具有时间与位置相关的两类平行机排序问题

研究带有维修时间限制的时间和位置效应平行机排序问题,涉及同型机和非同类机两种机器类型.工件的实际加工时间同时受到位置效应和时间效应影响,且机器具有维修限制.目标函数由机器负载,总完工时间与总等待时间组成.非同类机情形下,通过将排序问题转化为指派问题,给出多项式时间算法,其算法的时间复杂度为O（n^k+2/（k-1）!）.同型机情形下通过转化目标函数,使用匹配算法得出排序问题的多项式时间解,其时间复杂度为O（（2n+m+n log n）n^k-1/（k-1）!）.     

精确覆盖问题的加权分治算法

精确覆盖问题是组合优化中经典的NP-Hard问题之一,其在诸多领域具有广泛的应用价值。本文首先研究了精确覆盖问题的数学性质,并根据数学性质提出相应的分支降阶规则以缩小问题的规模;接着设计了一个基于分支降阶的回溯算法求解该问题;然后运用常规技术分析得出该精确算法的时间复杂度为O(1.4656^k);最后运用加权分治技术对该算法的时间复杂度进行分析,将该算法的时间复杂度降为O(1.3842^k)。文章最后通过一个示例进一步阐述该算法的原理,并与其他精确算法进行了对比分析,研究结果表明该算法是可行的,也是有效的。     

整数规划的布谷鸟算法

布谷鸟搜索算法是一种新型的智能优化算法．本文采用截断取整的方法将基本布谷鸟搜索算法用于求解整数规划问题．通过对标准测试函数进行仿真实验并与粒子群算法进行比较,结果表明本文所提算法比粒子群算法拥有更好的性能和更强的全局寻优能力,可以作为一种实用方法用于求解整数规划问题．     

目标为最小化工件运输时间和的单台机器带一个维修时间段的排序问题的一个改进算法

单台机器带一个维修时间段的排序问题,目标是最小化所有工件的运输时间和.在这篇文章里,重新研究了该问题,并给出了一个时间复杂性为O（n³）的近似算法,将性能比从3/2改进到5/4.     

整数非线性规划的一种直接搜索寻优算法

本文的工作是将Rosenbrock算法移殖求解整数非线性规划,得到一种求解整数非线性规划的直接搜索寻优算法,该算法只要求函数是可计算的,可适用于实际规划问题。     

现金押运路线问题——基于多类型的风险

以人民币现金押运为研究背景,考虑了一种基于多类型风险的现金押运路线问题,以在途风险成本、库存现金风险成本以及运输成本为优化目标,建立了混合整数线性规划模型,并提出了一种基于多样化策略和改进邻域搜索的混合遗传算法,其中遗传算法对押运路线进行选择,贪心算法用来求解各类风险指标。数值实验分别对问题特性和算法性能进行了分析。实验结果表明:1)混合遗传算法能求解更大规模的问题,得到较好的解,并很好地平衡了运行时间和求解质量;2)多类型风险影响了行驶路线;3)客户的期望需求影响了库存现金风险。     

约束全局整数规划问题的填充函数法

本文给出了一类新的求解箱约束全局整数规划问题的填充函数，并讨论了其填充性质．基于提出的填充函数，设计了一个求解带等式约束、不等式约束、及箱约束的全局整数规划问题的算法．初步的数值试验结果表明提出的算法是可行的。     

随机需求收益最大化分销网络设计问题

研究随机需求的供应链分销网络设计问题。考虑供应商可以选择所服务的零售商,且供应商通过定价决策确定所服务的零售商。针对此问题,建立了一个非线性整数规划模型和一个等价的集合包裹模型,并利用列生成算法求解集合包裹模型,同时提出一种O（ n3 logn）时间的算法求解列生成算法中产生的子问题。数值计算表明,本文所提出的算法具有很好的最优性和可行性。     

解线性目标规划的《量化优先因子法》—基于LP过程的算法

本文提出一种解线性目标规划及整数线性目标规划的《量化优先因子法》,即把目标规划中表示优先等级的优先因子 pl( l=1 ,2 ,… ,L)用能从数量级上刻划优先因子 Pl Pl+ 1的本质特征的数来表示 ,进而用 SAS/OR软件包中解线性规划的 LP过程即可求解此线性目标规划 .通过实例给出算法与用 LP过程求解的程序 .     

选址-库存-路径问题模型及其集成优化算法

设施选址、库存控制和车辆路径安排是物流系统优化中的三个关键问题,三者之间存在相互依赖的关系,应该根据这种关系来相应地进行综合优化与管理物流活动。以典型的单一生产基地、单一产品、采用不断审查的(Q, r)库存策略的供应链二级分销网络为研究对象,建立了一个随机型选址-库存-路径问题优化模型;在将非线性混合整数规划转化为线性整数集合覆盖模型的基础上,采用列生成算法来获得一个近似最优解,再用分支定价法对初始解进行改进,以实现对整个问题“完全集成”的优化。最后,用随机生成的方式,产生了10至160个客户的计算实例,分析了运输费用和库存费用对总成本的影响,算法运算时间表明本文给出的算法能较快地求解这一复杂问题。     

Regular expression searching on compressed text

We present a solution to the problem of regular expression searching on compressed text. The format we choose is the Ziv–Lempel family, specifically the LZ78 and LZW variants. Given a text of length u compressed into length n, and a pattern of length m, we report all the R occurrences of the pattern in the text in O(2^m+mn+Rmlogm) worst case time. On average this drops to O(m²+(n+Rm)logm) or O(m²+n+Ru/n) for most regular expressions. This is the first nontrivial result for this problem. The experimental results show that our compressed search algorithm needs half the time necessary for decompression plus searching, which is currently the only alternative.     

