- author = "Jonas Schmitt and Harald Koestler",
- title = "Evolving Generalizable Multigrid-Based Helmholtz Preconditioners with Grammar-Guided Genetic Programming",
- booktitle = "Proceedings of the 2022 Genetic and Evolutionary Computation Conference",
- year = "2022",
- editor = "Alma Rahat and Jonathan Fieldsend and Markus Wagner and Sara Tari and Nelishia Pillay and Irene Moser and Aldeida Aleti and Ales Zamuda and Ahmed Kheiri and Erik Hemberg and Christopher Cleghorn and Chao-li Sun and Georgios Yannakakis and Nicolas Bredeche and Gabriela Ochoa and Bilel Derbel and Gisele L. Pappa and Sebastian Risi and Laetitia Jourdan and Hiroyuki Sato and Petr Posik and Ofer Shir and Renato Tinos and John Woodward and Malcolm Heywood and Elizabeth Wanner and Leonardo Trujillo and Domagoj Jakobovic and Risto Miikkulainen and Bing Xue and Aneta Neumann and Richard Allmendinger and Inmaculada Medina-Bulo and Slim Bechikh and Andrew M. Sutton and Pietro Simone Oliveto",
- pages = "1009--1018",
- address = "Boston, USA",
- series = "GECCO '22",
- month = "9-13 " # jul,
- organisation = "SIGEVO",
- publisher = "Association for Computing Machinery",
- publisher_address = "New York, NY, USA",
- note = "Winner Gold Award 2022 HUMIES",
- keywords = "genetic algorithms, genetic programming, Grammars and context-free languages, Mathematics of computing, Solvers, Partial differential equations., Multigrid, Preconditioning, Helmholtz Equation, Grammar-Based, Shifted Laplacian, Generalisation, Multi-Objective, Partial Differential Equations, Artificial Intelligence, multiobjective, generalization, shifted laplacian, grammar-based, parallel C++ Code",
- isbn13 = "978-1-4503-9237-2",
-
URL = "
https://www.human-competitive.org/sites/default/files/humies_entry_schmitt.txt",
-
URL = "https://arxiv.org/abs/2204.12846",
-
URL = "
https://www.human-competitive.org/sites/default/files/article_a.pdf",
-
DOI = "
doi:10.1145/3512290.3528688",
-
video_url = "https://vimeo.com/723650631",
- size = "10 pages",
- abstract = "Solving the indefinite Helmholtz equation is not only crucial for the understanding of many physical phenomena but also represents an outstandingly-difficult benchmark problem for the successful application of numerical methods. we introduce a new approach for evolving efficient preconditioned iterative solvers for Helmholtz problems with multi-objective grammar-guided genetic programming. Our approach is based on a novel context-free grammar, which enables the construction of multigrid preconditioners that employ a tailored sequence of operations on each discretisation level. To find solvers that generalise well over the given domain, we propose a custom method of successive problem difficulty adaption,in which we evaluate a preconditioner efficiency on increasingly ill-conditioned problem instances. We demonstrate its effectiveness by evolving multigrid-based preconditioners for a two-dimensional indefinite Helmholtz problem that outperform several human-designed methods for different wavenumbers up to systems of linear equations with more than a million unknowns",
-
notes = "See also \cite{Schmitt:GPEM}
GECCO-2022 A Recombination of the 31st International Conference on Genetic Algorithms (ICGA) and the 27th Annual Genetic Programming Conference (GP)",
