Abstract Back in the 80’s clustering methods were considered state of the art for non-structured box constrained global optimization (GO). Their disappearance is mainly due to their increasing difficulties in solving even moderately size GO problems, yet the basic idea was indeed a brilliant one. More recently population methods and Differential Evolution (DE) in particular has gained much attention in the GO heuristic world due to their easy implementation and good exploration capabilities. In order to improve the exploitation capability of DE, some memetic variants have been proposed with success. In this paper, we revisit clustering methods and apply them both to standard low dimensional problems and to large scale ones; in particular we propose a novel approach to apply a clustering-type decision on when to start a local search to variants of memetic DE. The resulting algorithm, C-MDE (Clustering Memetic DE) outperforms the best-known methods both in quality of the returned solution and in the number of calls to the expensive local optimization phase, even in large dimension. For large dimensional problems, random projections are used in order to be able to decide on starting a local search on a limited number of features. The resulting GO method is a revisit of clustering techniques in which all of the defects which made those methods no more feasible are eliminated: in particular, the method is used within an adaptive population method and it efficiently runs also in large dimension. Thus we think the proposed approach will find a place in the top performing modern GO algorithms.

中文翻译：

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通过基于聚类的种群方法进行高效的大规模全局优化

摘要 早在 80 年代，聚类方法被认为是非结构化框约束全局优化 (GO) 的最新技术。它们的消失主要是因为它们在解决中等规模的 GO 问题时越来越困难，但其基本思想确实是一个绝妙的想法。最近的种群方法和差分进化（DE）由于其易于实施和良好的探索能力而在 GO 启发式世界中受到了广泛关注。为了提高DE的开发能力，一些模因变体已经被成功地提出。在本文中，我们重新审视了聚类方法并将它们应用于标准的低维问题和大规模问题；特别是，我们提出了一种新颖的方法，将聚类类型的决定应用于何时开始本地搜索到模因 DE 的变体。由此产生的算法 C-MDE（Clustering Memetic DE）在返回解决方案的质量和对昂贵的局部优化阶段的调用次数方面都优于最著名的方法，即使在大维度上也是如此。对于大维问题，使用随机投影以便能够决定对有限数量的特征进行局部搜索。由此产生的 GO 方法是对聚类技术的重新审视，其中消除了使这些方法不再可行的所有缺陷：特别是，该方法用于自适应种群方法，并且它也可以在大维度上有效运行。