Offspring population size matters when comparing evolutionary algorithms with self-adjusting mutation rates

Abstract

We analyze the performance of the 2-rate (1 + λ) Evolutionary Algorithm (EA) with self-adjusting mutation rate control, its 3-rate counterpart, and a (1 + λ) EA variant using multiplicative update rules on the OneMax problem. We compare their efficiency for offspring population sizes ranging up to λ = 3, 200 and problem sizes up to n = 100, 000.Our empirical results show that the ranking of the algorithms is very consistent across all tested dimensions, but strongly depends on the population size. While for small values of λ the 2-rate EA performs best, the multiplicative updates become superior for starting for some threshold value of λ between 50 and 100. Interestingly, for population sizes around 50, the (1 + λ) EA with static mutation rates performs on par with the best of the self-adjusting algorithms.We also consider how the lower bound p min for the mutation rate influences the efficiency of the algorithms. We observe that for the 2-rate EA and the EA with multiplicative update rules the more generous bound p min = 1/n 2 gives better results than p min = 1/n when λ is small. For both algorithms the situation reverses for large λ.

Mutation Rate Control in the $$(1+\lambda )$$ Evolutionary Algorithm with a Self-adjusting Lower Bound

“…The original algorithm in [4] uses as lower bound lb = 1/n. In our previous work [18], however, we observed that a more generous lower bound of 1/n 2 can be advantageous. In particular, we observed the following effects on OneMax, for problem dimension n up to 10 5 and offspring population size λ up to 32 • 10 3 :…”

“…We continue previous work summarized in [18], where we have studied the so-called 2-rate (1 + λ) EA r/2,2r algorithm suggested in [4]. The 2-rate (1 + λ) EA r/2,2r is an EA of (1 + λ) EA type with self-adjusting mutation rates.…”

“…Using the mentioned observations from the paper [18], we developed the 2-rate (1 + λ) EA r/2,2r with voting that is aimed to solve the issues of the conventional 2-rate (1 + λ) EA r/2,2r . The pseudocode of the proposed algorithm is shown in Algorithm 1.…”

Benchmarking discrete optimization heuristics with IOHprofiler

“…The N -queens problem (NQP) [Bell and Stevens(2009)] is defined as the task to place N queens on an N × N chessboard in such a way that they cannot attack each other. 3 Figure 3 provides an illustration for the 8-queens problem.…”

“…Note that most algorithms are parametrized, and we use here in this work only standard parametrizations (e.g., we use 1/n as mutation rates, etc.). Analyzing the effects of different parameter values as was done, for example in [Rodionova et al(2019)Rodionova, Antonov, Buzdalova, andDoerr, Dang and], would be very interesting, but is beyond the scope of this present work.…”