An introduction to simulated evolutionary optimization

Accurate estimation of ICA weight matrix by implicit constraint imposition using Lie group

This paper presents a new stochastic algorithm to optimize the independence criterion-mutual information-among multivariate data using local, global, and hybrid optimizers, in conjunction with techniques involving a Lie group and its corresponding Lie algebra, for implicit imposition of the orthonormality constraint among the estimated sources. The major advantage of the proposed algorithm is the increased accuracy with which the weight matrix in the independent component analysis (ICA) model is estimated, compared to conventional schemes. When the local optimizer with Lie group techniques and the fast fixed-point (fastICA) algorithm were experimented by inputting the same set of random vectors, the former method superseded the conventional one by producing accurate weight matrix estimates in a majority of the test cases. Importantly, in our approach, the use of a Lie group to "lock" the weight matrix estimates onto the constraint surface enabled easy realization of the hybrid optimizers to yield near-global-optimum solutions consistently in most of the test cases, compared to well-known global optimizers. The inherent computational overhead in the hybrid optimizers was lowered by preprocessing the input data and periodically integrating the local optimizers with the global one. The proposed algorithms were applied to six-dimensional multispectral satellite image data to emphasize their usefulness in terms of accurate ICA weight matrix estimation.

Trajectory planning of multiple coordinating robots using genetic algorithms

The paper focuses on the problem of trajectory planning of multiple coordinating robots. When multiple robots collaborate to manipulate one object, a redundant system is formed. There are a number of trajectories that the system can follow. These can be described in Cartesian coordinate space by an nth order polynomial. This paper presents an optimisation method based on the Genetic Algorithms (GAs) which chooses the parameters of the polynomial, such that the execution time and the drive torques for the robot joints are minimized. With the robot's dynamic constraints taken into account, the pitimised trajectories are realisable. A case study with two planar-moving robots, each having three degrees of freedom, shows that the method is effective.

GA-BASED ALTERNATIVE APPROACHES FOR THE DEGREE-CONSTRAINED SPANNING TREE PROBLEM

The degree-constrained minimum spanning tree (dc-MST) problem is of high practical importance. Up to now there are few effective algorithms to solve this problem because of its NP-hard complexity. More recently, a genetic algorithm (GA) approach for this problem was tried by using Prüfer number to encode a spanning tree. The Prüfer number is a skillful encoding for tree but not efficient enough to deal with the dc-MST problem. In this paper, a new tree-based encoding is developed directly based on the tree structure. We denote it as tree-based permutation encoding and apply it to the dc-MST problem by using the GA approach. Compared with the numerical results and CPU runtimes between two encodings, the new tree-based permutation is effective to deal with the dc-MST problem and even more efficient than the Prüfer number to evolve to the optimal or near-optimal solutions.

Genetic Network Programming with Rules

Genetic Network Programming (GNP) is an evolutionary approach which can evolve itself and find the optimal solutions. It is based on the idea of Genetic Algorithm and uses the data structure of directed graphs. Many papers have demonstrated that GNP can deal with complex problems in the dynamic environments very efficiently and effectively. As a result, recently, GNP is getting more and more attentions and is being used in many different areas such as data mining, extracting trading rules of stock markets, elevator systems, etc and GNP has obtained some outstanding results. In order to improve GNP's performance further, this paper proposes a new method called GNP with Rules. The aim of the proposed method is to balance exploitation and exploration of GNP, that is, to strengthen exploitation ability by using the exploited information extensively during the evolution process of GNP. The proposed method consists of 4 steps: rule extraction, rule selection, individual reconstruction and individual replacement. These 4 steps are added to the conventional algorithm of GNP. In order to measure the performance of the proposed method, the tileworld was used as the simulation environment. The simulation results show some advantages of GNP with Rules over conventional GNPs.

