The $(1+(λ,λ))$ Global SEMO Algorithm

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(n2), whereas the best runtime guarantee for the global SEMO is only O(n2 log n).