Landscape state machines: Tools for evolutionary algorithm performance analyses and landscape/algorithm mapping

Many evolutionary algorithm applications involve either fitness functions with high time complexity or large dimensionality (hence very many fitness evaluations will typically be needed) or both. In such circumstances, there is a dire need to tune various features of the algorithm well so that performance and time savings are optimized. However, these are precisely the circumstances in which prior tuning is very costly in time and resources. There is hence a need for methods which enable fast prior tuning in such cases. We describe a candidate technique for this purpose, in which we model a landscape as a finite state machine, inferred from preliminary sampling runs. In prior algorithm-tuning trials, we can replace the 'real' landscape with the model, enabling extremely fast tuning, saving far more time than was required to infer the model. Preliminary results indicate much promise, though much work needs to be done to establish various aspects of the conditions under which it can be most beneficially used. A main limitation of the method as described here is a restriction to mutation-only algorithms, but there are various ways to address this and other limitations.

Error analysis of a Monte Carlo algorithm for computing bilinear forms of matrix powers

In this paper we present error analysis for a Monte Carlo algorithm for evaluating bilinear forms of matrix powers. An almost Optimal Monte Carlo (MAO) algorithm for solving this problem is formulated. Results for the structure of the probability error are presented and the construction of robust and interpolation Monte Carlo algorithms are discussed. Results are presented comparing the performance of the Monte Carlo algorithm with that of a corresponding deterministic algorithm. The two algorithms are tested on a well balanced matrix and then the effects of perturbing this matrix, by small and large amounts, is studied.

Wiener-System subspace identification for mobile wireless mm-wave networks

We discuss the feasibility of wireless terahertz communications links deployed in a metropolitan area and model the large-scale fading of such channels. The model takes into account reception through direct line of sight, ground and wall reflection, as well as diffraction around a corner. The movement of the receiver is modeled by an autonomous dynamic linear system in state space, whereas the geometric relations involved in the attenuation and multipath propagation of the electric field are described by a static nonlinear mapping. A subspace algorithm in conjunction with polynomial regression is used to identify a single-output Wiener model from time-domain measurements of the field intensity when the receiver motion is simulated using a constant angular speed and an exponentially decaying radius. The identification procedure is validated by using the model to perform q-step ahead predictions. The sensitivity of the algorithm to small-scale fading, detector noise, and atmospheric changes are discussed. The performance of the algorithm is tested in the diffraction zone assuming a range of emitter frequencies (2, 38, 60, 100, 140, and 400 GHz). Extensions of the simulation results to situations where a more complicated trajectory describes the motion of the receiver are also implemented, providing information on the performance of the algorithm under a worst case scenario. Finally, a sensitivity analysis to model parameters for the identified Wiener system is proposed.

MIMO Wiener model identification for large scale fading of wireless mobile communications links

The large scale fading of wireless mobile communications links is modelled assuming the mobile receiver motion is described by a dynamic linear system in state-space. The geometric relations involved in the attenuation and multi-path propagation of the electric field are described by a static non-linear mapping. A Wiener system subspace identification algorithm in conjunction with polynomial regression is used to identify a model from time-domain estimates of the field intensity assuming a multitude of emitters and an antenna array at the receiver end.

A fast linear-in-the-parameters classifier construction algorithm using orthogonal forward selection to minimize leave-one-out misclassification rate

We propose a simple and computationally efficient construction algorithm for two class linear-in-the-parameters classifiers. In order to optimize model generalization, a forward orthogonal selection (OFS) procedure is used for minimizing the leave-one-out (LOO) misclassification rate directly. An analytic formula and a set of forward recursive updating formula of the LOO misclassification rate are developed and applied in the proposed algorithm. Numerical examples are used to demonstrate that the proposed algorithm is an excellent alternative approach to construct sparse two class classifiers in terms of performance and computational efficiency.

Backward elimination model construction for regression and classification using leave-one-out criteria

A fundamental principle in practical nonlinear data modeling is the parsimonious principle of constructing the minimal model that explains the training data well. Leave-one-out (LOO) cross validation is often used to estimate generalization errors by choosing amongst different network architectures (M. Stone, "Cross validatory choice and assessment of statistical predictions", J. R. Stast. Soc., Ser. B, 36, pp. 117-147, 1974). Based upon the minimization of LOO criteria of either the mean squares of LOO errors or the LOO misclassification rate respectively, we present two backward elimination algorithms as model post-processing procedures for regression and classification problems. The proposed backward elimination procedures exploit an orthogonalization procedure to enable the orthogonality between the subspace as spanned by the pruned model and the deleted regressor. Subsequently, it is shown that the LOO criteria used in both algorithms can be calculated via some analytic recursive formula, as derived in this contribution, without actually splitting the estimation data set so as to reduce computational expense. Compared to most other model construction methods, the proposed algorithms are advantageous in several aspects; (i) There are no tuning parameters to be optimized through an extra validation data set; (ii) The procedure is fully automatic without an additional stopping criteria; and (iii) The model structure selection is directly based on model generalization performance. The illustrative examples on regression and classification are used to demonstrate that the proposed algorithms are viable post-processing methods to prune a model to gain extra sparsity and improved generalization.