Using complicated, wide dynamic range driving to develop models of single neurons in single recording sessions

Neuron models are typically built by measuring individually, for each membrane conductance, its parameters (e.g., half-maximal voltages) and maximal conductance value (g(max)). However, neurons have extended morphologies with nonuniform conductance distributions, whereas models generally contain at most a few compartments. Both the original conductance measurements and the models therefore unavoidably contain error due to the electrical filtering of neurons and the differential placement of conductances on them. Model parameters (typically g(max) values) are therefore generally altered by hand or brute force to match model and neuron activity. We propose an alternative method in which complicated, rapidly changing driving input is used to optimize model parameters. This method also ensures that neuron and model dynamics match across a wide dynamic range, a test not performed in most modeling. We tested this concept using leech heartbeat and generic tonically firing models and lobster stomatogastric and generic bursting models as targets and g(max) values as optimized parameters. In all four cases optimization solutions excellently matched target activity. Complicated, wide dynamic range driving thus appears to be an excellent method to characterize neuron properties in detail and to build highly accurate models. In these completely defined targets, the method found each target's 8-13 g(max) values with high accuracy, and may therefore also provide an alternative, functionally based method of defining neuron g(max) values. The method uses only standard experimental and computational techniques, could be easily extended to optimize conductance parameters other than g(max), and should be readily applicable to real neurons.

Application of particle swarm system as a novel parameter optimization technique on spatiotemporal retina model

Center-surround spatiotemporal (ST) filter is a powerful tool to simulate the spatial and temporal properties of retina ganglion cells and encode visual information with electric spikes. This paper introduces the application of particle swarm optimization (PSO) algorithm to tune the parameters in the retina model consisting of a ST filter module and a back-propagation (BP) neural network module. Images are converted into electric spikes by the ST filters whose outputs are then fed into the BP neural network to reconstruct the output images. The parameters of the ST filters determine the electric spike sequences as well as the output image from the BP network. In order to get the expected output images, we employ PSO to iteratively tune the parameters. Euclidean distance between output and input image is used as scalar criteria to optimize the ST filter. The tuning process stops until the similarity between output and input images no longer improves. The results show that 62.3% of the images trained by PSO have better output image quality and less iteration time compared with those trained by the current evolution strategy (ES).

Inference of genetic regulatory networks with recurrent neural network models using particle swarm optimization

Genetic regulatory network inference is critically important for revealing fundamental cellular processes, investigating gene functions, and understanding their relations. The availability of time series gene expression data makes it possible to investigate the gene activities of whole genomes, rather than those of only a pair of genes or among several genes. However, current computational methods do not sufficiently consider the temporal behavior of this type of data and lack the capability to capture the complex nonlinear system dynamics. We propose a recurrent neural network (RNN) and particle swarm optimization (PSO) approach to infer genetic regulatory networks from time series gene expression data. Under this framework, gene interaction is explained through a connection weight matrix. Based on the fact that the measured time points are limited and the assumption that the genetic networks are usually sparsely connected, we present a PSO-based search algorithm to unveil potential genetic network constructions that fit well with the time series data and explore possible gene interactions. Furthermore, PSO is used to train the RNN and determine the network parameters. Our approach has been applied to both synthetic and real data sets. The results demonstrate that the RNN/PSO can provide meaningful insights in understanding the nonlinear dynamics of the gene expression time series and revealing potential regulatory interactions between genes.

Modeling of gene regulatory networks with hybrid differential evolution and particle swarm optimization

In the last decade, recurrent neural networks (RNNs) have attracted more efforts in inferring genetic regulatory networks (GRNs), using time series gene expression data from microarray experiments. This is critically important for revealing fundamental cellular processes, investigating gene functions, and understanding their relations. However, RNNs are well known for training difficulty. Traditional gradient descent-based methods are easily stuck in local minima and the computation of the derivatives is also not always possible. Here, the performance of three evolutionary-swarm computation technology-based methods, known as differential evolution (DE), particle swarm optimization (PSO), and the hybrid of DE and PSO (DEPSO), in training RNNs is investigated. Furthermore, the gene networks are reconstructed via the identification of the gene interactions, which are explained through corresponding connection weight matrices. The experimental results on two data sets studied in this paper demonstrate that the DEPSO algorithm performs better in RNN training. Also, the RNN-based model can provide meaningful insight in capturing the nonlinear dynamics of genetic networks and revealing genetic regulatory interactions.

Genetic Network Programming with Actor-Critic

A new graph-based evolutionary algorithm named “Genetic Network Programming, GNP” has been already proposed. GNP represents its solutions as graph structures, which can improve the expression ability and performance. In addition, GNP with Reinforcement Learning (GNP-RL) was proposed a few years ago. Since GNP-RL can do reinforcement learning during task execution in addition to evolution after task execution, it can search for solutions efficiently. In this paper, GNP with Actor-Critic (GNP-AC) which is a new type of GNP-RL is proposed. Originally, GNP deals with discrete information, but GNP-AC aims to deal with continuous information. The proposed method is applied to the controller of the Khepera simulator and its performance is evaluated.

