Self-adaptive Algorithms Research Articles

Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets

Consider the variational inequalityVI(C,F)of finding a pointx*∈Csatisfying the property〈Fx*,x-x*〉≥0, for allx∈C, whereCis the intersection of finite level sets of convex functions defined on a real Hilbert spaceHandF:H→His anL-Lipschitzian andη-strongly monotone operator. Relaxed and self-adaptive iterative algorithms are devised for computing the unique solution ofVI(C,F). Since our algorithm avoids calculating the projectionPC(calculatingPCby computing several sequences of projections onto half-spaces containing the original domainC) directly and has no need to know any information of the constantsLandη, the implementation of our algorithm is very easy. To prove strong convergence of our algorithms, a new lemma is established, which can be used as a fundamental tool for solving some nonlinear problems.

Extrema Propagation: Fast Distributed Estimation of Sums and Network Sizes

Aggregation of data values plays an important role on distributed computations, in particular, over peer-to-peer and sensor networks, as it can provide a summary of some global system property and direct the actions of self-adaptive distributed algorithms. Examples include using estimates of the network size to dimension distributed hash tables or estimates of the average system load to direct load balancing. Distributed aggregation using nonidempotent functions, like sums, is not trivial as it is not easy to prevent a given value from being accounted for multiple times; this is especially the case if no centralized algorithms or global identifiers can be used. This paper introduces Extrema Propagation, a probabilistic technique for distributed estimation of the sum of positive real numbers. The technique relies on the exchange of duplicate insensitive messages and can be applied in flood and/or epidemic settings, where multipath routing occurs; it is tolerant of message loss; it is fast, as the number of message exchange steps can be made just slightly above the theoretical minimum; and it is fully distributed, with no single point of failure and the result produced at every node.

Splitting extrapolation algorithms for solving the boundary integral equations of anisotropic Darcy’s equation on polygons by mechanical quadrature methods

In this paper we study the stability and convergence of the solution for the first kind integral equations of the anisotropic Darcy's equations by the mechanical quadrature methods on closed polygonal boundaries in ?2. Using the collectively compact theory, we construct numerical solutions which converge with the order $O\;(h^{3}_{\text{max}})$ , where $h_{\text{max}}$ is the mesh size. In addition, An a posteriori asymptotic error representation is derived by splitting extrapolation methods in order to construct self-adaptive algorithms, and the convergence rate $O\;(h^{5}_{\text{max}})$ can be achieved after using the splitting extrapolation methods once. Finally, the numerical examples show the efficiency of our methods.

A self-adaptive differential evolution algorithm based on ant system with application to estimate kinetic parameters

A self-adaptive differential evolution (DE) algorithm, in which an ant system is used to implement the self-adaptation of mutation and crossover control parameters, called ant system self-adaptive differential evolution (ASSDE), is proposed. First, the spaces of the mutation and crossover control parameters are divided into several regions and all regions are given the same initial intensity of pheromone trails. The probability of selecting parameter regions for each individual is influenced by the intensity of the region pheromone trails and its visibility. An individual will reinforce the trail of the selected regions with its own pheromone, when the offspring is better than its parent. The experiment results show that the ASSDE clearly outperforms the original DE algorithm and other existing self-adaptive DE algorithms for 16 benchmark functions. Furthermore, ASSDE is applied to develop the global kinetic model for hydropurification of terephthalic acid (HPTA), and satisfactory results are obtained.

Selection of Heterogeneous Fuzzy Model Ensembles Using Self-adaptive Genetic Algorithms

The problem of model selection to compose a heterogeneous bagging ensemble was addressed in the paper. To solve the problem, three self-adapting genetic algorithms were proposed with different control parameters of mutation, crossover, and selection adjusted during the execution. The algorithms were applied to create heterogeneous ensembles comprising regression fuzzy models to aid in real estate appraisals. The results of experiments revealed that the self-adaptive algorithms converged faster than the classic genetic algorithms. The heterogeneous ensembles created by self-adapting methods showed a very good predictive accuracy when compared with the homogeneous ensembles obtained in earlier research.

