The ant colony optimization (ACO) algorithm has the characteristics of positive feedback, essential parallelism, and global convergence, but it has the shortcomings of premature convergence and slow convergence speed. The co-evolutionary algorithm (CEA) emphasizes the existing interaction among different sub-populations, but it is overly formal, and does not form a very strict and unified definition. Therefore, a new adaptive co-evolutionary ant colony optimization (SCEACO) algorithm based on the complementary advantages and hybrid mechanism is proposed in this paper. Firstly, the pheromone update formula is improved and the pheromone range of the ACO algorithm is limited in order to achieve the adaptive update of the pheromone. The elitist strategy and co-evolutionary idea are used for reference, the symbiotic mechanism and hybrid mechanism are introduced to better utilize the advantages of the CEA and ACO. Then the multi-objective optimization problem is divided into several sub-problems, each sub-problem corresponds to one population. Each ant colony is divided into multiple sub-populations in a common search space, and each sub-population performs the search activity and pheromone updating strategy. The elitist strategy is used to retain the elitist individuals within the population and the min-max ant strategy is used to set pheromone concentration for each path. Next, the selection, crossover, and mutation operations of individuals are introduced to adaptively adjust the parameters and implement the information sharing of the population and the co-evolution. Finally, the gate assignment problem of a hub airport is selected to verify the optimization performance of the SCEACO algorithm. The experiment results show that the SCEACO algorithm can effectively solve the gate assignment problem of a hub airport and obtain the effective assignment result. The SCEACO algorithm improves the convergence speed, and enhances the local search ability and global search capability.

A motor bearing system is a nonlinear dynamics system with nonlinear support stiffness. It is an asymmetry system, which plays an extremely important role in rotating machinery. In this paper, a center frequency method of double thresholds is proposed to improve the variational mode decomposition (VMD) method, then an adaptive VMD (called DTCFVMD) method is obtained to extract the fault feature. In the DTCFVMD method, a center frequency method of double thresholds is a symmetry method, which is used to determine the decomposed mode number of VMD according to the power spectrum of the signal. The proposed DTCFVMD method is used to decompose the nonlinear and non-stationary vibration signals of motor bearing in order to obtain a series of intrinsic mode functions (IMFs) under different scales. Then, the Hilbert transform is used to analyze the envelope of each mode component and calculate the power spectrum of each mode component. Finally, the power spectrum is used to extract the fault feature frequency for determining the fault type of the motor bearing. To test and verify the effectiveness of the DTCFVMD method, the actual fault vibration signal of the motor bearing is selected in here. The experimental results show that the center frequency method of double thresholds can effectively determine the mode number of the VMD method, and the proposed DTCFVMD method can accurately extract the clear time frequency characteristics of each mode component, and obtain the fault characteristics of characteristics; frequency, rotating frequency, and frequency doubling and so on.