Hammerstein model identification algorithm using Bezier-Bernstein approximation

A new identification algorithm is introduced for the Hammerstein model consisting of a nonlinear static function followed by a linear dynamical model. The nonlinear static function is characterised by using the Bezier-Bernstein approximation. The identification method is based on a hybrid scheme including the applications of the inverse of de Casteljau's algorithm, the least squares algorithm and the Gauss-Newton algorithm subject to constraints. The related work and the extension of the proposed algorithm to multi-input multi-output systems are discussed. Numerical examples including systems with some hard nonlinearities are used to illustrate the efficacy of the proposed approach through comparisons with other approaches.

Synapsing variable length crossover: An algorithm for crossing and comparing variable length genomes

The Synapsing Variable Length Crossover (SVLC) algorithm provides a biologically inspired method for performing meaningful crossover between variable length genomes. In addition to providing a rationale for variable length crossover it also provides a genotypic similarity metric for variable length genomes enabling standard niche formation techniques to be used with variable length genomes. Unlike other variable length crossover techniques which consider genomes to be rigid inflexible arrays and where some or all of the crossover points are randomly selected, the SVLC algorithm considers genomes to be flexible and chooses non-random crossover points based on the common parental sequence similarity. The SVLC Algorithm recurrently "glues" or synapses homogenous genetic sub-sequences together. This is done in such a way that common parental sequences are automatically preserved in the offspring with only the genetic differences being exchanged or removed, independent of the length of such differences. In a variable length test problem the SVLC algorithm is shown to outperform current variable length crossover techniques. The SVLC algorithm is also shown to work in a more realistic robot neural network controller evolution application.

Comparison of the computational cost of a Monte Carlo and deterministic algorithm for computing bilinear forms of matrix powers

In this paper we consider bilinear forms of matrix polynomials and show that these polynomials can be used to construct solutions for the problems of solving systems of linear algebraic equations, matrix inversion and finding extremal eigenvalues. An almost Optimal Monte Carlo (MAO) algorithm for computing bilinear forms of matrix polynomials is presented. Results for the computational costs of a balanced algorithm for computing the bilinear form of a matrix power is presented, i.e., an algorithm for which probability and systematic errors are of the same order, and this is compared with the computational cost for a corresponding deterministic method.

Linear predicted hexagonal search algorithm with moments

A novel Linear Hashtable Method Predicted Hexagonal Search (LHMPHS) method for block based motion compensation is proposed. Fast block matching algorithms use the origin as the initial search center, which often does not track motion very well. To improve the accuracy of the fast BMA's, we employ a predicted starting search point, which reflects the motion trend of the current block. The predicted search centre is found closer to the global minimum. Thus the center-biased BMA's can be used to find the motion vector more efficiently. The performance of the algorithm is evaluated by using standard video sequences, considers the three important metrics: The results show that the proposed algorithm enhances the accuracy of current hexagonal algorithms and is better than Full Search, Logarithmic Search etc.

Linear algorithm and hexagonal search based two-pass algorithm for motion estimation

This paper presents a novel two-pass algorithm constituted by Linear Hashtable Motion Estimation Algorithm (LHMEA) and Hexagonal Search (HEXBS) for block base motion compensation. On the basis of research from previous algorithms, especially an on-the-edge motion estimation algorithm called hexagonal search (HEXBS), we propose the LHMEA and the Two-Pass Algorithm (TPA). We introduced hashtable into video compression. In this paper we employ LHMEA for the first-pass search in all the Macroblocks (MB) in the picture. Motion Vectors (MV) are then generated from the first-pass and are used as predictors for second-pass HEXBS motion estimation, which only searches a small number of MBs. The evaluation of the algorithm considers the three important metrics being time, compression rate and PSNR. The performance of the algorithm is evaluated by using standard video sequences and the results are compared to current algorithms, Experimental results show that the proposed algorithm can offer the same compression rate as the Full Search. LHMEA with TPA has significant improvement on HEXBS and shows a direction for improving other fast motion estimation algorithms, for example Diamond Search.

A comparison-based diagnosis algorithm tailored for crossed cube multiprocessor systems

Comparison-based diagnosis is an effective approach to system-level fault diagnosis. Under the Maeng-Malek comparison model (NM* model), Sengupta and Dahbura proposed an O(N-5) diagnosis algorithm for general diagnosable systems with N nodes. Thanks to lower diameter and better graph embedding capability as compared with a hypercube of the same size, the crossed cube has been a promising candidate for interconnection networks. In this paper, we propose a fault diagnosis algorithm tailored for crossed cube connected multicomputer systems under the MM* model. By introducing appropriate data structures, this algorithm runs in O(Nlog(2)(2) N) time, which is linear in the size of the input. As a result, this algorithm is significantly superior to the Sengupta-Dahbura's algorithm when applied to crossed cube systems. (C) 2004 Elsevier B.V. All rights reserved.

An oblivious shortest-path routing algorithm for fully connected cubic networks

Fully connected cubic networks (FCCNs) are a class of newly proposed hierarchical interconnection networks for multicomputer systems, which enjoy the strengths of constant node degree and good expandability. The shortest path routing in FCCNs is an open problem. In this paper, we present an oblivious routing algorithm for n-level FCCN with N = 8(n) nodes, and prove that this algorithm creates a shortest path from the source to the destination. At the costs of both an O(N)-parallel-step off-line preprocessing phase and a list of size N stored at each node, the proposed algorithm is carried out at each related node in O(n) time. In some cases the proposed algorithm is superior to the one proposed by Chang and Wang in terms of the length of the routing path. This justifies the utility of our routing strategy. (C) 2006 Elsevier Inc. All rights reserved.