On the limitations of classical benchmark functions for evaluating robustness of evolutionary algorithms

Although evolutionary algorithms (EAs) have some operators which let them explore the whole search domain, still they get trapped in local minima when multimodality of the objective function is increased. To improve the performance of EAs, many optimization techniques or operators have been introduced in recent years. However, it seems that these modified versions exploit some special properties of the classical multimodal benchmark functions, some of which have been noted in previous research and solutions to eliminate them have been proposed.In this article, we show that quite symmetric behavior of the available multimodal test functions is another example of these special properties which can be exploited by some EAs such as covariance matrix adaptation evolution strategy (CMA-ES). This method, based on its invariance properties and good optimization results for available unimodal and multimodal benchmark functions, is considered as a robust and efficient method. However, as far as black box optimization problems are considered, no special trend in the behavior of the objective function can be assumed; consequently this symmetry limits the generalization of optimization results from available multimodal benchmark functions to real world problems. To improve the performance of CMA-ES, the Elite search sub-algorithm is introduced and implemented in the basic algorithm. Importance and effect of this modification is illustrated experimentally by dissolving some test problems in the end.     

On the convergence of multiobjective evolutionary algorithms

We consider the usage of evolutionary algorithms for multiobjective programming (MOP), i.e. for decision problems with alternatives taken from a real-valued vector space and evaluated according to a vector-valued objective function. Selection mechanisms, possibilities of temporary fitness deterioration, and problems of unreachable alternatives for such multiobjective evolutionary algorithms (MOEAs) are studied. Theoretical properties of MOEAs such as stochastic convergence with probability 1 are analyzed.     

On the cut‐off phenomenon for the transitivity of randomly generated subgroups

Consider K ≥ 2 independent copies of the random walk on the symmetric group S_N starting from the identity and generated by the products of either independent uniform transpositions or independent uniform neighbor transpositions. At any time $nin mathbb{N}$, let G_n be the subgroup of S_N generated by the K positions of the chains. In the uniform transposition model, we prove that there is a cut‐off phenomenon at time N ln(N)/(2K) for the non‐existence of fixed point of G_n and for the transitivity of G_n, thus showing that these properties occur before the chains have reached equilibrium. In the uniform neighbor transposition model, a transition for the non‐existence of a fixed point of G_n appears at time of order $N^{1+frac{2}{K}}$ (at least for K ≥ 3), but there is no cut‐off phenomenon. In the latter model, we recover a cut‐off phenomenon for the non‐existence of a fixed point at a time proportional to N by allowing the number K to be proportional to ln(N). The main tools of the proofs are spectral analysis and coupling techniques. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2012     

On the performance of peeling algorithms

The peeling of a d-dimensional set of points is usually performed with successive calls to a convex hull algorithm; the optimal worst-case convex hull algorithm, known to have an O(n^˙ Log (n)) execution time, may give an O(n^˙n^˙ Log (n)) to peel all the set; an O(n^˙n) convex hull algorithm, m being the number of extremal points, is shown to peel every set with an O(n-n) time, and proved to be optimal; an implementation of this algorithm is given for planar sets and spatial sets, but the latter give only an approximate O(n^˙n) performance.     

On the Weyl-Heisenberg frames generated by simple functions

Let with , and let (?,a,1), 0<a?1 be a Weyl-Heisenberg system {e2πimx?(x−na):m,n∈Z}. We show that if E=[0,1] (and some modulo extension of E), then (?,a,1) is a frame for each 0<a?1 (for certain a, respectively) if and only if the analytic function has no zero on the unit circle {z:|z|=1}. These results extend the case of Casazza and Kalton (2002) [6] that and a=1, which brought together the frame theory and the function theory on the closed unit disk. Our techniques of proofs are based on the Zak transform and the distribution of fractional parts of {na}_n∈Z.     

A randomly generated program for automatic identity checking

A method for making secret programs for automatic identity checking with very high demands for security, is described. The consistency of the sequence of digits, which identifies the person, is tested by a sequence of transformations, chosen by means of a stored secret random table. The method has been implemented for a system of unattended cash dispenser terminals, equipped with microprocessors.     

Averaging of randomly perturbed evolutionary equations

Evolutionary equations with coefficients perturbed by diffusion processes are considered. It is proved that the solutions of these equations converge weakly in distribution, as a small parameter tends to zero, to a unique solution of a martingale problem that corresponds to an evolutionary stochastic equation in the case where the powers of a small parameter are inconsistent.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 7, pp. 963–971, July, 1993.     

