张量方法在信赖域算法中的应用

信赖域算法是求解无约束优化问题的一种有效的算法.对于该算法的子问题,本文将原来目标函数的二次模型扩展成四次张量模型,提出了一个带信赖域约束的四次张量模型优化问题的求解算法.该方法的最大特点是:不仅在张量模型的非稳定点可以得到下降方向及相应的迭代步长,而且在非局部极小值点的稳定点也可以得到下降方向及相应的迭代步长,从而在算法产生的迭代点列中存在一个子列收敛到信赖域子问题的局部极小值点.     

一类全局优化问题的线性化方法

本文对带有不定二次约束且目标函数为非凸二次函数的最优化问题提出了一类新的确定型全局优化算法,通过对目标函数和约束函数的线性下界估计,建立了原规划的松弛线性规划,通过对松弛线性规划可行域的细分以及一系列松弛线性规划的求解过程,得到原问题的全局最优解.我们从理论上证明了算法能收敛到原问题的全局最优解.     

关于求解随机用户均衡问题的截断拟牛顿型信赖域法研究

信赖域法是一种保证全局收敛性的优化算法,为避免Hessian矩阵的计算,基于拟牛顿校正公式构造了求解带线性等式约束的非线性规划问题的截断拟牛顿型信赖域法.首先给出了截断拟牛顿型信赖域法的构造过程及具体步骤;然后针对随机用户均衡模型中变量和约束的特点对算法进行了修正,并将多种拟牛顿校正公式下所得结果与牛顿型信赖域法的结果进行了比较,结果发现基于对称秩1校正公式的信赖域法更为合适.最后基于数值算例结果得到了一些在算法编程过程中的重要结论,对其它形式信赖域法的编程实现具有一定的参考意义.     

道路维修施工路段交通分流信控优化模型

针对道路维修施工期间常采用的部分路面封闭施工且利用辅路进行分流的情形,探讨了交通分流信控优化模型。借助交通流波动理论,分析了施工路段及其前后车流拥挤排队及疏散特征和规律,分析了对车流进行控制需满足的约束,并分析了车流的延误计算公式。以总的车辆行驶时间最小化目标,原路径及分流路径的绿时分配及信号周期为优化参数,考虑交通分流控制的各种约束,建立了道路施工路段交通分流信控优化模型。分析了该模型属于非凸问题,因此提出了一种近似求解最优解的办法。通过一个示例对模型和求解算法进行了验证,并对一些规律性结果进行了分析。     

边界约束非凸二次规划问题的分枝定界方法

本文是研究带有边界约束非凸二次规划问题,我们把球约束二次规划问题和线性约束凸二次规划问题作为子问题,分明引用了它们的一个求整体最优解的有效算法,我们提出几种定界的紧、松驰策略,给出了求解原问题整体最优解的分枝定界算法,并证明了该算法的收敛性,不同的定界组合就可以产生不同的分枝定界算法,最后我们简单讨论了一般有界凸域上非凸二次规划问题求整体最优解的分枝与定界思想。     

求解一类逆鲁棒优化问题的牛顿型扰动方法

逆优化问题是指通过调整目标函数和约束中的某些参数使得已知的一个解成为参数调整后的优化问题的最优解.本文考虑求解一类逆鲁棒优化问题.首先,我们将该问题转化为带有一个线性等式约束,一个二阶锥互补约束和一个线性互补约束的极小化问题;其次,通过一类扰动方法来对转化后的极小化问题进行求解,然后利用带Armijo线搜索的非精确牛顿法求解每一个扰动问题.最后,通过数值实验验证该方法行之有效.     

基于参数李雅普诺夫函数的鲁棒预测控制器

针对多包描述的不确定系统,提出一种新的鲁棒约束预测控制器.离线设计时引入参数Lyapunov函数以减少单一Lyapunov函数设计时的保守性,得到多包系统Worst-case情况下性能最优的不变集,在线求解多包系统无穷时域性能指标的min-max优化问题.设计采用了时变的终端约束集,扩大了初始可行域,而且能够获得较优的控制性能.仿真结果验证了该方法的有效性.     

记录值样本下具有“浴盆”型失效率寿命分布的最优置信集估计

本文针对具有一种具有“浴盆”型失效率曲线的寿命分布,在记录值样本下研究模型参数的置信集估计问题.通过构造枢轴量,首先建立了模型参数的精确置信区间和置信域.进一步,在给定显著性水平下,利用拉格朗日乘子法,构造了模型参数的最优置信区间和最优置信域估计.最后,通过算例分析研究了结果的优良性.     

基于模糊——随机规划的WEEE回收物流网络优化研究

针对废旧电子电气设备(WEEE)绿色回收问题,根据实际需求刻画其回收物流网络结构;在模型构建中.考虑参数为随机和模糊共存的情况,提出应用随机机会约束规划和模糊机会约束规划相结合的方法来建模;设模型参数是相互独立的,合理利用转换定理将不确定规划转变为常规数学规划,并借助LINGO软件求解最优方案.     

