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This paper focuses on the generalized arc routing problem. This problem is stated on an undirected graph in which some clusters are defined as pairwise-disjoint connected subgraphs, and a route is sought that traverses at least one edge of each cluster. Broadly speaking, the generalized arc routing problem is the arc routing counterpart of the generalized traveling salesman problem, where the set of vertices of a given graph is partitioned into clusters and a route is sought that visits at least one vertex of each cluster. A mathematical programming formulation that exploits the structure of the problem and uses only binary variables is proposed. Facets and families of valid inequalities are presented for the polyhedron associated with the formulation and the corresponding separation problem studied. The numerical results of a series of computational experiments with an exact branch and cut algorithm are presented and analyzed. 相似文献
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P. M. Akhmet'ev 《Journal of Mathematical Sciences》2001,105(2):1813-1818
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This paper studies a non-preemptive infinite-horizon scheduling problem with a single server and a fixed set of recurring jobs. Each job is characterized by two given positive numbers: job duration and maximum allowable time between the job completion and its next start. We show that for a feasible problem there exists a periodic schedule. We also provide necessary conditions for the feasibility, formulate an algorithm based on dynamic programming, and, since this problem is NP-hard, formulate and study heuristic algorithms. In particular, by applying the theory of Markov Decision Process, we establish natural necessary conditions for feasibility and develop heuristics, called frequency based algorithms, that outperform standard scheduling heuristics. 相似文献
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The Generalized Moment Problem with Complexity Constraint 总被引:1,自引:0,他引:1
In this paper, we present a synthesis of our differentiable approach to the generalized moment problem, an approach which
begins with a reformulation in terms of differential forms and which ultimately ends up with a canonically derived, strictly
convex optimization problem. Engineering applications typically demand a solution that is the ratio of functions in certain
finite dimensional vector space of functions, usually the same vector space that is prescribed in the generalized moment problem.
Solutions of this type are hinted at in the classical text by Krein and Nudelman and stated in the vast generalization of
interpolation problems by Sarason. In this paper, formulated as generalized moment problems with complexity constraint, we
give a complete parameterization of such solutions, in harmony with the above mentioned results and the engineering applications.
While our previously announced results required some differentiability hypotheses, this paper uses a weak form involving integrability
and measurability hypotheses that are more in the spirit of the classical treatment of the generalized moment problem. Because
of this generality, we can extend the existence and well-posedness of solutions to this problem to nonnegative, rather than
positive, initial data in the complexity constraint. This has nontrivial implications in the engineering applications of this
theory. We also extend this more general result to the case where the numerator can be an arbitrary positive absolutely integrable
function that determines a unique denominator in this finite-dimensional vector space. Finally, we conclude with four examples
illustrating our results. 相似文献
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F. G. Avkhadiev 《Siberian Mathematical Journal》2017,58(6):932-942
The Davies problem is connected with the maximal constants in Hardy-type inequalities. We study the generalizations of this problem to the Rellich-type inequalities for polyharmonic operators in domains of the Euclidean space. The estimates are obtained solving the generalized problem under an additional minimal condition on the boundary of the domain. Namely, for a given domain we assume the existence of two balls with sufficiently small radii and the following property: the balls have only a sole common point; one ball lies inside the domain and the other is disjoint from the domain. 相似文献
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借助于广义算子半群和广义积分算子半群的关系,讨论广义算子半群的Perron型指数稳定性,研究了广义积分算子半群的渐近行为. 相似文献
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在Banach空间中引入了一类广义F-互补问题,研究了它与一类变分不等式问题的等价性关系,给出了此类变分不等式问题的解的存在唯一性定理. 相似文献
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Yu. M. Berezansky 《Functional Analysis and Its Applications》2003,37(4):311-315
The classical power moment problem can be viewed as a theory of spectral representations of a positive functional on some classical commutative algebra with involution. We generalize this approach to the case in which the algebra is a special commutative algebra of functions on the space of multiple finite configurations. If the above-mentioned functional is generated by a measure on the space of finite ordinary configurations, then this measure is the correlation measure for a measure on the space of infinite configurations. The positiveness of the functional gives conditions for the measure to be a correlation measure. 相似文献
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Acta Mathematicae Applicatae Sinica, English Series - The generalized Riemann problem for a model of chromatography system in a conservative form is considered. The unique local solution in the... 相似文献
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For positive integers , a coloring of is called a -coloring if the edges of every receive at least and at most colors. Let denote the maximum number of colors in a -coloring of . Given we determine the largest such that all -colorings of have at most O(n) colors and we determine asymptotically when it is of order equal to . We give several bounds and constructions.
Received May 3, 1999 相似文献
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We prove an existence result for the time-dependent generalized Nash equilibrium problem under generalized convexity without neither a quasi-variational inequality reformulation nor a quasi-equilibrium problem reformulation. Furthermore, an application to the time-dependent abstract economy is considered. 相似文献
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Covert David Koh Doowon Pi Youngjin 《Journal of Fourier Analysis and Applications》2019,25(3):1026-1052
Journal of Fourier Analysis and Applications - Let $${\mathbb {F}}_q^d$$ be the d-dimensional vector space over the finite field $${\mathbb {F}}_q$$ with q elements. Given k sets $$E_j\subset... 相似文献
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We solve a generalized Gauss problem in the Euclidean plane which states that: Given a convex quadrilateral, a positive number (weight) that corresponds to each of its vertices and a length of a linear segment which connects two mobile interior points of the quadrilateral find the minimum weighted network, which connects two of the vertices with one interior point and the other two with another interior point (Generalized Gauss tree). Furthermore, we introduce a generalized Gauss variable which corresponds to the unknown weight of the given distance which connects the two mobile interior points and obtain a degenerate generalized Gauss tree which corresponds to a specific value of the generalized Gauss variable that minimizes the length of the induced generalized Gauss trees and the weighted Fermat–Torricelli tree for a specific value of the generalized Gauss variable that maximizes the length of the induced generalized Gauss trees. Following this technique, we introduce a new class of generalized Gauss trees that we call absorbing generalized Gauss trees and a new class of Fermat–Torricelli trees that we call absorbing Fermat–Torricelli trees with respect to the sum of the four given weights of the convex quadrilateral. 相似文献