TY - JOUR
AU - Zheng, Weijie
AU - Liu, Yufei
AU - Doerr, Benjamin
PY - 2022/06/28
Y2 - 2024/05/21
TI - A First Mathematical Runtime Analysis of the Non-dominated Sorting Genetic Algorithm II (NSGA-II)
JF - Proceedings of the AAAI Conference on Artificial Intelligence
JA - AAAI
VL - 36
IS - 9
SE - AAAI Technical Track on Search and Optimization
DO - 10.1609/aaai.v36i9.21283
UR - https://ojs.aaai.org/index.php/AAAI/article/view/21283
SP - 10408-10416
AB - The non-dominated sorting genetic algorithm II (NSGA-II) is the most intensively used multi-objective evolutionary algorithm (MOEA) in real-world applications. However, in contrast to several simple MOEAs analyzed also via mathematical means, no such study exists for the NSGA-II so far. In this work, we show that mathematical runtime analyses are feasible also for the NSGA-II. As particular results, we prove that with a population size larger than the Pareto front size by a constant factor, the NSGA-II with two classic mutation operators and three different ways to select the parents satisfies the same asymptotic runtime guarantees as the SEMO and GSEMO algorithms on the basic OneMinMax and LOTZ benchmark functions. However, if the population size is only equal to the size of the Pareto front, then the NSGA-II cannot efficiently compute the full Pareto front (for an exponential number of iterations, the population will always miss a constant fraction of the Pareto front). Our experiments confirm the above findings.
ER -