{"type":"ScholarlyArticle","title":"Choosing the Right Algorithm With Hints From Complexity Theory","authors":[{"name":"Shouda Wang","slug":"shouda-wang","given":"Shouda","family":"Wang","affiliation":"Laboratoire d'Informatique (LIX) , École Polytechnique , CNRS , Institut Polytechnique de Paris , France"},{"name":"Weijie Zheng","slug":"weijie-zheng","given":"Weijie","family":"Zheng","affiliation":"Guangdong Provincial Key Laboratory of Brain-inspired Intelligent Computation , Department of Computer Science and Engineering , Southern University of Science and Technology , China"},{"name":"Benjamin Doerr","slug":"benjamin-doerr","given":"Benjamin","family":"Doerr","affiliation":"Laboratoire d'Informatique (LIX) , École Polytechnique , CNRS , Institut Polytechnique de Paris , France"}],"abstract":"Choosing a suitable algorithm from the myriads of different search heuristics is difficult when faced with a novel optimization problem. In this work, we argue that the purely academic question of what could be the best possible algorithm in a certain broad class of black-box optimizers can give fruitful indications in which direction to search for good established optimization heuristics. We demonstrate this approach on the recently proposed DLB benchmark, for which the only known results are O(n^3) runtimes for several classic evolutionary algorithms and an O(n^2 log n) runtime for an estimation-of-distribution algorithm. Our finding that the unary unbiased black-box complexity is only O(n^2) suggests the Metropolis algorithm as an interesting candidate and we prove that it solves the DLB problem in quadratic time. Since we also prove that better runtimes cannot be obtained in the class of unary unbiased algorithms, we shift our attention to algorithms that use the information of more parents to generate new solutions. An artificial algorithm of this type having an O(n log n) runtime leads to the result that the significance-based compact genetic algorithm (sig-cGA) can solve the DLB problem also in time O(n log n). Our experiments show a remarkably good performance of the Metropolis algorithm, clearly the best of all algorithms regarded for reasonable problem sizes.","doi":"10.24963/ijcai.2021/234","url":"https://ijcai.org/proceedings/2021/234","pdf":"https://ijcai.org/proceedings/2021/0234.pdf","markdown":"https://ijcai.org/proceedings/2021/234.md","bibtex":"https://ijcai.org/proceedings/2021/bibtex/234","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":234,"pages":{"first":1697,"last":1703},"keywords":["Heuristic Search and Game Playing: Heuristic Search","Heuristic Search and Game Playing: Combinatorial Search and Optimisation","Heuristic Search and Game Playing: Meta-Reasoning and Meta-Heuristics"],"videos":[],"references":[{"position":1,"raw":"[Badkobeh et al., 2014] Golnaz Badkobeh, Per Kristian Lehre, and Dirk Sudholt. 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