Koki Matsumura

Genetic algorithms using low-discrepancy sequences

The random number generator is one of the important components of evolutionary algorithms (EAs). Therefore, when we try to solve function optimization problems using EAs, we must carefully choose a good pseudo-random number generator. In EAs, the pseudo-random number generator is often used for creating uniformly distributed individuals. As the low-discrepancy sequences allow us to create individuals more uniformly than the random number sequences, we apply the low-discrepancy sequence generator, instead of the pseudo-random number generator, to EAs in this study. The numerical experiments show that the low-discrepancy sequence generator improves the search performances of EAs.

Function approximation approach to the inference of reduced NGnet models of genetic networks

BackgroundThe inference of a genetic network is a problem in which mutual interactions among genes are deduced using time-series of gene expression patterns. While a number of models have been proposed to describe genetic regulatory networks, this study focuses on a set of differential equations since it has the ability to model dynamic behavior of gene expression. When we use a set of differential equations to describe genetic networks, the inference problem can be defined as a function approximation problem. On the basis of this problem definition, we propose in this study a new method to infer reduced NGnet models of genetic networks.ResultsThrough numerical experiments on artificial genetic network inference problems, we demonstrated that our method has the ability to infer genetic networks correctly and it was faster than the other inference methods. We then applied the proposed method to actual expression data of the bacterial SOS DNA repair system, and succeeded in finding several reasonable regulations. When our method inferred the genetic network from the actual data, it required about 4.7 min on a single-CPU personal computer.ConclusionThe proposed method has an ability to obtain reasonable networks with a short computational time. As a high performance computer is not always available at every laboratory, the short computational time of our method is a preferable feature. There does not seem to be a perfect model for the inference of genetic networks yet. Therefore, in order to extract reliable information from the observed gene expression data, we should infer genetic networks using multiple inference methods based on different models. Our approach could be used as one of the promising inference methods.

Inference of S-system models of genetic networks by solving one-dimensional function optimization problems

Voit and Almeida have proposed the decoupling approach as a method for inferring the S-system models of genetic networks. The decoupling approach defines the inference of a genetic network as a problem requiring the solutions of sets of algebraic equations. The computation can be accomplished in a very short time, as the approach estimates S-system parameters without solving any of the differential equations. Yet the defined algebraic equations are non-linear, which sometimes prevents us from finding reasonable S-system parameters. In this study, we propose a new technique to overcome this drawback of the decoupling approach. This technique transforms the problem of solving each set of algebraic equations into a one-dimensional function optimization problem. The computation can still be accomplished in a relatively short time, as the problem is transformed by solving a linear programming problem. We confirm the effectiveness of the proposed approach through numerical experiments.

Effective parameter estimation for S-system models using LPMs and evolutionary algorithms

An S-system model is considered as an ideal model for describing genetic networks. As one of effective techniques for inferring S-system models of genetic networks, the problem decomposition strategy has been proposed. This strategy defines the inference of a genetic network consisting of N genes as N subproblems, each of which is a 2(N+1)-dimensional function optimization problem. When we try to infer large-scale genetic networks consisting of many genes, however, it is not always easy for function optimization algorithms to solve 2(N + 1)-dimensional problems. In this study, we thus propose a new technique that transforms the 2(N + 1)-dimensional S-system parameter estimation problems into (N+2)-dimensional problems. The proposed technique reduces the search dimensions of the problems by solving linear programming problems. The transformed problems are then optimized using evolutionary algorithms. Finally, through numerical experiments on an artificial genetic network inference problem, we show that the proposed dimension reduction approach is more than 3 times faster than the problem decomposition approach.

