Evolution Strategies, Network Random Keys, and the One-Max Tree Problem

Evolution strategies (ES) are efficient optimization methods for continuous problems. However, many combinatorial optimization methods can not be represented by using continuous representations. The development of the network random key representation which represents trees by using real numbers allows one to use ES for combinatorial tree problems. In this paper we apply ES to tree problems using the network random key representation. We examine whether existing recommendations regarding optimal parameter settings for ES, which were developed for the easy sphere and corridor model, are also valid for the easy one-max tree problem. The results show that the 5 -success rule for the (1+1)-ES results in low performance because the standard deviation is continuously reduced and we get early convergence. However, for the (μ+λ)-ES and the (μ, λ)-ES the recommendations from the literature are confirmed for the parameters of mutation τ1 and τ2 and the ratio μ/λ. This paper illustrates how existing theory about ES is helpful in finding good parameter settings for new problems like the one-max tree problem.