Zhang Ruochen, Zhu Bin
School of Economics and Management, Xi'an Shiyou University, Xi'an, Shaanxi, China.
School of Public Health and Emergency Management, Southern University of Science and Technology, Shenzhen, Guangdong, China.
PLoS One. 2024 Dec 3;19(12):e0313757. doi: 10.1371/journal.pone.0313757. eCollection 2024.
Small-world effect plays an important role in the field of network science, and optimizing the small-world property has been a focus, which has many applications in computational social science. In the present study, we model the problem of optimizing small-world property as a multiobjective optimization, where the average clustering coefficient and average path length are optimized separately and simultaneously. A novel method for optimizing small-world property is then proposed based on the multiobjective evolutionary algorithm with decomposition. Experimental results have proved that the presented method is capable of solving this problem efficiently, where a uniform distribution of solutions on the Pareto-optional front can be generated. The optimization results are further discussed to find specific paths for optimizing different objective functions. In general, adding edges within the same community is helpful for promoting ACC, while adding edges between different communities is beneficial for reducing APL. The optimization on networks with the feature of community structure is more remarkable, but community structure has less impact on the optimization when the internal community is triangles-saturated.
小世界效应在网络科学领域发挥着重要作用，优化小世界特性一直是一个研究重点，其在计算社会科学中有诸多应用。在本研究中，我们将优化小世界特性的问题建模为一个多目标优化问题，其中平均聚类系数和平均路径长度被分别且同时进行优化。然后基于带分解的多目标进化算法提出了一种优化小世界特性的新方法。实验结果证明，所提出的方法能够有效地解决该问题，能够在帕累托最优前沿上生成均匀分布的解。进一步讨论了优化结果以找到优化不同目标函数的具体路径。一般来说，在同一社区内添加边有助于提高平均聚类系数，而在不同社区之间添加边有利于降低平均路径长度。对具有社区结构特征的网络进行优化更为显著，但当内部社区为三角形饱和时，社区结构对优化的影响较小。
