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Constructing rooted phylogenetic networks from rooted phylogenetic trees has become an important problem in molecular evolution. So far, many methods have been presented in this area, in which most efficient methods are based on the incompatible graph, such as the CASS, the LNETWORK, and the BIMLR. This paper will research the commonness of the methods based on the incompatible graph, the relationship between incompatible graph and the phylogenetic network, and the topologies of incompatible graphs. We can find out all the simplest datasets for a topology G and construct a network for every dataset. For any one dataset C, we can compute a network from the network representing the simplest dataset which is isomorphic to C. This process will save more time for the algorithms when constructing networks. [ABSTRACT FROM AUTHOR]

Finding an optimal set of discriminative features is still a crucial but challenging task in biomedical science. The complexity of the task is intensified when any of the two scenarios arise: a highly dimensioned dataset and a small sample-sized dataset. The first scenario poses a big challenge to existing machine learning approaches since the search space for identifying the most relevant feature subset is so diverse to be explored quickly while utilizing minimal computational resources. On the other hand, the second aspect poses a challenge of too few samples to learn from. Though many hybrid metaheuristic approaches (i.e., combining multiple search algorithms) have been proposed in the literature to address these challenges with very attractive performance compared to their counterpart standard standalone metaheuristics, more superior hybrid approaches can be achieved if the individual metaheuristics within the proposed hybrid algorithms are improved prior to the hybridization. Motivated by this, we propose a new hybrid Excited- (E-) Adaptive Cuckoo Search- (ACS-) Intensification Dedicated Grey Wolf Optimization (IDGWO), i.e., EACSIDGWO. EACSIDGWO is an algorithm where the step size of ACS and the nonlinear control strategy of parameter a → of the IDGWO are innovatively made adaptive via the concept of the complete voltage and current responses of a direct current (DC) excited resistor-capacitor (RC) circuit. Since the population has a higher diversity at early stages of the proposed EACSIDGWO algorithm, both the ACS and IDGWO are jointly involved in local exploitation. On the other hand, to enhance mature convergence at latter stages of the proposed algorithm, the role of ACS is switched to global exploration while the IDGWO is still left conducting the local exploitation. To prove that the proposed algorithm is superior in providing a good learning from fewer instances and an optimal feature selection from information-rich biomedical data, all these while maintaining a high classification accuracy of the data, the EACSIDGWO is employed to solve the feature selection problem. The EACSIDGWO as a feature selector is tested on six standard biomedical datasets from the University of California at Irvine (UCI) repository. The experimental results are compared with the state-of-the-art feature selection techniques, including binary ant-colony optimization (BACO), binary genetic algorithm (BGA), binary particle swarm optimization (BPSO), and extended binary cuckoo search algorithm (EBCSA). These results reveal that the EACSIDGWO has comprehensive superiority in tackling the feature selection problem, which proves the capability of the proposed algorithm in solving real-world complex problems. Furthermore, the superiority of the proposed algorithm is proved via various numerical techniques like ranking methods and statistical analysis. [ABSTRACT FROM AUTHOR]