Together with the NSGA-II, the SPEA2 is one of the most widely used domination-based multi-objective evolutionary algorithms. For both algorithms, the known runtime guarantees are linear in the population size; for the NSGA-II, matching lower bounds exist. With a careful study of the more complex selection mechanism of the SPEA2, we show that it has very different population dynamics. From these, we prove runtime guarantees for the OneMinMax, LeadingOnesTrailingZeros, and OneJumpZeroJump benchmarks that depend less on the population size. For example, we show that the SPEA2 with parent population size $μ\ge n - 2k + 3$ and offspring population size $λ$ computes the Pareto front of the OneJumpZeroJump benchmark with gap size $k$ in an expected number of $O( (λ+μ)n + n^{k+1})$ function evaluations. This shows that the best runtime guarantee of $O(n^{k+1})$ is not only achieved for $μ= Θ(n)$ and $λ= O(n)$ but for arbitrary $μ, λ= O(n^k)$. Thus, choosing suitable parameters -- a key challenge in using heuristic algorithms -- is much easier for the SPEA2 than the NSGA-II.

翻译：与NSGA-II一样，SPEA2是基于支配关系的多目标进化算法中使用最广泛的算法之一。对于这两种算法，已知的运行时保证在种群规模上是线性的；对于NSGA-II，存在匹配的下界。通过对SPEA2更复杂的选择机制进行仔细研究，我们发现它具有非常不同的种群动态。基于这些分析，我们证明了SPEA2在OneMinMax、LeadingOnesTrailingZeros和OneJumpZeroJump基准测试上的运行时保证对种群规模的依赖性较低。例如，我们证明当父种群规模$μ\ge n - 2k + 3$且子种群规模为$λ$时，SPEA2计算间隙大小为$k$的OneJumpZeroJump基准测试帕累托前沿的期望函数评估次数为$O( (λ+μ)n + n^{k+1})$。这表明最佳运行时保证$O(n^{k+1})$不仅能在$μ= Θ(n)$和$λ= O(n)$时实现，而且对于任意$μ, λ= O(n^k)$同样成立。因此，对于SPEA2而言，选择合适的参数——这是使用启发式算法时的关键挑战——比NSGA-II要容易得多。