Fast Implementation of the Steady-State NSGA-II Algorithm for Two Dimensions Based on Incremental Non-Dominated Sorting

Genetic algorithms (GAs) are widely used in multi-objective optimization for solving complex problems. There are two distinct approaches for GA design: generational and steady-state algorithms. Most of the current state-of-the-art GAs are generational, although there is an increasing interest to steady-state algorithms as well. However, for algorithms based on non-dominated sorting, most of steady-state implementations have higher computation complexity than their generational counterparts, which limits their applicability. We present a fast implementation of a steady-state version of the NSGA-II algorithm for two dimensions. This implementation is based on a data structure which has O(N) complexity for single solution insertion and deletion in the worst case. The experimental results show that our implementation works noticeably faster than steady-state NSGA-II implementations which use fast non-dominated sorting.