Computing rectangle enclosures

The rectangle enclosure problem is the problem of determining the subset of n iso-oriented planar rectangles that enclose a query rectangle Q. In this paper, we use a three layered data structure which is a combination of Range and Priority search trees and answers both the static and dynamic cases of the problem. Both the cases use O(n> log² n) space. For the static case, the query time is O(log² n log log n + K). The dynamic case is supported in O(log³ n + K) query time using O(log³ n) amortized time per update. K denotes the size of the answer. For the d-dimensional space the results are analogous. The query time is O(log^2d-2 n log log n + K) for the static case and O(log^2d-1 n + K) for the dynamic case. The space used is O(n> log^2d-2 n) and the amortized time for an update is O(log^2d-1 n). The existing bounds given for a class of problems which includes the present one, are O(log^2d n + K) query time, O(log^2d n) time for an insertion and O(log^2d-1 n) time for a deletion.     

Decomposably non-negative matrices

Let A be an mn- by - mn symmetric matrix. Partition A into m²n - by - n blocks and suppose that each of these blocks is also symmetric. Suppose that for every decomposable (rank one) tensor ν ⊗ w, we have (ν ⊗ w)^t A(ν otimes; w) ≥ 0. Here, ν is a column m-tuple and w is a column n-tuple. We study the maximum number of negative eigenvalues such a matrix can have, as well as obtaining alternative characterizations of such matrices.     

Full transversal matroids, strict gammoids, and the matroid components problem

We provide two algorithms for finding dependence graphs both in a full transversal matroid and in its dual, a strict gammoid. The first algorithm is based on directed paths in the directed graph associated with a strict gammoid; its complexity is O(|L|(|V-L|+|E|)), where L is the link-set of the gammoid. The second algorithm is based on a special property of Gaussian elimination in a matrix of indeterminates representing a full transversal matroid; it complexity is o(m²n), where m is the rank of the matroid and n the cardinality of the underlying set. We provide an algorithm for listing all bases in, and calculating the Whitney and Tutte polynomials for, a full transversal matroid or a strict gammoid. The complexity of this algorithm is 0(N(n-m) (|E| + m²)), where N is the number of bases.     

Direct fail-proof triangularization algorithms for AX + XB = C with Error-Free and parallel implementations

Two 0(mn³) inversion-free direct algorithms to compute a solution of the linear system AX +XB = C by triangularizing a Hessenberg matrix are presented. Without any loss of generality the matrix A is assumed upper Hessenberg and the order m of A the order n of B. The algorithms have an in-built consistency check, are capable of pruning redundant rows and converting the resulting matrix into a full row rank matrix, and permit A and —B to be any square matrices with common or distinct eigenvalues. In addition, these algorithms can also solve the homogeneous system AX +XB = 0 (null matrix C). An error-free implementation of the solution X using multiple modulus residue arithmetic as well as a parallelization of the algorithms is discussed.     

On-line construction of the upper envelope of triangles and surface patches in three dimensions

In this paper, we describe a randomized incremental algorithm for computing the upper envelope (i.e., the pointwise maximum) of a set of n triangles in three dimensions. This algorithm is an on-line algorithm. It is structure-sensitive: the expected cost of inserting the n-th triangle is O(log nΣ_r=1ⁿτ(r)/r²) and depends on the expected size τ(r) of an intermediate result for r triangles. Since τ(r) can be Θ(r²(r)) in the worst case, this cost is bounded in the worst case by O(n(n) log n). (The expected behaviour is analyzed by averaging over all possible orderings of the input.) The main new characteristics is the use of a two-level history graph. (The history graph is an auxiliary data structure maintained by randomized incremental algorithms.) Our algorithm is fairly simple and appears to be efficient in practice. It extends to surfaces and surface patches of fixed maximum algebraic degree.     

Biased partitions and judicious <Emphasis Type="Italic">k</Emphasis>-partitions of graphs

Let G = (V,E) be a graph with m edges. For reals p ∈ [0, 1] and q = 1- p, let m_p(G) be the minimum of qe(V₁) +pe(V₂) over partitions V = V₁ ∪ V₂, where e(V_i) denotes the number of edges spanned by V_i. We show that if mp(G) = pqm-δ, then there exists a bipartition V₁, V₂ of G such that e(V₁) ≤ p²m - δ + p√m/2 + o(√m) and e(V₂) ≤ q²m - δ + q √m/2 + o(√m) for δ = o(m^2/3). This is sharp for complete graphs up to the error term o(√m). For an integer k ≥ 2, let fk(G) denote the maximum number of edges in a k-partite subgraph of G. We prove that if fk(G) = (1 - 1/k)m + α, then G admits a k-partition such that each vertex class spans at most m/k² - Ω(m/k^7.5) edges for α = Ω(m/k⁶). Both of the above improve the results of Bollobás and Scott.     

Finding all essential terms of a characteristic maxpolynomial

Let us denote ab=max(a,b) and ab=a+b for and extend this pair of operations to matrices and vectors in the same way as in linear algebra. We present an O(n²(m+n log n)) algorithm for finding all essential terms of the max-algebraic characteristic polynomial of an n×n matrix over with m finite elements. In the cases when all terms are essential, this algorithm also solves the following problem: Given an n×n matrix A and k{1,…,n}, find a k×k principal submatrix of A whose assignment problem value is maximum.