Genetic algorithms (GAs) have been widely applied in Steiner tree optimization problems. However, as the core operation, existing crossover operators for tree-based GAs suffer from producing illegal offspring trees. Therefore, some global link information must be adopted to ensure the connectivity of the offspring, which incurs heavy computation. To address this problem, this article proposes a new crossover mechanism, called leaf crossover (LC), which generates legal offspring by just exchanging partial parent chromosomes, requiring neither the global network link information, encoding/decoding nor repair operations. Our simulation study indicates that GAs with LC outperform GAs with existing crossover mechanisms in terms of not only producing better solutions but also converging faster in networks of varying sizes.

中文翻译：

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一种新的 Steiner 树优化遗传算法交叉机制

遗传算法（GA）已广泛应用于斯坦纳树优化问题。然而，作为核心操作，现有的基于树的 GA 的交叉算子会产生非法的后代树。因此，必须采用一些全局链接信息来保证后代的连通性，计算量很大。为了解决这个问题，本文提出了一种新的交叉机制，称为叶交叉（LC），它只通过交换部分父染色体来产生合法的后代，不需要全局网络链接信息、编码/解码和修复操作。我们的模拟研究表明，具有 LC 的 GA 优于具有现有交叉机制的 GA，不仅可以产生更好的解决方案，而且可以更快地在不同规模的网络中收敛。