The (1 + (λ, λ)) genetic algorithm, first proposed at GECCO 2013, showed a surprisingly good performance on so me optimization problems. The theoretical analysis so far was restricted to the OneMax test function, where this GA profited from the perfect fitness-distance correlation. In this work, we conduct a rigorous runtime analysis of this GA on random 3-SAT instances in the planted solution model having at least logarithmic average degree, which are known to have a weaker fitness distance correlation.We prove that this GA with fixed not too large population size again obtains runtimes better than Θ(n log n), which is a lower bound for most evolutionary algorithms on pseudo-Boolean problems with unique optimum. However, the self-adjusting version of the GA risks reaching population sizes at which the intermediate selection of the GA, due to the weaker fitness-distance correlation, is not able to distinguish a profitable offspring from others. We show that this problem can be overcome by equipping the self-adjusting GA with an upper limit for the population size. Apart from sparse instances, this limit can be chosen in a way that the asymptotic performance does not worsen compared to the idealistic OneMax case. Overall, this work shows that the (1 + (λ, λ)) GA can provably have a good performance on combinatorial search and optimization problems also in the presence of a weaker fitness-distance correlation.

Genetic algorithms (GAs) are widely used in multi-objective optimization for solving complex problems. There are two distinct approaches for GA design: generational and steadystate algorithms. Most of the current state-of-the-art GAs are generational, although there is an increasing interest to steady-state algorithms as well. However, for algorithms based on non-dominated sorting, most of steady-state implementations have higher computation complexity than their generational counterparts, which limits their applicability.We present a fast implementation of a steady-state version of the NSGA-II algorithm for two dimensions. This implementation is based on a data structure which has O(N ) complexity for single solution insertion and deletion in the worst case. The experimental results show that our implementation works noticeably faster than steady-state NSGA-II implementations which use fast non-dominated sorting.

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