Runtime analysis has recently been applied to popular evolutionary multi-objective (EMO) algorithms like NSGA-II in order to establish a rigorous theoretical foundation. However, most analyses showed that these algorithms have the same performance guarantee as the simple (G)SEMO algorithm. To our knowledge, there are no runtime analyses showing an advantage of a popular EMO algorithm over the simple algorithm for deterministic problems. We propose such a problem and use it to showcase the superiority of popular EMO algorithms over (G)SEMO: OneTrapZeroTrap is a straightforward generalization of the well-known Trap function to two objectives. We prove that, while GSEMO requires at least $n^n$ expected fitness evaluations to optimise OneTrapZeroTrap, popular EMO algorithms NSGA-II, NSGA-III and SMS-EMOA, all enhanced with a mild diversity mechanism of avoiding genotype duplication, only require $O(n \log n)$ expected fitness evaluations. Our analysis reveals the importance of the key components in each of these sophisticated algorithms and contributes to a better understanding of their capabilities.

翻译：运行时间分析最近被应用于NSGA-II等主流进化多目标算法，旨在建立严格的理论基础。然而，多数分析表明这些算法具有与简单的(G)SEMO算法相同的性能保证。据我们所知，目前尚无运行时间分析能证明主流进化多目标算法在确定性问题上优于简单算法。我们提出了一个此类问题，并用以展示主流进化多目标算法相对于(G)SEMO的优越性：OneTrapZeroTrap是著名的Trap函数向双目标问题的直接推广。我们证明，虽然GSEMO优化OneTrapZeroTrap至少需要$n^n$次期望适应度评估，但主流进化多目标算法NSGA-II、NSGA-III和SMS-EMOA（均通过避免基因型重复的温和多样性机制进行增强）仅需$O(n \log n)$次期望适应度评估。我们的分析揭示了这些复杂算法中关键组件的重要性，有助于更深入理解其性能优势。