Robust Optimization for a Multi-Product Integrated Problem of Planning and Scheduling under Products Uncertainty

This paper presents robust optimization models for a multi-product integrated problem of planning and scheduling (based on the work of Terrazas-Moreno & Grossmann (2011) [1]) under products prices uncertainty. With the objective of maximizing the total profit in planning time horizon, the planning section determines the amount of each product, each product distributed to each market, and the inventory level in each manufacturing site during each scheduling time period;the scheduling section determines the products sequence, start and end time of each product running in each production site during each scheduling time period. The uncertainty sets used in robust optimization model are box set, ellipsoidal set, polyhedral set, combined box and ellipsoidal set, combined box and polyhedral set, combined box, ellipsoidal and polyhedral set. The genetic algorithm is utilized to solve the robust optimization models. Case studies show that the solutions obtained from robust optimization models are better than the solutions obtained from the original integrated planning and scheduling when the prices are changed.

Bad-scenario-set Robust Optimization Framework With Two Objectives for Uncertain Scheduling Systems

This paper proposes a robust optimization framework generally for scheduling systems subject to uncertain input data, which is described by discrete scenarios. The goal of robust optimization is to hedge against the risk of system performance degradation on a set of bad scenarios while maintaining an excellent expected system performance. The robustness is evaluated by a penalty function on the bad-scenario set. The bad-scenario set is identified for current solution by a threshold, which is restricted on a reasonable-value interval. The robust optimization framework is formulated by an optimization problem with two conflicting objectives. One objective is to minimize the reasonable value of threshold, and another is to minimize the measured penalty on the bad-scenario set. An approximate solution framework with two dependent stages is developed to surrogate the biobjective robust optimization problem. The approximation degree of the surrogate framework is analyzed. Finally, the proposed bad-scenario-set robust optimization framework is applied to a scenario job-shop scheduling system. An extensive computational experiment was conducted to demonstrate the effectiveness and the approximation degree of the framework. The computational results testified that the robust optimization framework can provide multiple selections of robust solutions for the decision maker. The robust scheduling framework studied in this paper can provide a unique paradigm for formulating and solving robust discrete optimization problems. © 2014 Chinese Association of Automation.

基于样本划分的数据驱动报童问题研究

大数据时代的到来为企业库存管理带来了前所未有的机遇,同时也对其相应的决策方法提出了新的挑战。高效利用实时市场数据支撑库存管理智能决策已经成为企业提升库存管理效率的关键。传统库存管理研究是基于需求预测的基础上再做库存决策。而近年来流行的数据驱动库存管理方法是跳过需求预测的过程,直接建立需求数据与库存决策的关系。本文研究数据驱动的经典报童问题,其随机需求分布是未知的,报童只有若干期历史的需求数据。本文基于数据样本划分提出了新的数据驱动鲁棒优化方法来解决报童的订货问题。该方法通过将需求数据样本划分成不同的区间来构造随机需求分布的模糊集,从而求解相应的鲁棒优化问题。理论证明了该方法随着样本量的增加,其解收敛于最优解。数值实验表明相对已有的鲁棒方法,新方法具有相对弱的鲁棒性,但平均性能更好,并且计算复杂度相对小很多。同时表明本文提出的样本划分鲁棒方法比SAA等数据驱动方法具有更好的平均性能和更强的鲁棒性。

基于矩不确定模糊集的分布鲁棒风险-回报优化模型研究

本文研究随机变量分布不确定下的风险-回报优化模型。针对传统的风险-回报三类典型问题和分布不确定性背景,提出了更一般性条件下的分布鲁棒风险-回报优化新模型;基于矩不确定集合和优化对偶理论,化简复杂的新优化模型为常规结构的非线性优化问题。理论上证明了分布鲁棒风险-回报三类优化模型效率前沿的等价性。数值实验验证了理论分析的有效性。

