可满足问题中的模型计数

模型计数问题是指计算给定问题的解的个数,这是一类比决策更困难的问题,也是人工智能领域研究的一个热点问题.对模型计数问题的研究不仅可以提高算法的求解效率,更能促进对问题困难本质的了解.以可满足问题（命题可满足（SAT）和约束可满足问题（CSP））为例,从精确算法和近似求解两方面综述了模型计数问题的研究现状,重点介绍了相关概念以及各个算法之间的优缺点,并提出了有待解决的开放性问题,对模型计数问题的研究予以了总结和展望.     

基于粒子群优化的蚁群算法在TSP中的应用

结合粒子群算法的问题,提出用混合蚁群算法来求解著名的旅行商问题.问题的核心是应用粒子群算法对蚁群算法的控制参数:启发式因子、信息素挥发系数、随机性选择阈值进行优化,以及运用蚁群系统算法寻找最短路径.新算法对于蚂蚁算法中的参数调整大大减低,减少了大量盲目的实验,力求在开发最优解和探究搜索空间上找到平衡点.对旅行商问题的仿真实验表明,新算法的优化质量和效率都优于传统蚁群算法和遗传算法,接近理论最佳值.新算法也可推广用于其他NP问题的求解.     

简约支持向量聚类

针对传统支持向量聚类(support vector clustering, SVC)的高耗费和低性能弊端,提出了简约支持向量聚类算法(reduced support vector clustering, RSVC).RSVC的核心是简约策略和新的簇划分方法.前者是基于薛定谔方程而设计,提取对模型生成有重要意义的数据构成简约子集,并在此子集之上完成优化过程.后者提出并证明了高斯核函数特征空间的几何性质,并以此设计方法完成对数据簇的辨识任务.理论分析和实验结果表明,和同类算法相比,RSVC可更有效地解决两个弊端,在实际应用中取得良好的聚类效果.     

求解子集和问题的采样格归约算法

子集和问题是计算机科学中的重要问题,也是构建多种公钥密码体制的基础.提出了采样归约算法,使用随机采样方法降低问题维度,将原问题分解并归约为多个更小规模的格上最短向量,降低了构造格的半径,从而提高求解的效率,得到原问题的精确解或提高近似解的逼近程度.给出了理论上采样归约算法最差情况的成功率.更进一步地,在目标解重量较低的情况下,可以进行分段采样,对问题增加限定条件,提高解题效率.实验结果表明,对于高维度的子集和问题,与CJLOSS等已有的格归约子集和问题方法相比,该算法可以更高效地求解出问题的精确解,而且可以提高近似解的逼近程度,输出近似解的平均长度达到了CJLOSS算法的0.55倍、DR算法的0.64倍.     

信用评级的简约神经网络算法

运用经济资源的“边际效用递减”原理,分析了信用评级知识的非线性特点,着眼于神经网络算法的结构、函数和收敛算法三部件逻辑独立性,分析了经典神经网络算法拓扑结构的复杂性引致的算法参数调整过度复杂问题,提出了简约神经网络的拓扑结构,证明了在全部结点函数线性且全部隐层结点函数过原点的条件下经典神经网络与简约神经网络具有等价性,设计了基于简约网络的算法,算法结果获得了较高的拟合精度。     

信用评级的简约神经网络算法研究

针对经典神经网络算法中参数调整过度复杂的问题，分析银行信用评级知识非线性的特点，提出简约神经网络的拓朴结构，证明了在全部节点函数线性且全部隐层节点函数过原点的条件下,经典神经网络与简约神经网络具有等价性。在此基础上，设计了基于简约网络的算法，简化了参数调整过程，算法结果获得了满意的拟合精度。     

Prufer编解码的最优算法

讨论标号树的Prufer编码的编解码算法.文献中常见的Prufer编解码算法需要O(n log n)时间.文献[1,2,4,9]提出了Prufer编解码的线性时间算法.这些算法都用到了整数排序算法,利用待排序整数的取值特殊性,得到线性时间整数排序算法.由此将Prufer编解码问题的计算归结为整数排序问题.本文从更直接的角度考察Prufer编解码问题,从简单算法出发,挖掘问题的本质特征,逐步简化,得到Prufer编码的一个非常简单实用的线性时间最优编解码算法.本文采用的解决问题的方法也具有一定的技巧,可供解决类似问题时借鉴.     

