Why Popular MOEAs are Popular: Proven Advantages in Approximating the Pareto Front
Mingfeng Li, Qiang Zhang, Weijie Zheng, Benjamin Doerr
Recent breakthroughs in the analysis of multi-objective evolutionary algorithms (MOEAs) are mathematical runtime analyses of those algorithms which are intensively used in practice. So far, most of these results show the same performance as previously known for simple algorithms like the GSEMO. The few results indicating advantages of the popular MOEAs share the same shortages: They consider the performance for the problem of computing the full Pareto front, (of some algorithms enriched with newly invented mechanisms,) and this on newly designed benchmarks. In this work, we overcome these shortcomings by analyzing how  existing popular MOEAs approximate the Pareto front of the established LargeFront benchmark. We prove that all popular MOEAs, including NSGA-II (sequential version), NSGA-III, SMS-EMOA, and SPEA2, only need an expected time of $O(n^2 \log n)$ function evaluations to compute an additive $\varepsilon$-approximation of the Pareto front of the LargeFront benchmark. This contrasts with the already proven exponential runtime (with high probability) of the GSEMO on the same task. % (which we also extend to any dominance-only black-box MOEA).  This result is the first mathematical runtime analysis showing and explaining the superiority of popular MOEAs over simple ones like the GSEMO for the central task of computing good approximations to the Pareto front.