共查询到20条相似文献,搜索用时 15 毫秒
1.
Recent literatures have suggested that multiobjective evolutionary algorithms (MOEAs) can serve as a more exploratory and effective tool in solving multiobjective optimization problems (MOPs) than traditional optimizers. In order to contain a good approximation of Pareto optimal set with wide diversity associated with the inherent characters and variability of MOPs, this paper proposes a new evolutionary approach—(μ, λ) multiobjective evolution strategy ((μ, λ)-MOES). Following the highlight of how to balance proximity and diversity of individuals in exploration and exploitation stages respectively, some cooperative techniques are devised. Firstly, a novel combinatorial exploration operator that develops strong points from Gaussian mutation of proximity exploration and from Cauchy mutation of diversity preservation is elaborately designed. Additionally, we employ a complete nondominance selection so as to ensure maximal pressure for proximity exploitation while a fitness assignment determined by dominance and population diversity information is simultaneous used to ensure maximal diversity preservation. Moreover, a dynamic external archive is introduced to store elitist individuals as well as relatively better individuals and exchange information with the current population when performing archive increase scheme and archive decrease scheme. By graphical presentation and examination of selected performance metrics on three prominent benchmark test functions, (μ, λ)-MOES is found to outperform SPEA-II to some extent in terms of finding a near-optimal, well-extended and uniformly diversified Pareto optimal front. 相似文献
2.
James Propp 《Advances in Applied Mathematics》2005,34(4):871
Consider the 2n-by-2n matrix with mi,j=1 for i,j satisfying |2i−2n−1|+|2j−2n−1|2n and mi,j=0 for all other i,j, consisting of a central diamond of 1's surrounded by 0's. When n4, the λ-determinant of the matrix M (as introduced by Robbins and Rumsey [Adv. Math. 62 (1986) 169–184]) is not well defined. However, if we replace the 0's by t's, we get a matrix whose λ-determinant is well defined and is a polynomial in λ and t. The limit of this polynomial as t→0 is a polynomial in λ whose value at λ=1 is the number of domino-tilings of a 2n-by-2n square. 相似文献
3.
We present a new construction for (n,w,λ)-optical orthogonal codes (OOCs). The construction is pleasingly simple, where codewords correspond to arcs, specifically normal rational curves. Moreover, our construction yields for each λ>1 an infinite family of OOCs which are asymptotically optimal (with respect to the Johnson bound). 相似文献
4.
Rubn A. Martínez-Avendao 《Journal of Functional Analysis》2002,190(2):418-446
We introduce a class of operators, called λ-Hankel operators, as those that satisfy the operator equation S*X−XS=λX, where S is the unilateral forward shift and λ is a complex number. We investigate some of the properties of λ-Hankel operators and show that much of their behaviour is similar to that of the classical Hankel operators (0-Hankel operators). In particular, we show that positivity of λ-Hankel operators is equivalent to a generalized Hamburger moment problem. We show that certain linear spaces of noninvertible operators have the property that every compact subset of the complex plane containing zero is the spectrum of an operator in the space. This theorem generalizes a known result for Hankel operators and applies to λ-Hankel operators for certain λ. We also study some other operator equations involving S. 相似文献
5.
Klaus Dohmen 《European Journal of Combinatorics》2000,21(8):989
We investigate the number of proper λ -colourings of a hypergraph extending a given proper precolouring. We prove that this number agrees with a polynomial in λ for any sufficiently largeλ , and we establish a generalization of Whitney’s broken circuit theorem by applying a recent improvement of the inclusion–exclusion principle. 相似文献
6.
Let A = (aij) be an n × n Toeplitz matrix with bandwidth k + 1, K = r + s, that is, aij = aj−i, i, J = 1,… ,n, ai = 0 if i > s and if i < -r. We compute p(λ)= det(A - λI), as well as p(λ)/p′(λ), where p′(λ) is the first derivative of p(λ), by using O(k log k log n) arithmetic operations. Moreover, if ai are m × m matrices, so that A is a banded Toeplitz block matrix, then we compute p(λ), as well as p(λ)/p′(λ), by using O(m3k(log2 k + log n) + m2k log k log n) arithmetic operations. The algorithms can be extended to the computation of det(A − λB) and of its first derivative, where both A and B are banded Toeplitz matrices. The algorithms may be used as a basis for iterative solution of the eigenvalue problem for the matrix A and of the generalized eigenvalue problem for A and B. 相似文献
7.
We give a new characterization of λ-supercompact cardinal κ in terms of (κ,λ)-Solovay pairs. We give some applications of (κ,λ)-Solovay pairs. 相似文献
8.
N. Mukhopadhyay 《Journal of multivariate analysis》1999,68(2):463
We consider the classical fixed-size confidence region estimation problem for the mean vectorμin theNp(μ, Σ) population where Σ is unknown but positive definite. We writeλ1for the largest characteristic root of Σ and assume thatλ1is simple. Moreover, we suppose that, in many practical applications, we will often have available a numberλ*(>0) and that we can assumeλ1>λ*. Given this addi- tional, and yet very minimal, knowledge regardingλ1, the two-stage procedure of Chatterjee (Calcutta Statist. Assoc. Bull.8(1959a), 121–148;9(1959b), 20–28;11(1962), 144–159) is revised appropriately. The highlight in this paper involves the verification ofsecond-order propertiesassociated with such revised two-stage estimation techniques, along with the maintenance of the nominal confidence coefficient. 相似文献
9.