Splitting extrapolation algorithms for solving the boundary integral equations of Steklov problems on polygons by mechanical quadrature methods

By the potential theory, Steklov eigenvalue problems are converted into boundary integral equations (BIEs). The singularities at corners and in the integral kernels are studied in this paper. Mechanical quadrature methods (MQMs) are presented to obtain approximations with a high accuracy order O ( h 3 ) . Moreover, the mechanical quadrature methods are simple without any singularly integral computation. Since the asymptotic expansions of the errors with the power O ( h 3 ) are shown, the high accuracy order O ( h 5 ) can be achieved for the solutions by using the splitting extrapolation algorithms (SEAs). A posteriori error estimate can also be obtained for self-adaptive algorithms. The efficiency of the algorithms is illustrated by examples.

Application Research of Classical and Advanced Filtering Techniques in Condition Monitoring and Fault Diagnosis

Filtering techniques have been successfully used in the field of condition monitoring and fault diagnosis. By the use of signal filtering, the impending system fault can be revealed effectively to prevent the system from malfunction. This paper discusses recent progress of classical and advanced filters for the condition monitoring and fault diagnosis. Excellent work is introduced from the aspects of the Wiener filtering algorithms, the Kalman filtering algorithms and the novel self-adaptive filtering algorithms. An overview of some promising algorithms for enhancement of filtering performance is presented. The review result suggests that the intelligent information fusion based fault diagnosis expert system with self-learning and self-updating abilities is the future research trend for the condition monitoring fault diagnosis based on filtering theory.

High accuracy eigensolution and its extrapolation for potential equations

From the potential theorem, the fundamental boundary eigenproblems can be converted into boundary integral equations (BIEs) with the logarithmic singularity. In this paper, mechanical quadrature methods (MQMs) are presented to obtain the eigensolutions that are used to solve Laplace’s equations. The MQMs possess high accuracy and low computation complexity. The convergence and the stability are proved based on Anselone’s collective and asymptotical compact theory. An asymptotic expansion with odd powers of the errors is presented. By the h 3-Richardson extrapolation algorithm (EA), the accuracy order of the approximation can be greatly improved, and an a posteriori error estimate can be obtained as the self-adaptive algorithms. The efficiency of the algorithm is illustrated by examples.

Design of optimum gain pyramidal horn using self-adaptive differential evolution algorithms

In this work, we apply classical and new self-adaptive differential evolution (DE) algorithms to the design of optimum gain pyramidal horns. The application of DE algorithms to pyramidal horn design allows the accurate calculation of their physical dimensions in a short amount of time. Moreover, self-adaptive DE does not require the prespecified choice of control parameters reducing significantly the users' effort. Representative examples demonstrate the applicability of our proposal. Our study shows that self-adaptive DE algorithms outperform or produce similar results with other methods in the literature in terms of solution accuracy and convergence speed. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011. © 2011 Wiley Periodicals, Inc.

On cost-aware monitoring for self-adaptive load sharing

Monitoring is an essential part of any self-adaptive management loop. While providing the necessary information for making management decisions, monitoring itself incurs a cost in terms of the system and network resources committed to this management task. Thus, one can pose a generic question: what is the right amount of monitoring that maximizes its utility for management? This question turns out to be difficult to answer in general. In this paper we focus on quantifying the utility of monitoring for self-adaptive load sharing, where a stream of jobs arrives at a collection of n identical servers. We propose a novel model, that we dubbed an Extended Supermarket Model (ESM) to study the tradeoff between the usefulness of the monitoring information and the cost of obtaining it. We show that for each service request rate, there exists an optimal number of servers that should be monitored to obtain minimal average service time at an optimal cost. Using these findings, we present self-adaptive load-sharing algorithms both for centralized and fully distributed settings and evaluate these algorithms using simulations and a real testbed. Our results show that in realistic scenarios, where monitoring cost is not negligible, the self-adaptive load balancing is clearly superior to any cost-oblivious load-sharing mechanisms. We also demonstrate that in a fully distributed setting, where no dedicated monitoring component is employed, our self-adaptive heuristics perform very well with respect to the current common practice.