Function Approximation Approach to the Inference of Normalized Gaussian Network Models of Genetic Networks

A model based on a set of differential equations can effectively capture various dynamics. This type of model is, therefore, ideal for describing genetic networks. The genetic network inference problem based on a set of differential equations is generally defined as a parameter estimation problem. On the basis of this problem definition, several computational methods have been proposed so far. On the other hand, the genetic network inference problem based on a set of differential equations can be also defined as a function approximation problem. For solving the defined function approximation problem, any type of function approximator is available. In this study, on the basis of the latter problem definition, we propose a new method for the inference of genetic networks using a normalized Gaussian network model. As the EM algorithm is available for the learning of the NGnet model, the computational time of the proposed method is much shorter than those of other inference methods. The effectiveness of the proposed inference method is verified through numerical experiments of several artificial genetic network inference problems.

Constrained multimodal function optimization using a simple evolutionary algorithm

Practical function optimization problems often contain several constraints. Although evolutionary algorithms (EAs) have been successfully applied to unconstrained real-parameter optimization problems, it is sometimes difficult for these methods even to find feasible solutions in constrained ones. In this study, we thus propose a technique that makes EAs possible to solve function optimization problems with several inequality and a single equality constraints. The proposed technique simply forces individuals newly generated to satisfy the equality constraint. In order to generate these individuals, this study utilizes a Markov chain Monte Carlo (MCMC) method and crossover kernels. While the proposed technique can be applied to any EA, this study applies it to a relatively simple one, UNDX/MGG. Experimental results show that UNDX/MGG with the proposed technique has an ability to solve unimodal and multimodal function optimization problems with constraints. Finally, we show that, although our approach cannot solve function optimization problems with multiple equality constraints, we can convert some of them into those with a single equality constraint.

Inference of Genetic Networks using a Reduced NGnet Model

The inference of genetic networks using a model based on a set of differential equations is generally time-consuming. In order to decrease its computational time, we have proposed the inference method using a normalized Gaussian network (NGnet) model. The inferred models however contain many false-positive regulations when we apply the NGnet approach to the genetic network inference problems. This paper proposes the reduced NGnet model and the gradual reduction strategy to overcome the drawbacks of the NGnet approach. Then, in order to verify their effectiveness, we apply the inference method using the proposed techniques to several artificial genetic network inference problems.

Inference of genetic networks using neural network models

We propose a new method for the inference of the genetic networks. The proposed method uses a neural network model to describe the genetic network. The inference of the neural network model of the genetic network is defined as the function optimization problem. As the function optimizer for this problem, a genetic local search is used. At this time, to enhance the probability of finding a reasonable solution, we introduce a priori knowledge about the genetic network into the objective function. In this paper, we also propose the method based on the sensitivity analysis to interpret the optimized neural network model. Through artificial genetic network inference problems, we verify the effectiveness of the proposed method.

Density estimation using crossover kernels and its application to a real-coded genetic algorithm

Sakuma and Kobayashi have proposed a density estimation method that utilizes real-coded crossover operators. However, their method was used only to estimate normal distribution functions. In order to estimate more complicated PDFs, this study proposes a new density estimation method of utilizing crossover operators. When we try to solve function optimization problems, on the other hand, real-coded genetic algorithms (GAs) show good performances if their crossover operators have an ability to estimate the PDF of the population well. Thus, this study then applies our density estimation method into a simple real-coded GA to improve its search performance. Finally, through numerical experiments, we verify the effectiveness of the proposed density estimation method.

Inference of S-system models of genetic networks by solving linear programming problems and sets of linear algebraic equations

For the inference of S-system models of genetic networks, this study proposes a new method, i.e., a two-phase estimation method. The two-phase estimation method is an extension of the decoupling approach proposed by Voit and Almeida. The decoupling approach defines the estimation of S-system parameters as a problem of solving sets of non-linear algebraic equations. Our method first transforms each set of non-linear algebraic equations, that is defined by the decoupling approach, into a set of linear ones. The transformation of the equations is easily accomplished by solving a linear programming problem. The proposed method then estimates S-system parameters by solving the transformed linear equations. As the proposed two-phase estimation method infers an S-system model only by solving linear programming problems and sets of linear algebraic equations, it always provides us with a unique solution. Moreover, its computational cost is very low. Finally, we confirm the effectiveness of the proposed method through numerical experiments.