粒子群算法求解无能力约束生产批量计划问题

经典的粒子群优化算法是一个在连续的定义域内搜索数值函数极值的有效方法.目前,粒子群算法(particle swarm optimization,PS0)已经成为优化领域中的一个重要的优化工具,其应用在很多优化问题中都可以见到.虽然粒子群算法的应用范围已经十分广泛,但是关于应用其求解多级生产批量计划问题(multilevel lot-sizing problem,MLLs)的文章并不多见.文章提出结合遗传算法(genetic algorithm,GA)变异算子的混合粒子群优化算法(hybrid particle swarm optimizatjon,HPSO)求解无能力约束装配结构MLLS问题.通过实验验证了算法的可行性和有效性.     

弹性约束CSP及其基于遗传算法的交互式求解Agent

本文在回顾了约束满足问题(CSP)及其演进优化算法的基础上,提出了弹性约束CSP模型(ECSP),并将该模型形式化为六元组。ECSP模型是对已有的PCSP模型的改进。为了寻求ECSP问题的决策满意解,我们还设计了集成多Ageng、GA优化以及分布式并行计算技术的一种交互式多Ageng体系。我们详细阐述了其中的GA求解器算法,包括适应函数的确定、编码方式的选择、算子定义以及初始种群定义等。最后,我们用一个简单的算例证明了方法的有效性。     

有顾客时间窗和发货量变化的紧急车辆调度研究

对紧急车辆调度系统进行了研究,探讨了紧急车辆调度问题实现的关键技术.对有顾客时间窗和发货量变化的紧急车辆调度问题,运用了禁忌算法(TS)进行优化.算法基于实数编码,应用GENI插入法产生初始解和进行邻域操作,设计了三种邻域,利用容量约束控制单条路径配送点数,采用惩罚函数处理时间窗约束,通过设计虚拟车场等方法实现了车辆的紧急调度.本文给出了一个具有代表性的算例试验结果,算例结果及其分析表明了此方法对优化紧急车辆调度问题的有效性.     

用混合遗传算法求解物流配送路径优化问题的研究

论文建立了物流配送路径优化问题的数学模型,并针对遗传算法在局部搜索能力方面的不足,提出将爬山算法与遗传算法相结合,从而构造了求解物流配送路径优化问题的混合遗传算法,并进行了实验计算。计算结果表明,用混合遗传算法求解物流配送路径优化问题,可以在一定程度上克服遗传算法在局部搜索能力方面的不足和爬山算法在全局搜索能力方面的不足,从而得到质量较高的解。     

等待时间受限的置换流水车间调度启发式算法

针对等待时间受限的置换流水车间调度问题,分析了其可行解与流水车间调度最优解的关系,给出了计算最大完工时间的有向图,证明了等待时间受限的置换流水车间调度问题的可逆性,并以此为基础提出了一种启发式算法.算法首先根据等待时间受限约束与无等待(no-wait)约束的相似特征,生成初始工件序列集;然后利用问题可逆性给出了复杂度为O(n2m)的插入优化机制,进一步优化初始解.数据实验的结果验证了启发式算法的可行性和有效性.     

基于约束的多目标投资组合优化研究

在金融市场上,投资组合决策是一个多目标优化问题,基于传统的方法并不能很好的解决该问题。本文提出了基于多目标粒子群算法(MOPSO)的优化解决方案,实现了对多目标优化问题的非劣最优解集的搜索,实验结果证明了算法的有效性。     

约束满足与邻域搜索结合的混合算法及应用

总结约束满足求解技术和邻域搜索算法,分析约束满足与邻域搜索单一算法的优劣,以及两者结合的优势,提出约束满足与邻域搜索相结合的混合算法的一般框架,并以Job Shop,调度优化问题为例对该算法框架进行实例说明.     

竞争决策算法及其在车辆路径问题中的应用

在分析自然界各种竞争机制和人类社会决策原理的基础上,利用竞争造就优化和决策左右结果的特性,提出了一种能广泛应用于组合优化难题的新型算法———竞争决策算法(CDA),并给出了CDA的通用模型.车辆路径问题(VRP)是一个著名的NP难题,也是物流领域内一个重要的调度问题,利用CDA的通用模型设计了一个针对VRP的快速求解算法,并用该算法求解了VRP标准测试库中的实例,经过大量数据测试和验证,获得了令人满意的效果,其中部分问题的解优于目前公布的最好解.     

