Speeding Up the NSGA-II via Dynamic Population Sizes

Abstract

Multi-objective evolutionary algorithms (MOEAs) are among the most widely and successfully applied optimizers for multi-objective problems. However, to store many optimal trade-offs (the Pareto optima) simultaneously, MOEAs are typically run with a large population of solution candidates. This slows down the algorithm and renders the choice of the population size a crucial design decision. In this work, we aim to overcome these difficulties by proposing the dynamic NSGA-II, a variant of the well-known NSGA-II that starts with a small initial population and doubles it after a user-specified number $\ddot{I}„$ of function evaluations, up to a maximum size of $N_{max}$. We prove that the dynamic NSGA-II with optimal parameters computes the Pareto front of the OneMinMax benchmark of size $n$ with high probability in $O(n{\log }^{2}n)$ function evaluations, which is considerably faster than the $\hat{I}˜(n^2\log n)$ runtime of the static NSGA-II with optimal parameters. For the OneJumpZeroJump benchmark with gap size $k$, we show a runtime of $O(n^k{\log }^{2}n)$, improving upon the known runtime of $\hat{I}˜(n^{k+1})$. We also propose a variant that uses the initial population size for a longer period and achieves slightly better performance. Finally, we show that a simple concurrent-run strategy turns our dynamic NSGA-II variants into parameter-less algorithms that exceed the above runtimes only by a logarithmic factor and hence still outperform the static NSGA-II by a factor of $\tilde{\hat{I}}\text{c◯}(n)$.

To appear in the proceedings of IJCAI 2026