponds to the optimal control decision sequence in the hybrid system. Practical examples, inspired from process-oriented industry applications, are provided to illustrate the solution approach.     

Scenario relaxation algorithm for finite scenario-based min–max regret and min–max relative regret robust optimization

Most practical decision-making problems are compounded in difficulty by the degree of uncertainty and ambiguity surrounding the key model parameters. Decision makers may be confronted with problems in which no sufficient historical information is available to make estimates of the probability distributions for uncertain parameter values. In these situations, decision makers are not able to search for the long-term decision setting with the best long-run average performance. Instead, decision makers are searching for the robust long-term decision setting that performs relatively well across all possible realizations of uncertainty without attempting to assign an assumed probability distribution to any ambiguous parameter. In this paper, we propose an iterative algorithm for solving min–max regret and min–max relative regret robust optimization problems for two-stage decision-making under uncertainty (ambiguity) where the structure of the first-stage problem is a mixed integer (binary) linear programming model and the structure of the second-stage problem is a linear programming model. The algorithm guarantees termination at an optimal robust solution, if one exists. A number of applications of the proposed algorithm are demonstrated. All results illustrate good performance of the proposed algorithm.     

区间不确定性需求下的D-LFLP模型及算法

考虑物流网络需求的不确定性,运用区间分析理念以区间数度量不确定性变量与参数,建立区间需求模式下的物流网络设计的混合整数规划模型,定义风险系数与最大约束偏差,对模型进行目标函数与约束条件的确定性转化,设计问题求解的区间递阶优化遗传算法,对不同情景状态下目标函数的区间最优解与节点决策方案进行运算。算例测试表明该算法可操作性更强,求解结果具有区间最优解与情景决策的优越性。     

Multi-instance classification based on regularized multiple criteria linear programming

Regularized multiple criteria linear programming (RMCLP) model is a new powerful method for classification and has been used in various real-life data mining problems. In this paper, a new Multi-instance Classification method based on RMCLP was proposed (called MI-RMCLP), which includes two algorithms for linearly separable case and nonlinearly case separately. The key point of this method, instead of a mixed integer quadratic programming in MI-SVM, is that it is able to deal with multi-instance learning problem by an iterative strategy solving sequential quadratic programming problems. All experiment results have shown that MI-RMCLP method can converge to the optimal value in limited iterative steps and be a competitive method in multi-instance learning classification.     

Minimising mean tardiness with alternative operations in two-machine flow-shop scheduling

This paper describes the development of a mixed binary integer programming (BIP) model for scheduling alternative operations in two-machine flow-shop problems with mean tardiness as the criterion. Although the mixed BIP model provides an optimal solution, its variables and constraints increase drastically as the number of jobs increases. Therefore, an optimal solution is not always attainable within the allowable time by solving the mixed BIP model. Consequently, two heuristics suitable for the formulated scheduling problems are proposed. Computational experiments are conducted to test the accuracy and efficiency of the heuristics in generating near optimal solutions for minimising the mean tardiness of jobs.     

枢纽成本约束下的零担物流轴辐式网络设计

针对考虑枢纽建造成本和货物流的不确定的枢纽新建方案问题,引入全寿命周期理论,建立以轴辐式运营网络总成本最小化为目标的混合整数线性规划模型,并提出改进的最大最小后悔值的不确定性决策方法。通过算例来分析投资年限、枢纽干线折扣系数和不确定枢纽建造成本对零担物流（LTL）轴辐式网络的设计的影响。实验结果表明, 采用改进的不确定性决策方法得到的最优方案的运营成本比5个场景的运营成本平均降低了2.17%,表明基于改进的最大最小后悔值的不确定性决策方法,能够降低整个零担物流轴辐式运营网络总成本。