基于模拟退火的蚁群算法求解Job-Shop问题

引用蚁群算法来解决Job-Shop问题(简称JSP),但是由于蚁群算法本身的原理和Job-Shop问题之间的差异性,使得用基本的蚁群算法来解决Job-Shop问题存在一些缺陷.从蚁群算法的改进入手,采用了不同策略的信息素更新方法,并采用模拟退火算法对搜索到的解进行处理,不仅加快了算法的收敛速度,而且能收敛到更好的解,最后用实例对算法的有效性进行了验证.     

基于蚁群算法求解最大团问题

最大团问题是一种典型的NP完全问题, 是图论中一个经典的组合优化问题.研究将蚁群算法应用于求解最大团问题,提出一种求解最大团问题蚁群算法.通过定义最大团问题蚁群算法中的各元素,并改进了蚂蚁搜索解的方法,有效地改善蚁群算法易于过早地收敛于局部最优解的缺陷.仿真实验表明,图中的顶点数较多时,也取得了较好的结果.     

时间依赖型车辆路径问题的一种改进蚁群算法

时间依赖型车辆路径规划问题(TDVRP),是研究路段行程时间随出发时刻变化的路网环境下的车辆路径优化.传统车辆路径问题(VRP)已被证明是NP-hard问题,因此,考虑交通状况时变特征的TDVRP问题求解更为困难.本文设计了一种TDVRP问题的改进蚁群算法,采用基于最小成本的最邻近法(NNC算法)生成蚁群算法的初始可行解,通过局部搜索操作提高可行解的质量,采用最大--最小蚂蚁系统信息素更新策略.测试结果表明,与最邻近算法和遗传算法相比,改进蚁群算法具有更高的效率,能够得到更优的结果;对于大规模TDVRP问题,改进蚁群算法也表现出良好的性能,即使客户节点数量达到1000,算法的优化时间依然在可接受的范围内.     

不确定旅行商问题的鲁棒模型及其算法研究

旅行商问题是一类重要的组合优化问题。针对不确定旅行商问题,采用区间数来描述其城市间的旅行时间。在鲁棒优化理论框架下,建立其模型。该模型的突出特点是其鲁棒性可调。提出了一类求解该模型的精确算法和蚁群算法。与精确算法相比较,结果表明了所提出的蚁群算法能在较短时间内求得最优或近优的解。最后,分析了模型的性能,结论表明,在不确定环境下,鲁棒解是有效的。     

基于混合算法的带时间窗的车辆路径问题求解

建立了有时间窗车辆路径问题的数学模型，针对遗传算法在局部搜索能力方面的不足，提出将模拟退火算法与遗传算法相结合，从而构造了有时间窗车辆路径问题的混合遗传算法，并进行了实验计算。结果表明，用混合遗传算法求解该优化问题，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模拟退火算法在全局搜索能力方面的不足，从而得到了质量较高的解。     

k-着色问题及其均场退火求解算法

均场退火方法既可以看作是一种新的神经网络计算模型,又可视为是对模拟退火的重大改进.该文把具有相邻约束的多层通孔最小化问题转换为更具广泛意义的k-着色问题,并提出了k-着色问题的均场退火求解算法.算法在线段相交图模型的基础上,提出了相邻矩阵和交叠矩阵等概念,并利用换位矩阵,将问题映射为相应的神经网络,再构造了该问题的能量函数.能量函数中的目标项、违背交叠约束的惩罚项、违背相邻约束的惩罚项和神经元归一化处理保证了网络能够求解到一个合法解.实验结果表明,这是一个有效的算法.     

Solving dynamic double row layout problem via combining simulated annealing and mathematical programming

Double row layout problem (DRLP) is to allocate facilities on two rows separated by a straight aisle. Aiming at the dynamic environment of product processing in practice, we propose a dynamic double-row layout problem (DDRLP) where material flows change over time in different processing periods. A mixed-integer programming model is established for this problem. A methodology combining an improved simulated annealing (ISA) with mathematical programming (MP) is proposed to resolve it. Firstly, a mixed coding scheme is designed to represent both of sequence of facilities and their exact locations. Secondly, an improved simulated annealing algorithm is suggested to produce a solution to DDRLP. Finally, MP is used to improve this solution by determining the optimal exact location for each facility. Experiments show that this methodology is able to obtain the optimal solutions for small size problems and outperforms an exact approach (CPLEX) for problems of realistic size.     