On the eigenvalue problem for toeplitz matrices generated by rational functions

Formulas are given for the characteristic polynomials {p_n (λ)}and the eigenvectors of the family {T_n }of Toeplitz matrices generated by a formal Laurent series of rational function R(z). The formulas are in terms of the zeros of a certain fixed polynomial with coefficients which are simple functions of λ and the coefficients of R(z). The complexity of the formulas is independent ofn.     

On the relationship of goal programming and utility functions

Summary We solve the problem under which circumstances the set of solutions of a goal program may also be considered as the set of points maximizing a continuous, concave, isotonic utility function. The converse question is also answered, and there are given conditions ensuring the efficiency of the optimal points of a goal program.

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Zusammenfassung Es werden Bedingungen für die Effizienz der Lösungen eines goal program entwickelt, ferner wird gezeigt, wann die Lösungsmenge eines goal program ebenfalls durch Maximierung konkaver, stetiger, isotoner Nutzenfunktionen zu erhalten ist. Schließlich wird die umgekehrte Frage beantwortet, unter welchen Bedingungen an eine Nutzenfunktion die zugehörige Lösungsmenge auch durch ein goal program, das mit einer normerzeugten Metrik arbeitet, induziert wird.

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This research has been supported by the Deutsche Forschungsgemeinschaft, project number 88/3.     

On the autocorrelation functions of wind generated ocean waves

Zusammenfassung Die statistische Beschreibung der Schwingungsweiten von winderzeugten Ozeanwellen mittels stationärer Gaußscher Prozesse ist ein Gegenstand moderner Forschung. Beträchtliche Anstrengungen sind gemacht worden, um das Energieverteilungsspektrum als eine Funktion der Schwingungszahl darzustellen, wobei mehrere Ausdrücke dafür vorgeschlagen worden sind. Es sind jedoch viel weniger Bemühungen gemacht worden, um die Auto-Korrelationsfunktion des Vorgangs abzuleiten. Da die üblichen Residuen-Methoden nicht geeignet sind, müssen besondere Verfahren angewandt werden, um diese Funktionen zu erhalten. Die Absicht dieses Artikels ist es über diese Verfahren zu berichten und die Auto-Korrelationsfunktion mittels Fourier-Kosinus-Transformationen des Neumann- und Pierson-Moskowitz-Spektrums abzuleiten.     

Sensitivity analysis incorporating fuzzy evaluation for scaling constants of multiattribute utility functions

A multiattribute utility function can be represented by a function of single-attribute utility functions if the decision maker’s preference satisfies additive independence or mutually utility independence. Additive independence is a preference condition stronger than mutually utility independence, and the multiattribute utility function is in the additive form if the former condition is satisfied, otherwise it is in the multiplicative form. In this paper, we propose a method for sensitivity analysis of multiattribute utility functions in multiplicative form, taking into account the imprecision of the decision maker’s judgment in the procedures for determining scaling constants (attribute weights).     

Autonomous operator management for evolutionary algorithms

The performance of an evolutionary algorithm strongly depends on the design of its operators and on the management of these operators along the search; that is, on the ability of the algorithm to balance exploration and exploitation of the search space. Recent approaches automate the tuning and control of the parameters that govern this balance. We propose a new technique to dynamically control the behavior of operators in an EA and to manage a large set of potential operators. The best operators are rewarded by applying them more often. Tests of this technique on instances of 3-SAT return results that are competitive with an algorithm tailored to the problem.     

Stability of evolutionary algorithms

We prove under mild conditions the convergence of some evolutionary algorithm to the solution of the global optimization problem. In the proof, the Lyapunov function's techniques is applied to some semi-dynamical system generated by a Foias operator on the space of the probability measures defined on the set of admissible solutions.     

On algebras generated by convolutions and discontinuous functions

Banach algebras generated by Fourier and Mellin convolution operators with discontinuous presymbols and by discontinuous functions in L_p (IR⁺, x) spaces with weight are investigated. The Fredholm properties are characterized by a symbol calculus and an index formula for such operators is presented. These results were obtained by H. O. Cordes in [3] for the case p=2, =0 and presymbols, which are discontinuous only at infinity and generalized in [20] for 1相似文献