Inferring sparse genetic regulatory networks based on maximum-entropy probability model and multi-objective memetic algorithm

Maximum-entropy probability models (MEPMs) have been widely used to reveal the structure of genetic regulatory networks (GRNs). However, owing to the inherent network sparsity and small sample size, most of the existing MEPMs use convex optimization to approximate the inference of GRNs which tend to be trapped in less accurate local optimal solutions. Evolutionary algorithms (EAs) can help address this issue thanks to their superior global search capability, yet the conventional EA-based methods cannot handle the sparsity of GRNs efficiently. To overcome this problem, we propose a multi-objective memetic algorithm in this study to infer the sparse GRNs with MEPMs. Particularly, the target inferring problem is formulated as a multi-objective optimization problem where the maximum entropy and the constraints of the MEPM are formulated as two objectives. We employ Graphical LASSO (Glasso) to generate prior knowledge for population initialization. The genetic operators are adopted to ensure the diversity and sparsity of the inferred GRNs. Local search based on the spatial relations among solutions and different Glasso results in the decision space is incorporated into the algorithm to improve the search efficiency. Experimental results on both simulated and real-world data sets suggest that the proposed method outperforms other state-of-the-art GRN inferring methods in terms of effectiveness and efficiency.