A First Mathematical Runtime Analysis of the Non-dominated Sorting Genetic Algorithm II (NSGA-II) (Hot-off-the-Press Track at GECCO 2022)

Zheng，Weijie1; Liu，Yufei2; Doerr，Benjamin2

10.1145/3520304.3534070

2022-07-09

GECCO 2022 Companion - Proceedings of the 2022 Genetic and Evolutionary Computation Conference

53-54

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. This paper for the Hot-off-the-Press track at GECCO 2022 summarizes the work Weijie Zheng, Yufei Liu, Benjamin Doerr: A First Mathematical Runtime Analysis of the Non-dominated Sorting Genetic Algorithm II (NSGA-II). AAAI2022, accepted [17].

multi-objective optimization NSGA-II runtime analysis theory

First

English

EI

20223312576718

Computation theory ; Genetic algorithms ; Population statistics ; Presses (machine tools)

Machine Tools, General:603.1 ; Computer Theory, Includes Formal Logic, Automata Theory, Switching Theory, Programming Theory:721.1 ; Optimization Techniques:921.5

2-s2.0-85136325504

Scopus

1.Department of Computer Science and Engineering,Southern University of Science and Technology,Shenzhen,China
2.Laboratoire d'Informatique (LIX),École Polytechnique,Cnrs,Institut Polytechnique de Paris,Palaiseau,France

Zheng，Weijie,Liu，Yufei,Doerr，Benjamin. A First Mathematical Runtime Analysis of the Non-dominated Sorting Genetic Algorithm II (NSGA-II) (Hot-off-the-Press Track at GECCO 2022)[C],2022:53-54.