Many real-world test optimization problems (e.g., test case prioritization) are multi-objective intrinsically and can be tackled using various multi-objective search algorithms (e.g., Non-dominated Sorting Genetic Algorithm (NSGA-II)). However, existing multi-objective search algorithms have certain randomness when selecting parent solutions for producing offspring solutions. In a worse case, suboptimal parent solutions may result in offspring solutions with bad quality, and thus affect the overall quality of the solutions in the next generation. To address such a challenge, we propose CBGA-ES+, a novel cluster-based genetic algorithm with non-dominated elitist selection to reduce the randomness when selecting the parent solutions to support multi-objective test optimization. We empirically compared CBGA-ES+ with random search and greedy (as baselines), four commonly used multi-objective search algorithms (i.e., Multi-objective Cellular genetic algorithm (MOCell), NSGA-II, Pareto Archived Evolution Strategy (PAES), and Strength Pareto Evolutionary Algorithm (SPEA2)), and the predecessor of CBGA-ES+ (named CBGA-ES) using five multi-objective test optimization problems with eight subjects (two industrial, one real world, and five open source). The results showed that CBGA-ES+ managed to significantly outperform the selected search algorithms for a majority of the experiments. Moreover, for the solutions in the same search space, CBGA-ES+ managed to perform better than CBGA-ES, MOCell, NSGA-II, PAES, and SPEA2 for 2.2, 13.6, 14.5, 17.4, and 9.9 percent, respectively. Regarding the running time of the algorithm, CBGA-ES+ was faster than CBGA-ES for all the experiments.

中文翻译：

---

CBGA-ES+：支持多目标测试优化的非支配精英选择的基于集群的遗传算法

许多现实世界的测试优化问题（例如，测试用例优先排序）本质上是多目标的，可以使用各种多目标搜索算法（例如，非支配排序遗传算法（NSGA-II））来解决。然而，现有的多目标搜索算法在选择父解以产生后代解时具有一定的随机性。在更坏的情况下，次优的父解可能会导致后代解的质量较差，从而影响下一代解的整体质量。为了应对这样的挑战，我们提出了 CBGA-ES+，一种新的基于集群的遗传算法，具有非支配精英选择，以减少选择父解决方案时的随机性，以支持多目标测试优化。我们凭经验将 CBGA-ES+ 与随机搜索和贪婪（作为基线）、四种常用的多目标搜索算法（即多目标细胞遗传算法 (MOCell)、NSGA-II、帕累托存档进化策略 (PAES) 和强度帕累托进化算法 (SPEA2))，以及 CBGA-ES+ 的前身（命名为 CBGA-ES）使用五个多目标测试优化问题，八个主题（两个工业，一个现实世界和五个开源）。结果表明，在大多数实验中，CBGA-ES+ 的性能明显优于所选的搜索算法。此外，对于相同搜索空间中的解决方案，CBGA-ES+ 的性能分别比 CBGA-ES、MOCell、NSGA-II、PAES 和 SPEA2 好 2.2%、13.6%、14.5%、17.4% 和 9.9%。关于算法的运行时间，