含电、冷、热、气的区域综合能源系统优化运行

区域综合能源系统(regional integrated energy system,RIES)含有风电、光伏等多种能源、冷热电负荷和蓄电池,具有提升可再生能源利用率等优势。首先,考虑风光出力的不确定性,构建多面体不确定集的鲁棒优化模型并对不确定性进行处理;然后,建立碳排放量最少和运行成本最小的多目标优化模型,引入碳排放惩罚因子,将多目标转换为单目标进行求解;最后,通过实际RIES进行仿真验证,仿真结果表明所提方法的准确性与有效性。所建模型可以很好地兼顾系统的环保性和经济性,能够更好地处理不确定性,实现系统的经济优化运行。

电动车辆路径问题:可调鲁棒数学模型与算法

针对行驶时间不确定的允许部分充电的带时间窗电动车辆路径问题,考虑多面体不确定集度量行驶时间的不确定性,建立了一个可调鲁棒优化模型,设计了基于行生成和集划分的求解算法,采用标号法对路径的可行性进行判定,并将不可行的路径作为新的约束加入到模型中.数值实验表明,94%的算例可求得最优解,这验证了本算法的效率;利用多面体不确定集进行度量对总行驶距离和车辆总数目具有正向的影响;相比于普通鲁棒优化,可调鲁棒优化的求解结果有显著提高,可以提升车辆调度的灵活性.

Fixed-time distributed robust optimization for economic dispatch with event-triggered intermittent control

This paper proposes a fixed-time distributed robust optimization approach for solving economic dispatch problems.Based on an integral sliding mode control scheme,the proposed multi-agent system converges to an optimal solution to an economic dispatch problem before a fixed time.In addition,the proposed multi-agent system can suppress the disturbance in a fixed time.To reduce the cost of sliding mode controls,we propose a distributed event-triggered intermittent control which reduces the sliding mode control time by setting a control triggering rule on the basis of two boundary functions of a Lyapunov function.The simulation results of three power systems illustrate the characteristics and effectiveness of the theoretical results.

全渠道电商库存路径及定价问题优化研究

针对全渠道模式下电商库存路径及定价问题,考虑各前置仓需求不确定因素,本文提出一种按照不同售卖渠道的商品差异化定价策略,通过设置电商关于需求不确定风险态度的保守系数,构建以总利润最大化为目标的混合整数非线性鲁棒优化模型,并设计自适应模拟退火粒子群算法进行求解。选取含有10个和20个前置仓的两组算例,验证本文模型算法的适用性和有效性。实验分析结果显示,相比于统一定价,差异化定价可以提高电商总利润分别约5%和6%。敏感性分析结果表明,提升线上客户的线下购物体验以增加线上自提渠道客户数量,并组织线上营销活动以提高线上客户对电商促销努力的敏感度,能给电商带来更高的利润;掌控未来市场波动风险并准确预测需求信息以降低电商保守系数和需求最大偏离系数,亦可提高电商总利润。研究结论可为电商制定前置仓库存配送路径策略与各渠道商品定价方案提供参考。

Optimal paths planning in dynamic transportation networks with random link travel times

A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent(STD). The methodology of relative robust optimization was applied as measures for comparing time-varying, random path travel times for a priori optimization. In accordance with the situation in real world, a stochastic consistent condition was provided for the STD networks and under this condition, a mathematical proof was given that the STD robust optimal path problem can be simplified into a minimum problem in specific time-dependent networks. A label setting algorithm was designed and tested to find travelers' robust optimal path in a sampled STD network with computation complexity of O(n2+n·m). The validity of the robust approach and the designed algorithm were confirmed in the computational tests. Compared with conventional probability approach, the proposed approach is simple and efficient, and also has a good application prospect in navigation system.

