考虑最坏中断损失下的P-中位设施选址问题的模型与算法研究

蓄意突袭以及恐怖袭击会造成设施服务的突然中断成为网络系统的主要危害之一,因此网络设施选址决策应该同时考虑正常和紧急状态下系统的运作成本.本文研究考虑最坏中断损失下的网络设施选址问题,建立了该问题的双层规划模型,上层规划涉及设施选址决策,下层规划研究确定设施位置后,设施中断产生最大损失的问题.本文运用基于拉格朗日松弛的混合遗传算法来求解该双层规划问题.将European150数据集作为研究对象,对比研究了本文研究问题与传统的P-中位选址问题的结果,分析不同选址策略下网络系统的效率被中断影响的程度是不同的.最后通过改变一些关键参数,比如常规运作权重、设施数量、中断设施数量,对相关结果进行了分析.     

多项目人力资源调度实证研究

针对某公寓大修项目,建立有关人力资源约束下的多项目进度管理问题混合整数规划模型。其中考虑了多种约束,如项目对人员能力、水平的不同要求,而人员又具有多种能力及水平;目标为满足约束的条件下总成本最小化,其中包含按时间计费的工资,和福利等的固定费用。为了简化计算,采用列生成法把复杂的多项目模型分解为一个主问题和多个子问题并协调主问题和子问题求解。同时由于子问题的复杂性难以精确求解,采用启发式算法求解:首先由基于优先原则的启发式方法给出问题的初始解,再由遗传算法寻优。最后通过该实际案例的应用,表明此方法能够快速有效的解决实际问题,给决策者提供信息,帮助指导实践。     

限制性卖空的均值-半绝对偏差投资组合模型及其旋转算法研究

本文提出了限制性卖空的均值-半绝对偏差投资组合模型,通过变量替换将该模型转变为一般线性规划问题,从而运用线性规划的旋转算法进行求解。最后,文章以一个具体的算例验证了该算法的有效性,并证明将限制性卖空引入到投资组合中,有助于增强市场效率,降低市场风险。     

一种基于PIM与核方法的模糊聚类新算法

本文针对模糊C均值聚类在大数据量时收敛较慢以及不能对多种数据结构有效聚类的缺点,结合PIM算法与核方法提出了一种新的高效聚类算法———KPIM算法,并从理论上证明了该算法的收敛性.最后利用标准实验数据IRIS数据集测试,结果表明KPIM算法在保证收敛速度的同时,聚类效果更有效.     

动态联盟中伙伴选择问题的区间规划模型及其求解

伙伴选择和风险管理是动态联盟中的重要决策问题,当考虑失败风险时,失败概率无法给出精确值,因此,考虑采用不确定性规划描述此类问题.提出动态联盟中伙伴选择问题的区间规划模型,模型中用区间数表示联盟伙伴的失败概率.为了求解该模型,引入序关系,并利用Nakahara和Ishibuchi的定理,将区间规划模型转化为等价的清晰双目标模型.设计带自适应适值函数的遗传算法,求出问题的全部非劣解.经过对多个问题的仿真,证明了算法的有效性.     

Hard‐to‐Solve Bimatrix Games

The Lemke–Howson algorithm is the classical method for finding one Nash equilibrium of a bimatrix game. This paper presents a class of square bimatrix games for which this algorithm takes, even in the best case, an exponential number of steps in the dimension d of the game. Using polytope theory, the games are constructed using pairs of dual cyclic polytopes with 2d suitably labeled facets in d‐space. The construction is extended to nonsquare games where, in addition to exponentially long Lemke–Howson computations, finding an equilibrium by support enumeration takes on average exponential time.     

Penalty guided genetic search for redundancy optimization in multi-state series-parallel power system

This paper presents a genetic algorithm (GA) for parallel redundancy optimization in series-parallel power systems exhibiting multi-state behavior, optimizing the reliability subject to constraints. The components are binary and chosen from a list of products available in the market, and are being characterized by their feeding capacity, reliability, cost and weight. System reliability is defined as the ability to satisfy consumer demand and is presented as a piecewise cumulative load curve. In GA, to handle infeasible solutions penalty strategies are used. Penalty technique keep a certain amount of infeasible solutions in each generation so as to enforce genetic search towards an optimal solution from sides of, both, feasible and infeasible regions. We here present a dynamic adaptive penalty function which helps the algorithm to search efficiently for optimal/near optimal solution. To evaluate system reliability, a fast procedure, based on universal generating function, is used. An example considering a multi-state series-parallel power system is solved considering both homogeneous and heterogeneous types of redundancy. Also an example considering price discounts is solved. The effectiveness of the penalty function and the proposed algorithm is studied and shown graphically.     

Optimal algorithms for uncovering synteny problem

The syntenic distance between two genomes is the minimum number of fusions, fissions, and translocations that can transform one genome to the other, ignoring the gene order within chromosomes. As the problem is NP-hard in general, some particular classes of synteny instances, such as linear synteny, exact synteny and nested synteny, are examined in the literature. In this paper, we propose a new special class of synteny instances, called uncovering synteny. We first present a polynomial time algorithm to solve the connected case of uncovering synteny optimally. By performing only intra-component moves, we then solve the unconnected case of uncovering synteny. We will further calculate the diameters of connected and unconnected uncovering synteny, respectively.     

一种求解双目标flow shop排序问题的进化算法

提出一种求解双目标flow shop排序的递进多目标进化算法.算法采用改进的精英复制策略,在实现精英保留的前提下降低了计算复杂性;通过递进进化模式增加群体多样性,改善了算法收敛性;通过群体进化过程中对非劣解集进行竞争型可变邻域启发式搜索,增强了算法局部搜索性能.采用新算法和参照算法NSGA-II对31个标准双目标flow shop算例进行优化.研究结果表明,新算法在所有算例的求解中均获得了优于NSGA-II的非劣解集,验证了算法的有效性.     

On Inverse Problems of Optimum Perfect Matching

As far as we know, for most polynomially solvable network optimization problems, their inverse problems under l ₁ or l norm have been studied, except the inverse maximum-weight matching problem in non-bipartite networks. In this paper we discuss the inverse problem of maximum-weight perfect matching in a non-bipartite network under l ₁ and l norms. It has been proved that the inverse maximum-weight perfect matching under l norm can be formulated as a maximum-mean alternating cycle problem of an undirected network, and can be solved in polynomial time by a binary search algorithm and in strongly polynomial time by an ascending algorithm, and under l ₁ norm it can be solved by the ellipsoid method. Therefore, inverse problems of maximum-weight perfect matching under l ₁ and l norms are solvable in polynomial time.