On the Choice of the Population Size

On the impact of objective function transformations on evolutionary and black-box algorithms

“…The proof is similar to the one in [7]. After an expected number of O(µn 2 ) steps an element p i , i > n − n/3 , is included in the population.…”

“…Therefore, the previous result will be amplified in the function similar than it was realized in [7]. Let s 0 , .…”

“…, s n/ log n n/ log n , where s 0 := 1 n− n/3 0 n/3 , denote a path which consists of elements with at least n − n/3 ones and furthermore, the Hamming distance of s i , i ≥ 0, and s i+j equals j for 0 ≤ j ≤ n/ log n and the Hamming distance is at least n/ log n for j > n/ log n . A construction of such a path is presented in [7]. In order to describe the construction we remember the Gray code.…”

“…Let us assume without simplifying the setting that the search space S equals {0, 1} n , i.e., we investigate pseudo-Boolean functions. Moreover, the investigated mutation-based steady-state (µ+1) EA rank is defined as follows (see [7]). …”

On the effect of populations in evolutionary multi-objective optimization

“…For example, there are problems where reducing the parent population size by one leads to an exponential increase in the runtime [10].…”