The $(1+(λ,λ))$ Global SEMO Algorithm
This work addresses runtime efficiency in multi-objective evolutionary algorithms for discrete optimization, offering incremental improvements over existing methods.
The paper tackles the problem of extending the efficient single-objective (1+(λ,λ)) genetic algorithm to multi-objective optimization by proposing the (1+(λ,λ)) global SEMO algorithm, proving it optimizes the OneMinMax benchmark asymptotically faster than the classic global SEMO and achieves a runtime of O(n^2) with a dynamic parameter setting, compared to O(n^2 log n) for the best previous guarantee.
The $(1+(λ,λ))$ genetic algorithm is a recently proposed single-objective evolutionary algorithm with several interesting properties. We show that its main working principle, mutation with a high rate and crossover as repair mechanism, can be transported also to multi-objective evolutionary computation. We define the $(1+(λ,λ))$ global SEMO algorithm, a variant of the classic global SEMO algorithm, and prove that it optimizes the OneMinMax benchmark asymptotically faster than the global SEMO. Following the single-objective example, we design a one-fifth rule inspired dynamic parameter setting (to the best of our knowledge for the first time in discrete multi-objective optimization) and prove that it further improves the runtime to $O(n^2)$, whereas the best runtime guarantee for the global SEMO is only $O(n^2 \log n)$.