模糊随机需求下多产品报童问题的均衡策略

针对模糊随机需求下单制造商多零售商的分布控制型多产品报童问题, 建立了含资金约束的期望利润最大化两层规划模型.结合模糊随机模拟技术与遗传算法, 设计了求解模型的混合智能算法.该算法不仅可获得上层制造商的最优折扣批发价及下层零售商的最优订购量,亦可求得该折扣形式的起始折扣点(折扣区间).算例分析表明,当制造商采取最优数量折扣策略时:1)促使零售商订货量增加至资金约束上限;2)部分产品订货量可达模糊随机市场需求的最大可能值:3)零售商和制造商的利润均增加.     

A genetic algorithm for optimal operating parameters of VMI system in a two-echelon supply chain

This paper deals with the operational issues of a two-echelon single vendor–multiple buyers supply chain (TSVMBSC) model under vendor managed inventory (VMI) mode of operation. The operational parameters to the above model are: sales quantity and sales price that determine the channel profit of the supply chain, and contract price between the vendor and the buyer, which depends upon the understanding between the partners on their revenue sharing. In order to find out the optimal sales quantity for each buyer in TSVMBSC problem, a mathematical model is formulated. Optimal sales price and acceptable contract price at different revenue share are subsequently derived with the optimal sales quantity. A genetic algorithm (GA) based heuristic is proposed to solve this TSVMBSC problem, which belongs to nonlinear integer programming problem (NIP). The proposed methodology is evaluated for its solution quality. Furthermore, the robustness of the model with its parameters, which fluctuate frequently and are sensitive to operational features, is analysed.     

A cutting plane algorithm for MV portfolio selection model

This paper deals with a portfolio selection problem with fuzzy return rates. A possibilistic mean variance (FMVC) portfolio selection model was proposed. The possibilistic programming problem can be transformed into a linear optimal problem with an additional quadratic constraint by possibilistic theory. For such problems there are no special standard algorithms. We propose a cutting plane algorithm to solve (FMVC). The nonlinear programming problem can be solved by sequence linear programming problem. A numerical example is given to illustrate the behavior of the proposed model and algorithm.     

A new distributionally robust p-hub median problem with uncertain carbon emissions and its tractable approximation method

The p-hub median problem is to determine the optimal location for p hubs and assign the remaining nodes to hubs so as to minimize the total transportation costs. Under the carbon cap-and-trade policy, we study this problem by addressing the uncertain carbon emissions from the transportation, where the probability distributions of the uncertain carbon emissions are only partially available. A novel distributionally robust optimization model with the ambiguous chance constraint is developed for the uncapacitated single allocation p-hub median problem. The proposed distributionally robust optimization problem is a semi-infinite chance-constrained optimization model, which is computationally intractable for general ambiguity sets. To solve this hard optimization model, we discuss the safe approximation to the ambiguous chance constraint in the following two types of ambiguity sets. The first ambiguity set includes the probability distributions with the bounded perturbations with zero means. In this case, we can turn the ambiguous chance constraint into its computable form based on tractable approximation method. The second ambiguity set is the family of Gaussian perturbations with partial knowledge of expectations and variances. Under this situation, we obtain the deterministic equivalent form of the ambiguous chance constraint. Finally, we validate the proposed optimization model via a case study from Southeast Asia and CAB data set. The numerical experiments indicate that the optimal solutions depend heavily on the distribution information of carbon emissions. In addition, the comparison with the classical robust optimization method shows that the proposed distributionally robust optimization method can avoid over-conservative solutions by incorporating partial probability distribution information. Compared with the stochastic optimization method, the proposed method pays a small price to depict the uncertainty of probability distribution. Compared with the deterministic model, the proposed method generates the new robust optimal solution under uncertain carbon emissions.     

Computational method for optimal control of switched systems with input and state constraints

In this paper, we consider an optimal control problem of switched systems with input and state constraints. Since the complexity of such constraint and switching laws, it is difficult to solve the problem using standard optimization techniques. In addition, although conjugate gradient algorithms are very useful for solving nonlinear optimization problem, in practical implementations, the existing Wolfe condition may never be satisfied due to the existence of numerical errors. And the mode insertion technique only leads to suboptimal solutions, due to only certain mode insertions being considered. Thus, based on an improved conjugate gradient algorithm and a discrete filled function method, an improved bi-level algorithm is proposed to solve this optimization problem. Convergence results indicate that the proposed algorithm is globally convergent. Three numerical examples are solved to illustrate the proposed algorithm converges faster and yields a better cost function value than existing bi-level algorithms.     