Probabilistic Robust Linear Parameter-varying Control of a Small Helicopter Using Iterative Scenario Approach

In this paper, we present an iterative scenario approach (ISA) to design robust controllers for complex linear parameter-varying (LPV) systems with uncertainties. The robust controller synthesis problem is transformed to a scenario design problem, with the scenarios generated by identically extracting random samples on both uncertainty parameters and scheduling parameters. An iterative scheme based on the maximum volume ellipsoid cutting-plane method is used to solve the problem. Heuristic logic based on relevance ratio ranking is used to prune the redundant constraints, and thus, to improve the numerical stability of the algorithm. And further, a batching technique is presented to remarkably enhance the computational efficiency. The proposed method is applied to design an output-feedback controller for a small helicopter. Multiple uncertain physical parameters are considered, and simulation studies show that the closed-loop performance is quite good in both aspects of model tracking and dynamic decoupling. For robust LPV control problems, the proposed method is more computationally efficient than the popular stochastic ellipsoid methods. © 2014 Chinese Association of Automation.

基于粒子群优化算法在NP难问题中的应用研究

为解决NP难问题中算法应用领域划分问题,分别运用不同算法对不同问题规模的TSP问题进行求解,寻求最优路径规划.采用随机数据来最大化模拟实际情况,设置了5、10、15、20、30和100个随机城市坐标点,分别采用PSO算法、C-PSO算法、GA算法和ACO算法进行求解,求解一条经过各城市且一次的旅行最低费用的路线,分析比较四种算法的鲁棒性与实效性.结果表明:基于C-PSO算法在NP难问题中的具有良好鲁棒性和较短的运行时间,在问题规模小时,可以采用PSO算法和ACO算法;在问题规模大时,可以采用C-PSO算法.

基于Predictive&Prescriptive框架的鲁棒最优潮流

目前解决不确定性潮流问题的主要方法是先对不确定量进行预测,再根据预测结果进行分析决策,但预测与决策分离可能会导致次优解。将预测过程融入求解不确定性潮流问题的决策过程中,提出基于Predictive&Prescriptive框架的鲁棒最优潮流模型。利用k近邻算法预测并构造表示风电功率不确定性的最小体积椭球集,建立考虑风电不确定性的鲁棒二阶锥最优潮流模型,并利用对偶理论将该模型转换为可求解的混合整数规划模型进行高效求解。IEEE 14和IEEE 118节点系统算例仿真结果表明,所提模型能有效降低预测、决策过程分离时最优解的劣化程度,在保证系统安全运行的前提下提高系统经济性。

需求不确定下的生物质物流系统的选址与路径问题

为有效解决在生物质资源开发和利用过程中物流系统成本较高等问题,通过研究需求不确定性对生物质物流系统选址与路径问题的影响,提出生物质物流系统选址与路径的鲁棒优化模型。使用混合整数非线性规划对该问题进行数学描述,再根据强对偶理论将非线性模型转化为等价的线性鲁棒优化模型。利用CPLEX软件进行数值计算和分析,结果表明:需求不确定性会对生物质物流系统的最优决策产生影响。基于该模型的特殊性开发相关的自适应遗传算法,通过算法自适应机制避免陷入问题的局部最优情况,从而更精确地接近问题的最优解,最后通过大型算例验证所提出的自适应遗传算法相比于传统的遗传算法具有更加良好的性能。

应急物资储备中心选址研究

为了提高应急救援效率,保障应急物资供给及时性,通过熵权法改进的TOPSIS选出应急物资储备中心备选区域,进一步利用多面体不确定集合刻画需求和速度的不确定性,并以物资供应成本和交通运输时间为目标函数构建具有库存双容量限制和救援时效性限制的鲁棒优化选址模型,通过鲁棒优化选址确定最终选址,保证突发公共卫生事件下各需求点所需的物资都能得到满足.结果表明,鲁棒优化选址方案能够合理分配应急物资资源,物资供应平均运输时间2.06 h,需求满足率达到91.69%,且鲁棒优化模型在解决不确定性问题具有更好的表现.

