The edge minimum sum-of-squares clustering problem (E-MSSC) aims at finding p prototypes such that the sum of squares of distances from a set of vertices to their closest prototype is minimized, where a prototype is either a vertex or an interior point of an edge. This paper proposes a highly effective memetic algorithm for E-MSSC that combines a dedicated crossover operator for solution generation with a reformulation local search for solution improvement. Reformulation local search is a recent algorithmic framework for continuous location problems that is based on an alternation between original (continuous) and discrete formulations of a given problem. Furthermore, the proposed algorithm uses a simple strategy for population updating, and a mutation operator to prevent from premature convergence. The computational results obtained on three sets of 132 benchmark instances show that the proposed algorithm competes very favorably with the existing state-of-the-art algorithms in terms of both solution quality and computational efficiency. We also analyze several essential components of the proposed algorithm to understand their contribution to the algorithm’s performance.

边缘最小平方和聚类问题（E-MSSC）旨在找到p原型，以使从一组顶点到最接近的原型的距离的平方和最小，其中原型是顶点或边的内点。本文提出了一种针对E-MSSC的高效模因算法，该算法将专用的交叉算子用于解决方案生成，并通过重新制定局部搜索来改进解决方案。重新制定局部搜索是一种针对连续位置问题的最新算法框架，该框架基于给定问题的原始（连续）和离散形式之间的交替。此外，提出的算法使用简单的策略进行总体更新，并使用变异算子来防止过早收敛。在三组132个基准实例上获得的计算结果表明，无论是在解决方案质量还是计算效率上，该算法都与现有的最新算法竞争非常好。我们还分析了所提出算法的几个基本组成部分，以了解它们对算法性能的贡献。