A graph-based evolutionary algorithm: Genetic Network Programming (GNP) and its extension using reinforcement learning

This paper proposes a graph-based evolutionary algorithm called Genetic Network Programming (GNP). Our goal is to develop GNP, which can deal with dynamic environments efficiently and effectively, based on the distinguished expression ability of the graph (network) structure. The characteristics of GNP are as follows. 1) GNP programs are composed of a number of nodes which execute simple judgment/processing, and these nodes are connected by directed links to each other. 2) The graph structure enables GNP to re-use nodes, thus the structure can be very compact. 3) The node transition of GNP is executed according to its node connections without any terminal nodes, thus the past history of the node transition affects the current node to be used and this characteristic works as an implicit memory function. These structural characteristics are useful for dealing with dynamic environments. Furthermore, we propose an extended algorithm, "GNP with Reinforcement Learning (GNPRL)" which combines evolution and reinforcement learning in order to create effective graph structures and obtain better results in dynamic environments. In this paper, we applied GNP to the problem of determining agents' behavior to evaluate its effectiveness. Tileworld was used as the simulation environment. The results show some advantages for GNP over conventional methods.

Parameter estimation in stochastic mammogram model by heuristic optimization techniques

The appearance of disproportionately large amounts of high-density breast parenchyma in mammograms has been found to be a strong indicator of the risk of developing breast cancer. Hence, the breast density model is popular for risk estimation or for monitoring breast density change in prevention or intervention programs. However, the efficiency of such a stochastic model depends on the accuracy of estimation of the model's parameter set. We propose a new approach-heuristic optimization-to estimate more accurately the model parameter set as compared to the conventional and popular expectation-maximization (EM) algorithm. After initial segmentation of a given mammogram, the finite generalized Gaussian mixture (FGGM) model is constructed by computing the statistics associated with different image regions. The model parameter set thus obtained is estimated by particle swarm optimization (PSO) and evolutionary programming (EP) techniques, where the objective function to be minimized is the relative entropy between the image histogram and the estimated density distributions. When our heuristic approach was applied to different categories of mammograms from the Mini-MIAS database, it yielded lower floor of estimation error in 109 out of 112 cases (97.3 %), and 101 out of 102 cases (99.0%), for the number of image regions being five and eight, respectively, with the added advantage of faster convergence rate, when compared to the EM approach. Besides, the estimated density model preserves the number of regions specified by the information-theoretic criteria in all the test cases, and the assessment of the segmentation results by radiologists is promising.

Improving the efficiency of evolutionary de novo peptide design: strategies for probing configuration and parameter settings

Evolutionary molecular design based on genetic algorithms (GAs) has been demonstrated to be a flexible and efficient optimization approach with potential for locating global optima. Its efficacy and efficiency are largely dependent on the operations and control parameters of the GAs. Accordingly, we have explored new operations and probed good parameter setting through simulations. The findings have been evaluated in a helical peptide design according to "Parameter setting by analogy" strategy; highly helical peptides have been successfully obtained with a population of only 16 peptides and 5 iterative cycles. The results indicate that new operations such as multi-step crossover-mutation are able to improve the explorative efficiency and to reduce the sensitivity to crossover and mutation rates (CR-MR). The efficiency of the peptide design has been furthermore improved by setting the GAs at the good CR-MR setting determined through simulation. These results suggest that probing the operations and parameter settings through simulation in combination with "Parameter setting by analogy" strategy provides an effective framework for improving the efficiency of the approach. Consequently, we conclude that this framework will be useful for contributing to practical peptide design, and gaining a better understanding of evolutionary molecular design.

Genetic Algorithm On Line Controller for the Flexible Inverted Pendulum Problem

This paper presents a real time controller for a highly non-linear system. The Flexible Pole-Cart Balancing Problem (FPCBP) is used as the test case to investigate the learning capability of Genetic Algorithm (GA) in physical application. The controller developed is initially trained using a set of data taken from on line dynamics of the flexible pole cart balancing system. Based from the physical data of the system, the weights W1 to W6 are optimized by the genetic algorithm in order to determine the correct value of the force applied to the cart. The trained GA-based controller then controls the physical Flexible Pole-Cart Balancing system for infinite time. Analysis on the behavior of the GA model developed is presented. Results of the physical experiments show that the controller developed is accurate, adaptive and robust.