Extrapolation Algorithms for Solving Mixed Boundary Integral Equations of the Helmholtz Equation by Mechanical Quadrature Methods

This paper presents mechanical quadrature methods with high accuracy for solving mixed boundary integral equations of the Helmholtz equation. By estimating the range of eigenvalues for the discretization matrix of the integral equations and applying the collectively compact convergent theory, we prove the stability and convergence of numerical solutions, which is a challenging task for this method. Moreover, the asymptotic error expansions show the method is of order $h^3$. Hence, extrapolation algorithms can be introduced to achieve higher approximation accuracy degree $(\mathcal{O}(h^5))$. Meanwhile, an a posteriori asymptotic error estimate is derived, which can be used to construct self-adaptive algorithms. The numerical examples support our theoretical analysis.

A novel adaptive differential evolution algorithm with application to estimate kinetic parameters of oxidation in supercritical water

A new version of differential evolution (DE) algorithm containing the adaptive mutation and crossover operators, named adaptive differential evolution (ADE), is proposed. In ADE, the control parameters of ADE are generated for each individual and the value of the parameters are based on individual's current generation number and parent's fitness value. With population evolution, the ADE algorithm gradually changes from being exploratory at the early stages to being exploitationary at the later stages. At the same time, in certain generations, low fitness individuals or high fitness individuals are assigned with small parameters to accelerate the convergence of these individuals. The experiments conducted show that the ADE generally outperforms the original DE algorithm and other existing self-adaptive DE algorithms for 11 benchmark functions. Furthermore, ADE is applied to develop the global kinetic model of the 2-chlorophenol oxidation in supercritical water, and satisfactory results are obtained.

Mechanical quadrature methods and their splitting extrapolations for boundary integral equations of first kind on open arcs

This paper presents the mechanical quadrature methods (MQMs) for solving boundary integral equations (BIEs) of the first kind on open arcs. The spectral condition number of MQMs is only O ( h − 1 ) , where h is the maximal mesh width. The errors of MQMs have multivariate asymptotic expansions, accompanied with O ( h i 3 ) for all mesh widths h i . Hence, once discrete equations with coarse meshes are solved in parallel, the accuracy order of numerical approximations can be greatly improved by splitting extrapolation algorithms (SEAs). Moreover, a posteriori asymptotic error estimates are derived, which can be used to formulate self-adaptive algorithms. Numerical examples are also provided to support our algorithms and analysis. Furthermore, compared with the existing algorithms, such as Galerkin and collocation methods, the accuracy order of the MQMs is higher, and the discrete matrix entries are explicit, to prove that the MQMs in this paper are more promising and beneficial to practical applications.

An Immune Self-adaptive Differential Evolution Algorithm with Application to Estimate Kinetic Parameters for Homogeneous Mercury Oxidation

A new version of differential evolution (DE) algorithm, in which immune concepts and methods are applied to determine the parameter setting, named immune self-adaptive differential evolution (ISDE), is proposed to improve the performance of the DE algorithm. During the actual operation, ISDE seeks the optimal parameters arising from the evolutionary process, which enable ISDE to alter the algorithm for different optimization problems and improve the performance of ISDE by the control parameters' self-adaptation. The performance of the proposed method is studied with the use of nine benchmark problems and compared with original DE algorithm and other well-known self-adaptive DE algorithms. The experiments conducted show that the ISDE clearly outperforms the other DE algorithms in all benchmark functions. Furthermore, ISDE is applied to develop the kinetic model for homogeneous mercury (Hg) oxidation in flue gas, and satisfactory results are obtained.

