The elucidation of gene regulatory networks (GRNs) is one of the central challenges of systems biology, which is crucial for understanding pathogenesis and curing diseases. Various computational methods have been developed for GRN inference, but identifying redundant regulation remains a fundamental problem. Although considering topological properties and edge importance measures simultaneously can identify and reduce redundant regulations, how to address their respective weaknesses whilst leveraging their strengths is a critical problem faced by researchers. Here, we propose a network structure refinement method for GRN (NSRGRN) that effectively combines the topological properties and edge importance measures during GRN inference. NSRGRN has two major parts. The first part constructs a preliminary ranking list of gene regulations to avoid starting the GRN inference from a directed complete graph. The second part develops a novel network structure refinement (NSR) algorithm to refine the network structure from local and global topology perspectives. Specifically, the Conditional Mutual Information with Directionality and network motifs are applied to optimise the local topology, and the lower and upper networks are used to balance the bilateral relationship between the local topology’s optimisation and the global topology’s maintenance. NSRGRN is compared with six state-of-the-art methods on three datasets (26 networks in total), and it shows the best all-round performance. Furthermore, when acting as a post-processing step, the NSR algorithm can improve the results of other methods in most datasets.
There are usually multiple constraints in constrained multi-objective optimization. Those constraints reduce the feasible area of the constrained multi-objective optimization problems (CMOPs) and make it difficult for current multiobjective optimization algorithms (CMOEAs) to obtain satisfactory feasible solutions. In order to solve this problem, this paper studies the relationship between constraints, then obtains the priority between constraints according to the relationship between the Pareto Front (PF) of the single constraint and their common PF. Meanwhile, this paper proposes a multi-stage CMOEA and applies this priority, which can save computing resources while helping the algorithm converge. The proposed algorithm completely abandons the feasibility in the early stage to better explore the objective space, and obtains the priority of constraints according to the relationship; Then the algorithm evaluates a single constraint in the medium stage to further explore the objective space according to this priority, and abandons the evaluation of some less-important constraints according to the relationship to save the evaluation times; At the end stage of the algorithm, the feasibility will be fully considered to improve the quality of the solutions obtained in the first two stages, and finally get the solutions with good convergence, feasibility, and diversity. The results on five CMOP suites and three realworld CMOPs show that the algorithm proposed in this paper can have strong competitiveness in existing constrained multiobjective optimization.
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