Biological engineering applications of feedforward neural networks designed and parameterized by genetic algorithms

Two neural network (NN) applications in the field of biological engineering are developed, designed and parameterized by an evolutionary method based on the evolutionary process of genetic algorithms. The developed systems are a fault detection NN model and a predictive modeling NN system. An indirect or 'weak specification' representation was used for the encoding of NN topologies and training parameters into genes of the genetic algorithm (GA). Some a priori knowledge of the demands in network topology for specific application cases is required by this approach, so that the infinite search space of the problem is limited to some reasonable degree. Both one-hidden-layer and two-hidden-layer network architectures were explored by the GA. Except for the network architecture, each gene of the GA also encoded the type of activation functions in both hidden and output nodes of the NN and the type of minimization algorithm that was used by the backpropagation algorithm for the training of the NN. Both models achieved satisfactory performance, while the GA system proved to be a powerful tool that can successfully replace the problematic trial-and-error approach that is usually used for these tasks.

Survey of clustering algorithms

Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the profusion of options causes confusion. We survey clustering algorithms for data sets appearing in statistics, computer science, and machine learning, and illustrate their applications in some benchmark data sets, the traveling salesman problem, and bioinformatics, a new field attracting intensive efforts. Several tightly related topics, proximity measure, and cluster validation, are also discussed.

Efficient electromagnetic source imaging with adaptive standardized LORETA/FOCUSS

Functional brain imaging and source localization based on the scalp's potential field require a solution to an ill-posed inverse problem with many solutions. This makes it necessary to incorporate a priori knowledge in order to select a particular solution. A computational challenge for some subject-specific head models is that many inverse algorithms require a comprehensive sampling of the candidate source space at the desired resolution. In this study, we present an algorithm that can accurately reconstruct details of localized source activity from a sparse sampling of the candidate source space. Forward computations are minimized through an adaptive procedure that increases source resolution as the spatial extent is reduced. With this algorithm, we were able to compute inverses using only 6% to 11% of the full resolution lead-field, with a localization accuracy that was not significantly different than an exhaustive search through a fully-sampled source space. The technique is, therefore, applicable for use with anatomically-realistic, subject-specific forward models for applications with spatially concentrated source activity.

Monte Carlo modelling of the spectral reflectance of the human eye

The interpretation of in vivo spectral reflectance measurements of the ocular fundus requires an accurate model of radiation transport within the eye. As well as considering the scattering and absorption processes, it is also necessary to account for appropriate histological variation. This variation results in experimentally measured spectra which vary, both with position in the eye, and between individuals. In this paper the results of a Monte Carlo simulation are presented. Three histological variables are considered: the RPE melanin concentration, the choriodal haemoglobin concentration and the choroidal melanin concentration. By considering these three variables, it is possible to generate model spectra which agree well with in vivo experimental measurements of the nasal fundus. The model has implications for the problem of extracting histological parameters from spectral reflectance measurements. These implications are discussed and a novel approach to interpretation of images of the ocular fundus suggested.

A convergence analysis of unconstrained and bound constrained evolutionary pattern search

We present and analyze a class of evolutionary algorithms for unconstrained and bound constrained optimization on R(n): evolutionary pattern search algorithms (EPSAs). EPSAs adaptively modify the step size of the mutation operator in response to the success of previous optimization steps. The design of EPSAs is inspired by recent analyses of pattern search methods. We show that EPSAs can be cast as stochastic pattern search methods, and we use this observation to prove that EPSAs have a probabilistic, weak stationary point convergence theory. This convergence theory is distinguished by the fact that the analysis does not approximate the stochastic process of EPSAs, and hence it exactly characterizes their convergence properties.

Empirical modelling of genetic algorithms

This paper addresses the problem of reliably setting genetic algorithm parameters for consistent labelling problems. Genetic algorithm parameters are notoriously difficult to determine. This paper proposes a robust empirical framework, based on the analysis of factorial experiments. The use of a graeco-latin square permits an initial study of a wide range of parameter settings. This is followed by fully crossed factorial experiments with narrower ranges, which allow detailed analysis by logistic regression. The empirical models derived can be used to determine optimal algorithm parameters and to shed light on interactions between the parameters and their relative importance. Refined models are produced, which are shown to be robust under extrapolation to up to triple the problem size.