一种改进的TSP问题启发式算法

旅行推销商问题(TSP)属于组合优化领域中一个典型的NP Hard问题。本文在最近城市搜索法的基础上,提出一种改进的启发式算法———两端延伸最近城市搜索法,这种方法能够很快得到最优解(近优解),且大大降低了计算复杂度。同时,对TSP问题进行了分类,并给出相应的启发式解法。     

基于改进量子进化算法的车货供需匹配方法研究

为了提高货运供需匹配效率,建立了一种车货供需匹配数学模型,描述了车货匹配问题的目标与相关约束,对量子进化算法进行设计与改进用于对此问题求解,提出了有约束惩罚的适应度衰减方法,解决了量子群初期无强可行解时最优量子个体的选择问题,引入量子群成熟度对量子进化算法的退出机制进行改进。在实验中,使用改进的量子进化算法和标准遗传进化算法进行对比,并对算法参数进行优化,实验中量子进化算法表现出更好的收敛速度,准确性和稳定性,但是量子群规模存在“瓶颈问题”,更大规模的量子群对算法优化效果并不明显且需要耗费更长的计算机时间,量子旋转角增量与算法收敛速度正相关,与全局搜索能力负相关。结果表明,改进的量子进化算法可以高效地搜索到较为优秀的车货匹配方案,为车主和货主推荐较为合理的车货供需信息资源。     

Subset sum problems with digraph constraints

We introduce and study optimization problems which are related to the well-known Subset Sum problem. In each new problem, a node-weighted digraph is given and one has to select a subset of vertices whose total weight does not exceed a given budget. Some additional constraints called digraph constraints and maximality need to be satisfied. The digraph constraint imposes that a node must belong to the solution if at least one of its predecessors is in the solution. An alternative of this constraint says that a node must belong to the solution if all its predecessors are in the solution. The maximality constraint ensures that no superset of a feasible solution is also feasible. The combination of these constraints provides four problems. We study their complexity and present some approximation results according to the type of input digraph, such as directed acyclic graphs and oriented trees.     

Packing of Unequal Spheres and Automated Radiosurgical Treatment Planning

We study an optimization problem of packing unequal spheres into a three-dimensional (3D) bounded region in connection with radiosurgical treatment planning. Given an input (R, V, S, L), where R is a 3D bounded region, V a positive integer, S a multiset of spheres, and L a location constraint on spheres, we want to find a packing of R using the minimum number of spheres in S such that the covered volume is at least V; the location constraint L is satisfied; and the number of points on the boundary of R that are touched by spheres is maximized. Such a packing arrangement corresponds to an optimal radiosurgical treatment planning. Finding an optimal solution to the problem, however, is computationally intractable. In particular, we show that this optimization problem and several related problems are NP-hard. Hence, some form of approximations is needed. One approach is to consider a simplified problem under the assumption that spheres of arbitrary (integral) diameters are available with unlimited supply, and there are no location constraints. This approach has met with certain success in medical applications using a dynamic programming algorithm (Bourland and Wu, 1996; Wu, 1996). We propose in this paper an improvement to the algorithm that can greatly reduce its computation cost.     

Optimization and equilibrium problems with equilibrium constraints

This paper concerns optimization and equilibrium problems with the so-called equilibrium constraints mathematical programs with equilibrium constraint (MPEC) and equilibrium problems with equilibrium constraint (EPEC), which frequently appear in applications to operations research. These classes of problems can be naturally unified in the framework of multiobjective optimization with constraints governed by parametric variational systems (generalized equations, variational inequalities, complementarity problems, etc.). We focus on necessary conditions for optimal solutions to MPECs and EPECs under general assumptions in finite-dimensional spaces. Since such problems are intrinsically nonsmooth, we use advanced tools of generalized differentiation to study optimal solutions by methods of modern variational analysis. The general results obtained are concretized for special classes of MPECs and EPECs important in applications.     

考虑通行约束和运力限制的灾后应急物资联合调度优化研究

考虑到灾后路网受损难以运输应急物资，本文研究了应急响应中车辆-直升机联合调度的路径优化问题。针对受灾地区的实时路况，通往灾区的救援工具受到数量以及装载量的约束，本文将受灾点等待救援的平均时间最短以及应急网络总费用最低设为目标，构建运力受限条件下带通行约束的救援物资联合运输多目标优化模型，然后根据随机邻域搜索变异和分级交叉的思想构建出一种带精英策略的非支配排序混合进化算法（NSHEA-II）得到模型的解，并利用算例分析对该算法进行可行性检验。结果发现，本文构建的NSHEA-II算法相对NSGA-II算法能够得到较好的结果且波动性较小，这为决策者制定救援物资的配送方案提供有效的技术支撑。     