D. S. Franzblau Doron Zeilberger 《Journal of Algorithms in Cognition, Informatics and Logic》1982,3(4):317-343
A well-known theorem of Frame, Robinson, and, Thrall states that if λ is a partition of n, then the number of Standard Young Tableaux of shape λ is n! divided by the product of the hook-lengths. We give a new combinatorial proof of this formula by exhibiting a bijection between the set of unsorted Young Tableaux of shape λ, and the set of pairs (T, S), where T is a Standard Young Tableau of shape λ and S is a “Pointer” Tableau of shape λ. 相似文献
10.
In this paper we prove three conjectures of Revers on Lagrange interpolation for fλ(t)=|t|λ,λ>0, at equidistant nodes. In particular, we describe the rate of divergence of the Lagrange interpolants LN( fλ,t) for 0<|t|<1, and discuss their convergence at t=0. We also establish an asymptotic relation for max|t|1| |t|λ−LN( fλ,t)|. The proofs are based on strong asymptotics for |t|λ−LN( fλ,t), 0|t|<1. 相似文献
11.
Kh. K. Ishkin 《Mathematical Notes》2005,78(1-2):64-75
We consider the Sturm-Liouville operator on a convex smooth curve lying in the complex plane and connecting the points 0 and 1. We prove that if the eigenvalues λk with large numbers are localized near a single ray, then this ray is the positive real semiaxis. Moreover, if the eigenvalues λk are numbered with algebraic multiplicities taken into account, then λk ∼ π · k as k → +∞.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 72–84.Original Russian Text Copyright © 2005 by Kh. K. Ishkin. 相似文献
12.
We give a strong converse inequality of type B in terms of unified K-functional Kλα( f,t2)(0λ1, 0<α<2) for Baskakov operators. 相似文献
13.
D.E. Littlewood proved two branching theorems for decomposing the restriction of an irreducible finite-dimensional representation of a unitary group to a symmetric subgroup. One is for restriction of a representation of U(n) to the rotation group SO(n) when the given representation τλ of U(n) has nonnegative highest weight λ of depth n/2. It says that the multiplicity in τλ|SO(n) of an irreducible representation of SO(n) of highest weight ν is the sum over μ of the multiplicities of τλ in the U(n) tensor product τμτν, the allowable μ's being all even nonnegative highest weights for U(n). Littlewood's proof is character-theoretic. The present paper gives a geometric interpretation of this theorem involving the tensor products τμτν explicitly. The geometric interpretation has an application to the construction of small infinite-dimensional unitary representations of indefinite orthogonal groups and, for each of these representations, to the determination of its restriction to a maximal compact subgroup. The other Littlewood branching theorem is for restriction from U(2r) to the rank-r quaternion unitary group Sp(r). It concerns nonnegative highest weights for U(2r) of depth r, and its statement is of the same general kind. The present paper finds an analogous geometric interpretation for this theorem also. 相似文献
14.
We present several forcing posets for adding a non-reflecting stationary subset of Pω1(λ), where λ≥ω2. We prove that PFA is consistent with dense non-reflection in Pω1(λ), which means that every stationary subset of Pω1(λ) contains a stationary subset which does not reflect to any set of size 1. If λ is singular with countable cofinality, then dense non-reflection in Pω1(λ) follows from the existence of squares. 相似文献
15.
N. M. Bujurke N. N. Katagi V. B. Awati 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,61(2):836-851
The computer extended perturbation series method is used to analyze the problem of steady viscous flow in slender tubes. The objective is to obtain an expansion in a power series of λ (= ɛ R, ɛ is a small parameter and
R = \fracMLnR = \frac{M}{{L\nu }}
is a streamwise Reynolds number) and look for its analytic continuation. Such an expansion was usually terminated at the second or third order term and consequently they have a very limited utility. Sufficiently large number of terms in the series, representing physical quantities are, generated for the detail analysis which enables to get converging Pade’ sums for large λ. Domb-Sykes plot enables in finding singularity restricting the convergence of the series. Useful results valid up to λ = 15 are obtained for different derived quantities whereas in earlier findings [6], analysis could be done only up to λ = 10 resulting into a substantial improvement in the present study. 相似文献
16.
In this article, we consider the following eigenvalue problems('∗ where λ>0, N2 and is the upper semi-strip domain with a hole in . Under some suitable conditions on f and h, we show that there exists a positive constant λ* such that Eq. (*)λ has at least two solutions if λ(0,λ*), a unique positive solution if λ=λ*, and no positive solution if λ>λ*. We also obtain some further properties of the positive solutions of (*)λ. 相似文献
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17.
Fordyce A. Davidson Bryan P. Rynne 《Journal of Mathematical Analysis and Applications》2004,300(2):491-504
Let TR be a time-scale, with a=infT, b=supT. We consider the nonlinear boundary value problem (2) (4)
u(a)=u(b)=0,