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961.
Yuriy Stoyan Alexander Pankratov Tatiana Romanova 《The Journal of the Operational Research Society》2016,67(5):786-800
We further improve our methodology for solving irregular packing and cutting problems. We deal with an accurate representation of objects bounded by circular arcs and line segments and allow their continuous rotations and translations within rectangular and circular containers. We formulate a basic irregular placement problem which covers a wide spectrum of packing and cutting problems. We provide an exact non-linear programming (NLP) model of the problem, employing ready-to-use phi-functions. We develop an efficient solution algorithm to search for local optimal solutions for the problem in a reasonable time. The algorithm reduces our problem to a sequence of NLP subproblems and employs optimization procedures to generate starting feasible points and feasible subregions. Our algorithm allows us to considerably reduce the number of inequalities in NLP subproblems. To show the benefits of our methodology we give computational results for a number of new challenger and the best known benchmark instances. 相似文献
962.
Clemens Nothegger Alfred Mayer Andreas Chwatal Günther R. Raidl 《Annals of Operations Research》2012,194(1):325-339
In this work we present a new approach to tackle the problem of Post Enrolment Course Timetabling as specified for the International Timetabling Competition 2007 (ITC2007), competition track 2. The heuristic procedure is
based on Ant Colony Optimization (ACO) where artificial ants successively construct solutions based on pheromones (stigmergy) and local information. The key feature of our algorithm is the use of two distinct but simplified pheromone matrices
in order to improve convergence but still provide enough flexibility for effectively guiding the solution construction process.
We show that by parallelizing the algorithm we can improve the solution quality significantly. We applied our algorithm to
the instances used for the ITC2007. The results document that our approach is among the leading algorithms for this problem;
in all cases the optimal solution could be found. Furthermore we discuss the characteristics of the instances where the algorithm
performs especially well. 相似文献
963.
We prove that the MacWilliams duality holds for bent functions. It enables us to derive the concept of formally self-dual
Boolean functions with respect to their near weight enumerators. By using this concept, we prove the Gleason-type theorem
on self-dual bent functions. As an application, we provide the total number of (self-dual) bent functions in two and four
variables obtaining from formally self-dual Boolean functions. 相似文献
964.
Fortuné Massamba 《Mathematica Slovaca》2012,62(2):315-344
We investigate some geometric aspects of lightlike hypersurfaces of indefinite Kenmotsu manifolds, tangent to the structure
vector field, by paying attention to the geometry of leaves of integrable distributions. Theorems on parallel vector fields,
Killing distribution, geodesibility of their leaves are obtained. The geometric configuration of such lightlike hypersurfaces
and leaves of its screen integrable distributions are established. We show that no totally contact umbilical leaf of a screen
integrable distribution of a lightlike hypersurface can be an extrinsic sphere. We also prove that the geometry of any leaf
of an integrable distribution is closely related to the geometry of a normal bundle. 相似文献
965.
Joan Porti 《Geometriae Dedicata》2012,156(1):165-170
We prove that, among all convex hyperbolic polygons with given angles, the perimeter is minimized by the unique polygon with
an inscribed circle. The proof relies on work of Schlenker (Trans Am Math Soc 359(5): 2155–2189, 2007). 相似文献
966.
In this paper, we study the semilocal convergence for a fifth-order method for solving nonlinear equations in Banach spaces.
The semilocal convergence of this method is established by using recurrence relations. We prove an existence-uniqueness theorem
and give a priori error bounds which demonstrates the R-order of the method. As compared with the Jarratt method in Hernández
and Salanova (Southwest J Pure Appl Math 1:29–40, 1999) and the Multi-super-Halley method in Wang et al. (Numer Algorithms 56:497–516, 2011), the differentiability conditions of the convergence of the method in this paper are mild and the R-order is improved. Finally,
we give some numerical applications to demonstrate our approach. 相似文献
967.
This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative
low-rank matrices X and Y so that the product XY approximates a nonnegative data matrix M whose elements are partially known (to a certain accuracy). This problem aggregates two existing problems: (i) nonnegative
matrix factorization where all entries of M are given, and (ii) low-rank matrix completion where nonnegativity is not required. By taking the advantages of both nonnegativity
and low-rankness, one can generally obtain superior results than those of just using one of the two properties. We propose
to solve the non-convex constrained least-squares problem using an algorithm based on the classical alternating direction
augmented Lagrangian method. Preliminary convergence properties of the algorithm and numerical simulation results are presented.
Compared to a recent algorithm for nonnegative matrix factorization, the proposed algorithm produces factorizations of similar
quality using only about half of the matrix entries. On tasks of recovering incomplete grayscale and hyperspectral images,
the proposed algorithm yields overall better qualities than those produced by two recent matrix-completion algorithms that
do not exploit nonnegativity. 相似文献
968.
We obtain an intertwining relation between some Riemann–Liouville operators of order α ∈ (1, 2), connecting through a certain multiplicative identity in law the one-dimensional marginals of reflected completely
asymmetric α-stable Lévy processes. An alternative approach based on recurrent extensions of positive self-similar Markov processes and
exponential functionals of Lévy processes is also discussed. 相似文献
969.
Zdzisław Naniewicz 《Set-Valued and Variational Analysis》2011,19(3):417-456
The existence solution for a class of economic equilibrium type problems in reflexive Banach space is considered. New results concerning the variational inequality approach to Arrow–Debreu model of economic equilibrium introduced in Naniewicz (Math Oper Res 32:436–466, 2007) are found and applied to ensure the existence of Pareto optimal solutions for a class of multiobjective optimization problems with so-called budget-like constraints. To achieve this goal, the theory of pseudo-monotone multivalued mappings combined with some fixed point technique for multivalued mappings with nonconvex values is used. 相似文献
970.
We discuss the proof of Kazhdan and Lusztig of the equivalence of the Drinfeld category \({\mathcal D}({\mathfrak g},\hbar)\) of \({\mathfrak g}\)-modules and the category of finite dimensional \(U_q{\mathfrak g}\)-modules, \(q=e^{\pi i\hbar}\), for \(\hbar\in{\mathbb C}\setminus{\mathbb Q}^*\). Aiming at operator algebraists the result is formulated as the existence for each \(\hbar\in i{\mathbb R}\) of a normalized unitary 2-cochain \({\mathcal F}\) on the dual \(\hat G\) of a compact simple Lie group G such that the convolution algebra of G with the coproduct twisted by \({\mathcal F}\) is *-isomorphic to the convolution algebra of the q-deformation G q of G, while the coboundary of \({\mathcal F}^{-1}\) coincides with Drinfeld’s KZ-associator defined via monodromy of the Knizhnik–Zamolodchikov equations. 相似文献