Engineering design optimization in real life is a challenging global optimization problem, and many meta-heuristic algorithms have been proposed to obtain the global best solutions. An excellent meta-heuristic algorithm has two symmetric search capabilities: local search and global search. In this paper, an improved Butterfly Optimization Algorithm (BOA) is developed by embedding the cross-entropy (CE) method into the original BOA. Based on a co-evolution technique, this new method achieves a proper balance between exploration and exploitation to enhance its global search capability, and effectively avoid it falling into a local optimum. The performance of the proposed approach was evaluated on 19 well-known benchmark test functions and three classical engineering design problems. The results of the test functions show that the proposed algorithm can provide very competitive results in terms of improved exploration, local optima avoidance, exploitation, and convergence rate. The results of the engineering problems prove that the new approach is applicable to challenging problems with constrained and unknown search spaces.

Global optimization, especially on a large scale, is challenging to solve due to its nonlinearity and multimodality. In this paper, in order to enhance the global searching ability of the firefly algorithm (FA) inspired by bionics, a novel hybrid meta-heuristic algorithm is proposed by embedding the cross-entropy (CE) method into the firefly algorithm. With adaptive smoothing and co-evolution, the proposed method fully absorbs the ergodicity, adaptability and robustness of the cross-entropy method. The new hybrid algorithm achieves an effective balance between exploration and exploitation to avoid falling into a local optimum, enhance its global searching ability, and improve its convergence rate. The results of numeral experiments show that the new hybrid algorithm possesses more powerful global search capacity, higher optimization precision, and stronger robustness.

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The phenomenon of knowledge withholding is a vital issue that undermines knowledge sharing and innovation, hinders the development of offline and online organizations. Clarifying the relationship between influencing factors and knowledge withholding is significant to improve the phenomenon of knowledge withholding in offline and online organizations. Few types of research focus on the online virtual academic community and integrate the three factors of knowledge, individual, and environment to research knowledge withholding. To solve the limitation, this research is based on sociology and psychology-related theories. The two dimensions of enabling and inhibition are divided into factors affecting knowledge withholding. An attempt is made to explore the path between the three types of factors influencing knowledge, individual and environment, and knowledge withholding. This study collected data from 616 users in China’s virtual academic community. It used a structural equation model combined with a cross-layer connected neural network to conduct an empirical analysis on the proposed hypothesis. The results found that: in the virtual academic community, knowledge power in the enabling dimension is the main reason for users to form knowledge psychological ownership, which affects users’ knowledge withholding. However, the effect of professional commitment on users’ knowledge psychological ownership is not significant. After SEM-ANN model fitting, the combined inhibitory effect of community privacy protection and community reciprocity on user knowledge withholding in the inhibition dimension is significantly improved. This research has a specific guiding significance for enhancing the knowledge withholding phenomenon of the virtual academic community and creating an excellent academic exchange atmosphere.