This paper proposes an improved cuckoo search (CS) algorithm combining nonlinear inertial weight and differential evolution algorithm (WCSDE) to overcome the shortcomings of the CS algorithm, such as low convergence accuracy, lack of information exchange within the population, and inadequate local search capabilities. Compared with other CS variants, two strategies are proposed in this paper to improve the properties of the WCSDE. On the one hand, a non-linearly decreasing inertia weight with the number of evolutionary iterations is employed in the WCSDE to improve the update method of the bird's nest position, enhance the balance between the exploration and development capabilities, and strengthen the local optimization capability. On the other hand, the mutation and cross-selection mechanisms of the differential evolution (DE) algorithm are introduced to make up for the lack of the mutual relationship between the populations, avoid the loss of practical information, and increase the convergence accuracy. In the experiment part, 13 classic benchmark functions are selected to execute the function optimization tasks among the standard CS, the WCSDE, and other four CS variants to verify the effectiveness of the proposed algorithm from two aspects. The results and corresponding statistical analysis reveal that the proposed algorithm has better global search ability and strengthener robustness.

In recent years, multi-objective cuckoo search (MOCS) has been widely used to settle the multi-objective (MOP) optimization issue. However, some drawbacks still exist that hinder the further development of the MOCS, such as lower convergence accuracy and weaker efficiency. An improved MOCS (IMOCS) is proposed in this manuscript by investigating the balance between development and exploration to obtain more accurate solutions while solving the MOP. The main contributions of the IMOCS could be separated into two aspects. Firstly, a dynamic adjustment is utilized to enhance the efficiency of searching non-dominated solutions in different periods utilizing the Levy flight. Secondly, a reconstructed local dynamic search mechanism and disturbance strategy are employed to strengthen the accuracy while searching non-dominated solutions and to prevent local stagnation when solving complex problems. Two experiments are implemented from different aspects to verify the performance of the IMOCS. Firstly, seven different multi-objective problems are optimized using three typical approaches, and some statistical methods are used to analyze the experimental results. Secondly, the IMOCS is applied to the obstacle avoidance problem of multiple unmanned aerial vehicles (UAVs), for seeking a safe route through optimizing the coordinated formation control of UAVs to ensure the horizontal airspeed, yaw angle, altitude, and altitude rate are converged to the expected level within a given time. The experimental results illustrate that the IMOCS can make the multiple UAVs converge in a shorter time than other comparison algorithms. The above two experimental results indicate that the proposed IMOCS is superior to other algorithms in convergence and diversity.

Fault diagnosis based on the expert system (ES) is still a research topic of manufacturing in the Industry 4.0 because of the stronger interpretability. As the core component of the ES, fault diagnosis accuracy is positively correlated to the precise of the knowledge base. But it is difficult for users to understand the knowledge obtained from the original dataset utilizing the existing knowledge extraction method. Therefore, it is of great significance to extract easy-to-understand and exact rules from the NN framework. This paper proposes a hybrid extraction framework to perform the rule extraction for overcoming this drawback. First, an improved adaptive genetic algorithm (GA) using a logistic function, namely LAGA, is proposed to solve the traditional GA's insufficient prediction performance issue. Compared with the other three mainstream adaptive GAs, the experiment results of optimizing six selected test functions by these GA variants show that the LAGA algorithm's convergence accuracy and speed have been greatly improved, especially for high latitude functions. On this basis, a rule extraction method based on symbol rule and NN, namely the LAGA-BP framework, is discussed in this manuscript to classify the real-valued attributes. This framework obtains hidden knowledge (knowledge refinement process) by NN and further transforms the acquired hidden knowledge into more easy-to-understand rule knowledge (rule extraction process). The execution of the LAGA-BP framework could be separated into two phases. The first phase is to optimize a back propagation NN (BPNN) using the LAGA and refine prediction classification knowledge over the optimized BPNN. In the second phase, an attribute reduction algorithm using multi-layered NN (SD algorithm) based on two different superposed networks is used on this framework to reduce data-set attributes and then uses the K-means clustering algorithm to extract the ifthen rule from the simplified attributes. the Wisconsin breast cancer data-set is used as a case study to reveal the correctness and robustness of the proposed LAGA-BP method. Consulting relevant medical personnel and referencing relevant data shows that the rules extracted using this method help verify the diagnosis results, thus verifying the proposed framework's feasibility and practicality.

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