Applying self-adaptive evolutionary algorithms to two-dimensional packing problems using a four corners’ heuristic

This paper proposes a four corners’ heuristic for application in evolutionary algorithms (EAs) applied to two-dimensional packing problems. The four corners’ (FC) heuristic is specifically designed to increase the search efficiency of EAs. Experiments with the FC heuristic are conducted on 31 problems from the literature both with rotations permitted and without rotations permitted, using two different EA algorithms: a self-adaptive parallel recombinative simulated annealing (PRSA) algorithm, and a self-adaptive genetic algorithm (GA). Results on bin packing problems yield the smallest trim losses we have seen in the published literature; with the FC heuristic, zero trim loss was achieved on problems of up to 97 rectangles. A comparison of the self-adaptive GA to fixed-parameter GAs is presented and the benefits of self-adaption are highlighted.

Metabolic Flux Estimation-A Self-Adaptive Evolutionary Algorithm with Singular Value Decomposition

Metabolic flux analysis is important for metabolic system regulation and intracellular pathway identification. A popular approach for intracellular flux estimation involves using 13C tracer experiments to label states that can be measured by nuclear magnetic resonance spectrometry or gas chromatography mass spectrometry. However, the bilinear balance equations derived from 13C tracer experiments and the noisy measurements require a nonlinear optimization approach to obtain the optimal solution. In this paper, the flux quantification problem is formulated as an error-minimization problem with equality and inequality constraints through the 13C balance and stoichiometric equations. The stoichiometric constraints are transformed to a null space by singular value decomposition. Self-adaptive evolutionary algorithms are then introduced for flux quantification. The performance of the evolutionary algorithm is compared with ordinary least squares estimation by the simulation of the central pentose phosphate pathway. The proposed algorithm is also applied to the central metabolism of Corynebacterium glutamicum under lysine-producing conditions. A comparison between the results from the proposed algorithm and data from the literature is given. The complexity of a metabolic system with bidirectional reactions is also investigated by analyzing the fluctuations in the flux estimates when available measurements are varied.

Performance comparison of self-adaptive and adaptive differential evolution algorithms

Differential evolution (DE) has been shown to be a simple, yet powerful, evolutionary algorithm for global optimization for many real problems. Adaptation, especially self-adaptation, has been found to be highly beneficial for adjusting control parameters, especially when done without any user interaction. This paper presents differential evolution algorithms, which use different adaptive or self-adaptive mechanisms applied to the control parameters. Detailed performance comparisons of these algorithms on the benchmark functions are outlined.

A simple and robust adaptive parasitic antenna

A novel Uda-Yagi adaptive antenna is numerically and experimentally investigated. The antenna consists of an active element and a relatively large number of parasitic elements closed on two different loads selectable by simple electronic switches. The use of fuzzy-logic based cost function and self-adaptive biological beamforming algorithms allows to obtain quite good performances both in terms of signal to interference plus noise ratio and voltage standing wave ratio. The antenna is simple, low cost, and is robust with respect to mechanical and electrical tolerances and with respect to failures of some passive elements. Experimental results on two different prototypes confirm the good performances of the proposed antenna.

Mobile Agents Based Self-Adaptive Join for Wide-Area Distributed Query Processing

In this article, optimization of decision support queries is considered in the context of wide-area distributed databases. An original approach based on the “mobile agent” paradigm is proposed and evaluated. Agents’ autonomy and reactivity allow operators of the execution plan to adapt dynamically to estimation errors on relations and to evolutions in the state of the execution system, avoiding time overheads commonly associated with centralized monitoring. We present decentralized self-adaptive algorithms for dynamic optimization of join operators, and their implementations in Java using mobile agents. Then, we evaluate performance depending on error rate on statistical information on database, and on communication bandwidth and CPU frequency. The results show that the agent-based approach can lead to a significant reduction of response time and provide decision criteria for developing an effective migration policy.

Self-adaptive projection algorithms for general variational inequalities

In this paper, we consider and analyze a new class of self-adaptive projection algorithms for solving general variational inequalities by using the technique of updating the solution. We prove that the convergence of these new methods only requires the pseudomonotonicity, which is a weaker condition than monotonicity. These new methods differ from the previously known splitting methods for solving variational inequalities and related complementarity problems. Proof of convergence is very simple. As special cases, we can obtain a number of four-step forward–backward splitting methods of Noor for solving variational inequalities.