Adaptive -Ranking and Distribution Search on Evolutionary Many-objective Optimization

In this work, we study the effectiveness of Adaptive -Ranking for distribution search in the context of many-objective optimization. Adaptive -Ranking re-classifies sets of non-dominated solutions using iteratively a randomized sampling procedure that applies -dominance with a mapping function f(x) 7→ f (x) to bias selection towards the distribution of solutions implicit in the mapping. We analyze the effectiveness of Adaptive -Ranking with three linear mapping functions for -dominance and study the importance of recombination to properly guide the algorithm towards the distribution we seek to find. As test problems, we use functions of the DTLZ family with M = 6 objectives, varying the number of variables N from 10 to 50.