Mathematical formulation and a new metaheuristic for the constrained double-floor corridor allocation problem

A layout plan for a manufacturing system that is designed without any facility constraints will most likely be infeasible when confronted with reality. Additionally, considering that land available for building industrial plants is limited and its cost is high, it is necessary to investigate the layout planning of two and multi-floor facilities. To address these shortages in the scientific literature, we focus on the double-floor corridor allocation problem (DFCAP) which covers a wide range of complex facility constraints, such as fixed floor constraints, fixed row constraints, fixed positioning constraints, mutual floor constraints, mutual row constraints, sequencing constraints and adjacency constraints. For the model mentioned above, we term it as a constrained DFCAP (cDFCAP). A mixed-integer linear programming model is formulated for the cDFCAP. In order to solve larger realistic problems, a constrained metaheuristic with the memetic algorithm framework customised for solving the cDFCAP is introduced in this work. In our algorithm, four problem-specific heuristic rules to construct a set of initial solutions are developed. In addition, an ideal parameter combination for our constrained memetic algorithm is determined through a Taguchi experimental design. Finally, the results of a set of cDFCAP instances with different sizes (n = 10∼80) report that our provided approach is effective for the considered problem.     

Reliability-aware automatic composition approach for web services

In this paper,we study the reliability-aware synthesis problem for composing available services automatically and guaranteeing that the composed result satisfies the specification,such as temporal constraints of functionality and reliability,centered on a synthesis model for mediator of web services composition (CSM).This approach focuses on handling attributes and state relations,and permitting users and services to operate over them,i.e.,read /write their data values and compare them according to a dense state order.We show that the reliability-aware synthesis problem for the specification is EXPTIME-complete and we give an exponential-time algorithm (CSM-NSA) which for a given formula ψ and a synthesis model,synthesizes available services in the library satisfying ψ over the synthesis model (if they exist) or responds with "not satisfiable" (otherwise).The specification ψ is a fragment of PCTL (probabilistic computation tree logic),obtained from "ordinary" CTL (computation tree logic) by replacing the EX,AX,EU and AU operation with their quantitative counterparts X >p,X =1,U >p,and U =1,respectively.As opposed to NSA,we provide a more effective algorithm to replace the NSA algorithm called CSM-HSA (heuristic synthesis algorithm).Though HSA is an incomplete algorithm,the answer is correct.The experiments show that the HSA algorithm solves the problem of reliability-aware service synthesis effectively and efficiently.     

Modelling of the inventory replenishment problem with a two-segment piecewise linear demand

The classical inventory replenishment problem with a linear function in demand uses a ‘single-segment’ linear function as its demand and can be modelled by a simple algorithm. Moreover, this article extends the algorithm to provide a heuristic solution for the inventory replenishment model with a two-segment linear function in demand called the ‘two-segment piecewise linear demand model’. In addition, this article proposes a general procedure for solving both models. Meanwhile, several examples taken from the literature illustrate our algorithm for these two models with convincing results. Furthermore, this study shows that when the demand is a two-segment piecewise linear function over time, it is better to use the proposed algorithm rather than devising a decoupled solution approach by treating segments separately. Finally, a sensitivity analysis of two factors, demand and cost, is performed. The model is highly extensible and applicable, so it can serve as an inventory planning tool to solve the replenishment problem.     

基于混合离散免疫算法的轧制计划编排

为了保证轧制调度计划的可行性，提高排程的效率，根据热轧生产模式和轧制计划的特点，利用车辆路径问题模型来建模轧制调度问题，并用一种基于离散人工免疫算法的混合优化算法来解决这一问题。该方法利用离散人工免疫算法的全局搜索能力来寻找全局最优解，利用模拟退火方法来避免陷入局部最优．对某钢厂实际生产数据仿真结果表明，所提出的模型和算法对于求解热轧调度问题具有可行性和高效性。     

求解带平衡约束圆形Packing问题的快速局部搜索算法

带平衡性约束的圆集在圆容器内的布局优化问题,属于NP困难问题。针对此问题,提出了一种快速的局部搜索算法。该算法首先构造出等价的物理模型,定义系统的能量函数,再利用最速下降法对能量函数进行优化,从而间接得到问题的近似解。在局部搜索算法中引入加速策略,提高了计算效率。最后通过两个算例的数值计算,验证了该方法的可行性和有效性。