一种求解鲁棒优化问题的多目标进化方法

鲁棒优化问题(Robust Optimization Problem,ROP)是进化算法(Evolutionary Algorithms,EAs)研究的重要方面之一,对于许多实际工程优化问题,通常需要得到鲁棒最优解。利用多目标优化中的Pareto思想优化ROP的鲁棒性和最优性,将ROP转化为一个两目标的优化问题,一个目标为解的鲁棒性,一个目标为解的最优性。针对ROP与多目标优化的特点,利用动态加权思想,设计一种求解ROP的多目标进化算法。通过测试函数的实验仿真,验证了该方法的有效性。

实时电力市场阻塞管理算法研究

作者提出了一种新的优化类算法用于解决实时电力市场的阻塞管理问题。基于市场成员的调整报价,实时阻塞管理问题被描述为调整成本最小的优化问题。通过将优化问题转化为等价的非线性方程组,避免了起作用约束的识别问题,提高了计算效率;方程组的求解利用了半光滑牛顿类算法,从而具有较快的收敛速度;步长搜索策略的使用确保了算法的全局收敛性,从而使算法具有较强的鲁棒性。算例分析以及与传统算法的比较证明,本文的算法是一种有效的阻塞消除算法。

随机需求应急物流多阶段定位-路径鲁棒优化研究

为提高应急物流系统的应急反应能力,论文针对需求随机变化的应急物流定位-路径问题,利用鲁棒优化的思想将灾区物资需求量表示为区间型数据,将应急救援过程划分为多个阶段,以总救援时间和系统总成本最小为目标,构建了多物资多运输车辆应急物流定位-路径优化模型,设计了改进的遗传算法对其进行求解。实例计算结果表明,该模型和算法可以有效地解决应急物流系统中需求随机变化的定位-路径问题,为政府机构应对重大突发事件提供科学的决策参考。

考虑路径风险的需求不确定应急物流定位-路径问题

针对自然灾害对路网造成的破坏性和受灾点物资需求量的不确定性,综合考虑应急物流路径风险和物资分配的时间公平性,将路径风险定量化为路径通行能力风险、路径损毁风险和路径复杂性,基于鲁棒优化理论,以最小化车辆最长配送时间和应急物流系统总成本为目标,建立了双目标多物资定位-路径优化模型,采用遗传算法对其求解,以汶川地震应急救援相关数据为例进行了数据仿真实验。实验结果的对比分析表明:在考虑路径风险下,随着控制系数的增加,系统总成本和最长配送时间目标值均呈现增大的趋势;受灾点的物资需求扰动越大,构建应急物流系统的总成本越高。算例结果也验证了鲁棒优化方法在处理不确定需求方面的有效性,为解决自然灾害后应急设施点的开设和救援物资的安全及时准确配送提供了有效的方法。

不确定需求生鲜电商配送路径规划多目标模型

综合考虑配送成本、生鲜产品新鲜度、碳排放和客户需求不确定等因素,建立配送路径规划多目标优化模型。基于鲁棒优化处理不确定问题的方法,针对离散需求隶属于椭球不确定集情况,优化配送路径规划多目标模型,并应用主要目标法和果蝇算法对模型进行求解。算例验证所建模型及算法具有良好的鲁棒性,能有效抑制需求为不确定情况下所带来的扰动。对于完善生鲜电商企业配送路径规划模型和配送网络优化方法提供了重要的理论支持和实践思路。

应急设施鲁棒优化选址模型及算法

为解决不确定情况下应急设施选址问题,采用鲁棒优化方法处理应急节点权重的区间估计,基于最优的设施选址到各个应急节点的赋权距离之和最小,建立有限期要求的不确定性应急设施选址模型,并给出了模型的求解算法,比较分析了鲁棒解与确定情况下的最优解。分析结果表明:当情况发生变化后,在确定情况下得到的最优解将发生较大的偏差,而在所有可能发生的情况下,鲁棒解与最优解目标函数值的最大偏差最小,因此,不确定性应急设施选址模型的解可以有效规避风险。