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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.

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.

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.

Recently, we proposed a genetic network inference method using linear programming machines (LPMs). As this method infers genetic networks by solving linear programming problems, its computational time is very short. However, generic networks inferred by the method using the LPMs often contain a large number of false-positive regulations. When we try to apply the inference method to actual problems, we must experimentally validate the inferred regulations. Therefore, it is important to reduce the number of false-positive regulations. To decrease the number of regulations we must validate, this study assigns confidence values to all of the possible regulations. For this purpose, we combine a bootstrap method and the method using the LPMs. Through numerical experiments on artificial genetic network inference problems, we check the effectiveness of assessing the confidence values of the regulations.

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.

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.