Hybrid simulated annealing and MIP-based heuristics for stochastic lot-sizing and scheduling problem in capacitated multi-stage production system

This paper addresses lot sizing and scheduling problem of a flow shop system with capacity constraints, sequence-dependent setups, uncertain processing times and uncertain multi-product and multi-period demand. The evolution of the uncertain parameters is modeled by means of probability distributions and chance-constrained programming (CCP) theory. A new mixed-integer programming (MIP) model with big bucket time approach is proposed to formulate the problem. Due to the complexity of problem, two MIP-based heuristics with rolling horizon framework named non-permutation heuristic (NPH) and permutation heuristic (PH) have been performed to solve this model. Also, a hybrid meta-heuristic based on a combination of simulated annealing, firefly algorithm and proposed heuristic for scheduling is developed to solve the problem. Additionally, Taguchi method is conducted to calibrate the parameters of the meta-heuristic and select the optimal levels of the algorithm’s performance influential factors. Computational results on a set of randomly generated instances show the efficiency of the hybrid meta-heuristic against exact solution algorithm and heuristics.     

Simplicial Branch-and-Reduce Algorithm for Convex Programs with a Multiplicative Constraint

Optimization problems that involve products of convex functions in the objective function or in the constraints arise in a variety of applications. These problems are difficult global optimization problems. During the past 15 years, however, a number of practical algorithms have been proposed for globally solving these types of problems. In this article, we present and validate a branch-and-reduce algorithm for finding a global optimal solution to a convex program that contains an additional constraint on the product of several convex functions. To globally solve this problem, the algorithm instead globally solves an equivalent master problem. At any stage of the algorithm, a disconnected set consisting of a union of simplices is constructed. This set is guaranteed to contain a portion of the boundary of the feasible region of the master problem where a global optimal solution lies. The algorithm uses a new branch-and-reduce scheme to iteratively reduce the sizes of these sets until a global optimal solution is found. Several potential computational advantages of the algorithm are explained, and a numerical example is solved.     

Heston随机波动率市场中带VaR约束的最优投资策略

本文研究了Heston随机波动率市场下, 基于VaR约束下的动态最优投资组合问题。
假设Heston随机波动率市场由一个无风险资产和一个风险资产构成,投资者的目标为最大化其终端的期望效用。与此同时, 投资者将动态地评估其待选的投资组合的VaR风险,并将其控制在一个可接受的范围之内。本文在合理的假设下,使用动态规划的方法,来求解该问题的最优投资策略。在特定的参数范围内,利用数值方法计算出近似的最优投资策略和相应值函数, 并对结果进行了分析。     

Mean–variance optimal trading problem subject to stochastic dominance constraints with second order autoregressive price dynamics

The efficient modeling of execution price path of an asset to be traded is an important aspect of the optimal trading problem. In this paper an execution price path based on the second order autoregressive process is proposed. The proposed price path is a generalization of the existing first order autoregressive price path in literature. Using dynamic programming method the analytical closed form solution of unconstrained optimal trading problem under the second order autoregressive process is derived. However in order to incorporate non-negativity constraints in the problem formulation, the optimal static trading problems under second order autoregressive price process are formulated. For a risk neutral investor, the optimal static trading problem of minimizing expected execution cost subject to non-negativity constraints is formulated as a quadratic programming problem. Whereas, for a risk averse investor the variance of execution cost is considered as a measure for the timing risk, and the mean–variance problem is formulated. Moreover, the optimal static trading problem subject to stochastic dominance constraints with mean–variance static trading strategy as the reference strategy is studied. Using Static approximation method the algorithm to solve proposed optimal static trading problems is presented. With numerical illustrations conducted on simulated data and the real market data, the significance of second order autoregressive price path, and the optimal static trading problems is presented.     

Terminal constrained robust hybrid iterative learning model predictive control for complex time-delayed batch processes

This work mainly addresses terminal constrained robust hybrid iterative learning model predictive control against time delay and uncertainties in a class of complex batch processes with input and output constraints. In this work, an equivalently novel extended two-dimensional switched system is first constructed to represent the process model by introducing state difference, output error and new relaxation variable information. Then, a hybrid predictive updating controller is proposed and an optimal performance index function including terminal constraints is designed. Under the condition that the switching signal meets certain conditions, the solvable problem of model predictive control is realized by Lyapunov stability theory. Meanwhile, the design scheme of controller parameters is also given. In addition, the robust constraint set is adopted to overcome the disadvantage that the traditional asymptotic stability cannot converge to the origin when it involves disturbances, such that the system state converges to the constraint set and meets its expected value. Finally, the effectiveness of the proposed algorithm is verified by controlling the speed and pressure parameters of the injection molding process.     

政府促进银行实施绿色信贷的多目标优化策略研究

传统的绿色信贷研究中存在着模型简单、非动态参数以及只能获取纳什均衡点的局限性。为改善这些局限性,研究了一种基于数据驱动多目标优化算法的政府促进银行实施绿色信贷的策略计算方法。首先针对绿色信贷的最优策略求解问题建立数据驱动的多目标优化算法框架,再基于历史数据建立算法框架中的最优策略马可夫状态转移模型,最后使用多目标粒子群优化算法对政府和银行的长远总收益进行最优策略求解。与传统的基于近似模型及博弈论的方法不同,本文提出的方法可以获得历史数据中的经验,从而制定出具有更加长远收益的策略,避免了传统方法中的“短视”现象。分析结果表明,绿色信贷的收益不会在短时间内显现,因此政府在做决策时,必须根据绿色信贷收益的回报周期作出长远的判断。