{"type":"ScholarlyArticle","title":"Faster Guarantees of Evolutionary Algorithms for Maximization of Monotone Submodular Functions","authors":[{"name":"Victoria G. Crawford","slug":"victoria-g-crawford","given":"Victoria G.","family":"Crawford","affiliation":""}],"abstract":"In this paper, the monotone submodular maximization problem (SM) is studied. SM is to find a subset of size kappa from a universe of size n that maximizes a monotone submodular objective function f . We show using a novel analysis that the Pareto optimization algorithm achieves a worst-case ratio of (1 − epsilon)(1 − 1/e) in expectation for every cardinality constraint kappa < P , where P ≤ n + 1 is an input, in O(nP ln(1/epsilon)) queries of f . In addition, a novel evolutionary algorithm called the biased Pareto optimization algorithm, is proposed that achieves a worst-case ratio of (1 − epsilon)(1 − 1/e − epsilon) in expectation for every cardinality constraint kappa < P in O(n ln(P ) ln(1/epsilon)) queries of f . Further, the biased Pareto optimization algorithm can be modified in order to achieve a a worst-case ratio of (1 − epsilon)(1 − 1/e − epsilon) in expectation for cardinality constraint kappa in O(n ln(1/epsilon)) queries of f . An empirical evaluation corroborates our theoretical analysis of the algorithms, as the algorithms exceed the stochastic greedy solution value at roughly when one would expect based upon our analysis.","doi":"10.24963/ijcai.2021/229","url":"https://ijcai.org/proceedings/2021/229","pdf":"https://ijcai.org/proceedings/2021/0229.pdf","markdown":"https://ijcai.org/proceedings/2021/229.md","bibtex":"https://ijcai.org/proceedings/2021/bibtex/229","volume":{"slug":"2021","title":"Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2021","url":"https://ijcai.org/proceedings/2021/","year":2021,"location":"Montreal","dates":"19-27 August 2021","editors":"Prof. Zhi-Hua Zhou","isbn":"978-0-9992411-9-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2021"},"section":"Heuristic Search and Game Playing","track":"Main Track","number":229,"pages":{"first":1661,"last":1667},"keywords":["Heuristic Search and Game Playing: Combinatorial Search and Optimisation"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}