When the Plus Strategy Outperforms the Comma Strategyand When Not

The choice of the offspring population size in the (1,λ) EA

“…We have extended results by Jägersküpper and Storch [4] on the performance of the (1,λ) EA. There is a sharp threshold for the choice of λ at log e e−1 n ≈ 5 log 10 n. Any smaller values render the algorithm inefficient on larger problems with a unique optimum.…”

“…Jägersküpper and Storch [4] have shown that the running time of the (1,λ) EA on OneMax is exponential if λ ≤ 1/14· ln n. Neumann, Oliveto and Witt [12] showed an exponential lower bound for a similar algorithm in a related setting if λ ≤ 1/4 · ln n. Here, we relax on these conditions and show that the threshold from Theorem 6 is tight. −Ω(n ε/2 ) , for some constant c > 0.…”

“…As shown in [4], the algorithm needs exponential time on any function with a unique optimum if λ ≤ (ln n)/14, with high probability. The reason is that the number of offspring is so small that the algorithm tends to move away from the global optimum once it gets close.…”

“…Contrarily, if λ ≥ 3 ln n the algorithm can effectively perform hill climbing and approach the global optimum on easy functions like OneMax. Moreover, there are examples of multimodal functions for which the (1,λ) EA is provably more efficient than the (1+λ) EA [4].…”

“…Jägersküpper and Storch [4] were among the first to investigate comma strategies like the (1,λ) EA. The (1,λ) EA creates λ offspring independently and selects the best among these as parent.…”