Finding multiple solutions based on an evolutionary algorithm for inference of genetic networks by S-system

This paper presents the Network-Structure-Search Evolutionary Algorithm (NSS-EA) for inference of genetic networks by S-system. NSS-EA efficiently finds multiple different network structures which explain gene-expression time-course data observed in biological experiments. In inference of genetic networks by S-system, we are required to find as many network structures that explain experimentally-observed data as possible. This is because, in general, it is difficult to obtain sufficient time-course data by which we can determine a network structure uniquely. A network structure is determined by whether each system parameter of its S-system is positive, negative or zero. Tominaga et al. and Ueda et al. have proposed methods that repeatedly run real-coded genetic algorithms (GAs) for searching the system parameters of S-system with different random number series in each GA run to obtain multiple different network structures. These methods have two serious problems that the same network structures can be repeatedly found in multiple GA runs and that a biological knowledge that the number of substances interacting with one substance is relatively small is not taken into account. This is because how many and what kind of structures are found by real-coded GAs depend on the random number series used by the GAs. In this paper, we try to solve the above problems by explicitly separating the process of searching network structures, i.e. searching the signs of system parameters of S-system, and that of searching the values of the system parameters. Through some numerical experiments, we show that the proposed method, NSS-EA, can efficiently find more different kinds of network structures than the conventional methods.