{"type":"ScholarlyArticle","title":"A First Runtime Analysis of NSGA-III on a Many-Objective Multimodal Problem: Provable Exponential Speedup via Stochastic Population Update","authors":[{"name":"Andre Opris","slug":"andre-opris","given":"Andre","family":"Opris","affiliation":""}],"abstract":"The NSGA-III is a prominent algorithm in evolutionary many-objective optimization. It is well-suited for optimizing functions with more than three objectives, setting it apart from the classic NSGA-II. However, theoretical insights about NSGA-III of when and why it performs well are still in its early development. This paper addresses this point and conducts a rigorous runtime analysis of NSGA-III on the many-objective OneJumpZeroJump benchmark (OJZJ for short), providing runtime bounds where the number of objectives is constant. We show that NSGA-III finds the Pareto front of OJZJ in time O(n^(k+d/2)+ N n ln(n)) where n is the problem size, d is the number of objectives, k is the gap size, a problem specific parameter, if its population size N is in 2^(O(n)) and at least (2n/d+1)^(d/2). Notably, NSGA-III is faster than NSGA-II by a factor of N/n^(d/2) for N=omega(n^(d/2)) . We also show that a stochastic population update provably guarantees a speedup of order (k/b)^(k-1) in the runtime where b>0 is a constant. Besides a paper of Wietheger and Doerr (PPSN 2024), this is the first rigorous runtime analysis of NSGA-III on OJZJ. Proving these bounds requires a much deeper understanding of the population dynamics of NSGA-III than previous papers achieved.","doi":"10.24963/ijcai.2025/990","url":"https://ijcai.org/proceedings/2025/990","pdf":"https://ijcai.org/proceedings/2025/0990.pdf","markdown":"https://ijcai.org/proceedings/2025/990.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/990","volume":{"slug":"2025","title":"Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2025","url":"https://ijcai.org/proceedings/2025/","year":2025,"location":"Montreal, Canada","dates":"16-22 August 2025","editors":"James Kwok","isbn":"978-1-956792-06-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2025"},"section":"Search","track":"Main Track","number":990,"pages":{"first":8903,"last":8911},"keywords":["Search: S: Combinatorial search and optimisation","Search: S: Heuristic search","Search: S: Evolutionary computation"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}