IEEE Trans Cybern. 2017 Jun;47(6):1510-1522. doi: 10.1109/TCYB.2016.2550502. Epub 2016 May 19.
Maintaining diversity is one important aim of multiobjective optimization. However, diversity for many-objective optimization problems is less straightforward to define than for multiobjective optimization problems. Inspired by measures for biodiversity, we propose a new diversity metric for many-objective optimization, which is an accumulation of the dissimilarity in the population, where an L -norm-based ( ) distance is adopted to measure the dissimilarity of solutions. Empirical results demonstrate our proposed metric can more accurately assess the diversity of solutions in various situations. We compare the diversity of the solutions obtained by four popular many-objective evolutionary algorithms using the proposed diversity metric on a large number of benchmark problems with two to ten objectives. The behaviors of different diversity maintenance methodologies in those algorithms are discussed in depth based on the experimental results. Finally, we show that the proposed diversity measure can also be employed for enhancing diversity maintenance or reference set generation in many-objective optimization.
保持多样性是多目标优化的一个重要目标。然而，与多目标优化问题相比，许多目标优化问题的多样性定义不太直接。受生物多样性度量的启发，我们提出了一种新的许多目标优化多样性度量，它是种群差异的积累，其中采用基于 L 范数的（）距离来度量解的差异。实证结果表明，我们提出的度量标准可以更准确地评估各种情况下解决方案的多样性。我们使用所提出的多样性度量标准，在具有两到十个目标的大量基准问题上，比较了四种流行的多目标进化算法获得的解决方案的多样性。基于实验结果，深入讨论了这些算法中不同多样性维护方法的行为。最后，我们表明所提出的多样性度量标准也可用于增强许多目标优化中的多样性维护或参考集生成。
