Arising from the need of all time for optimization of irrigation systems, distribution network and cable network, Clustered Shortest-Path Tree Problem (CluSPT) has been attracting a lot of attention and interest from the research community. On the other hand, the Multifactorial Evolutionary Algorithm (MFEA) is one of the most recently exploited realms of Evolutionary Algorithms (EAs) and its performance in solving optimization problems has been very promising. Considering these characteristics, this paper describes a new approach using the MFEA for solving the CluSPT. The MFEA has two tasks: the goal of the first task is to determine the best tree (w.r.t. cost minimization) which envelops all vertices of the CluSPT while the goal of the second task is to find the fittest solution possible for the problem. The purpose of the second task is to find good materials for implicit genetic transfer process in MFEA to improve the quality of CluSPT. To apply this new algorithm, a decoding scheme for deriving individual solutions from the unified representation in the MFEA is also introduced in this paper. Furthermore, evolutionary operators such as population initialization, crossover and mutation operators are also proposed. These operators are applicable for constructing valid solution from both sparse and complete graph. Although the proposed algorithm is slightly complicated for implementation, it can enhance ability to explore and exploit the Unified Search Space (USS). To prove this increment in performance i.e, to assess the effectiveness of the proposed algorithm and methods, the authors implemented them on both Euclidean and Non-Euclidean instances. Experiment results show that the proposed MFEA outperformed existing heuristic algorithms in most of the test cases. The impact of the proposed MFEA was analyzed and a possible influential factor that may be useful for further study was also pointed out.

中文翻译：

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使用多因素优化解决聚类的最短路径树问题的有效策略

由于始终需要优化灌溉系统，配电网络和电缆网络，因此，群集最短路径树问题（CluSPT）引起了研究界的广泛关注和关注。另一方面，多因子进化算法（MFEA）是进化算法（EA）领域中开发最广泛的领域之一，其在解决优化问题方面的性能非常有前途。考虑到这些特性，本文介绍了一种使用MFEA解决CluSPT的新方法。MFEA有两个任务：第一个任务的目标是确定包围CluSPT所有顶点的最佳树（最小化wrt成本），而第二个任务的目标是找到解决该问题的最合适解决方案。第二个任务的目的是为MFEA中的隐性遗传转移过程寻找好的材料，以提高CluSPT的质量。为了应用这种新算法，本文还介绍了一种从MFEA中的统一表示派生单个解的解码方案。此外，还提出了进化算子，例如种群初始化，交叉算子和变异算子。这些运算符适用于从稀疏图和完整图构造有效的解决方案。尽管所提出的算法实现起来有些复杂，但是它可以增强探索和利用统一搜索空间（USS）的能力。为了证明性能的提高，即评估所提出算法和方法的有效性，作者在欧几里得实例和非欧几里得实例上都实现了它们。实验结果表明，在大多数测试案例中，提出的MFEA均优于现有的启发式算法。分析了提议的MFEA的影响，并指出了可能对进一步研究有用的影响因素。