The Ordered Cutting Stock Problem

The one‐dimensional cutting stock problem (CSP) is a classic combinatorial optimization problem in which a number of parts of various lengths must be cut from an inventory of standard‐size material. The classic CSP ensures that the total demand for a given part size is met but ignores the fact that parts produced by a given cutting pattern may be destined for different jobs. As a result, applying the classic CSP in a dynamic production environment may result in many jobs being open (or partially complete) at any point in time—requiring significant material handling or sorting operations. This paper identifies and discusses a new type of one‐dimensional CSP, called the ordered CSP, which explicitly restricts to one the number of jobs in a production process that can be open, or in process, at any given point in time. Given the growing emphasis on mass customization in the manufacturing industry, this restriction can help lead to a reduction in both in‐process inventory levels and material handling activities. A formal mathematical formulation is provided for the new CSP model, and its applicability is discussed with respect to a production problem in the custom door and window manufacturing industry. A genetic algorithm (GA) solution approach is then presented, which incorporates a customized heuristic for reducing scrap levels. Several different production scenarios are considered, and computational results are provided that illustrate the ability of the GA‐based approach to significantly decrease the amount of scrap generated in the production process.     

基于遗传算法的微电网负荷优化分配

负荷优化分配是电力系统中的一类重要优化问题,即在满足各类系统约束条件下,实现发电总成本最低。为了促进微电网的优化运行,本文研究了包含柴油发电机、微型燃气轮机、光伏发电机和风力发电机组成的微电网的负荷优化分配问题。首先简要分析了各个微电源的发电特征和成本函数,然后分别建立了孤岛模式和并网模式下的微电网负荷优化分配模型,孤岛模式下优化模型的目标函数是包含燃料成本和运行维护成本的总成本,约束条件包括发电能力约束和系统功率平衡约束,并网模式下的优化模型则在此基础上,在目标函数中增加了其与大电网交易的收入和支出,在约束条件中增加了电力交易约束。最后,通过遗传算法分别对两种模式下的优化模型进行仿真求解。结果表明,本文提出的负荷优化分配方法可以有效降低微电网的运行成本,促进微电网的优化运行。     

基于不同预期报价决策的电力市场动态演化及其混沌控制

基于市场参与者不同预期的报价决策方式,提出了考虑输电网约束的电力市场动态模型,即内嵌市场清算优化问题的差分动态模型.该模型刻画出发电方和需求方同时报价的不用决策行为,并准确反映出独立系统调度员ISO的统一市场清算过程,考虑了输电网固有物理特性所赋予电力市场的复杂约束.借助非线性互补函数,对应不同的输电网运行状态:阻塞和不阻塞,分析比较了电力市场处于Nash均衡、周期和混沌的经济表现.针对经济表现差的市场混沌态,提出电力市场状态和参数时滞反馈控制方法,给出电力市场由混沌到Nash均衡的调控措施和手段,从而为有效提高电力市场的经济效益提供了理论依据.     

Bounding the scaling window of random constraint satisfaction problems

The model \(k\)-CSP is a random CSP model with moderately growing arity \(k\) of constraints. By incorporating certain linear structure, \(k\)-CSP is revised to a random linear CSP, named \(k\)-hyper-\({\mathbb F}\)-linear CSP. It had been shown theoretically that the two models exhibit exact satisfiability phase transitions when the constraint density \(r\) is varied accordingly. In this paper, we use finite-size scaling analysis to characterize the threshold behaviors of the two models with finite problem size \(n\). A series of experimental studies are carried out to illustrate the scaling window of the model \(k\)-CSP.     

Joint chance-constrained staffing optimization in multi-skill call centers

This paper concerns the staffing optimization problem in multi-skill call centers. The objective is to find a minimal cost staffing solution while meeting a target level for the quality of service (QoS) to customers. We consider a staffing problem in which joint chance constraints are imposed on the QoS of the day. Our joint chance-constrained formulation is more rational capturing the correlation between different call types, as compared to separate chance-constrained versions considered in previous studies. We show that, in general, the probability functions in the joint-chance constraints display S-shaped curves, and the optimal solutions should belong to the concave regions of the curves. Thus, we propose an approach combining a heuristic phase to identify solutions lying in the concave part and a simulation-based cut generation phase to create outer-approximations of the probability functions. This allows us to find good staffing solutions satisfying the joint-chance constraints by simulation and linear programming. We test our formulation and algorithm using call center examples of up to 65 call types and 89 agent groups, which shows the benefits of our joint-chance constrained formulation and the advantage of our algorithm over standard ones.