A variety of general strategies have been applied to enhance the performance of multi-objective optimization algorithms for many-objective optimization problems (those with more than three objectives). One of these strategies is to split the solutions to cover different regions of the search space (clusters) and apply an optimizer to each region with the aim of producing more diverse solutions and achieving a better distributed approximation of the Pareto front. However, the effectiveness of clustering in this context depends on a number of issues, including the characteristics of the objective functions. In this paper we show how the choice of the clustering strategy can greatly influence the behavior of an optimizer. We investigate the relation between the characteristics of a multi-objective optimization problem and the efficiency of the use of a clustering combination (clustering space, metric) in the resolution of this problem. Using as a case study the Iterated Multi-swarm (I-Multi) algorithm, a recently introduced multi-objective particle swarm optimization algorithm, we scrutinize the impact that clustering in different spaces (of variables, objectives and a combination of both) can have on the approximations of the Pareto front. Furthermore, employing two difficult multi-objective benchmarks of problems with up to 20 objectives, we evaluate the effect of using different metrics for determining the similarity between the solutions during the clustering process. Our results confirm the important effect of the clustering strategy on the behavior of multi-objective optimizers. Moreover, we present evidence that some problem characteristics can be used to select the most effective clustering strategy, significantly improving the quality of the Pareto front approximations produced by I-Multi.

中文翻译：

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多目标优化中的聚类策略研究：以I-Multi算法为例

已经应用了各种通用策略来增强多目标优化问题（具有三个以上目标的问题）的多目标优化算法的性能。这些策略之一是将解决方案拆分为覆盖搜索空间的不同区域（群集），并将优化器应用于每个区域，以产生更多种不同的解决方案并实现帕累托前沿的更好的分布式近似。但是，在这种情况下，聚类的有效性取决于许多问题，包括目标函数的特征。在本文中，我们展示了聚类策略的选择如何极大地影响优化器的行为。我们研究了多目标优化问题的特征与解决该问题的聚类组合（聚类空间，度量）的使用效率之间的关系。作为案例研究，最近引入了多目标粒子群优化算法-迭代多群（I-Multi）算法，我们研究了聚类在不同空间（变量，目标和两者的组合）中可能产生的影响在帕累托前沿的近似值上。此外，我们采用了两个具有多达20个目标的难题的多目标困难基准，我们评估了在聚类过程中使用不同度量来确定解决方案之间相似性的效果。我们的结果证实了聚类策略对多目标优化器行为的重要影响。此外，我们提供的证据表明，某些问题特征可用于选择最有效的聚类策略，从而显着提高I-Multi产生的Pareto前沿逼近的质量。