Greedy permanent magnet optimization. (1st March 2023)

• Record Type: Journal Article
• Authors: Kaptanoglu, Alan A.; Conlin, Rory; Landreman, Matt
• Is Part Of: Nuclear fusion. Volume 63:Number 3(2023)
• Publication Date: 2023-03-01
• Subjects: permanent magnets -- stellarators -- greedy algorithms -- sparse regression -- combinatorial optimization -- binary quadratic programs -- quadratic knapsack problems; Nuclear fusion -- Periodicals; 621.48405
• DOI: 10.1088/1741-4326/acb4a9
• Languages: English
• ISSNs: 0029-5515

Abstract

Abstract: A number of scientific fields rely on placing permanent magnets in order to produce a desired magnetic field. We have shown in recent work that the placement process can be formulated as sparse regression. However, binary, grid-aligned solutions are desired for realistic engineering designs. We now show that the binary permanent magnet problem can be formulated as a quadratic program with quadratic equality constraints, the binary, grid-aligned problem is equivalent to the quadratic knapsack problem with multiple knapsack constraints, and the single-orientation-only problem is equivalent to the unconstrained quadratic binary problem. We then provide a set of simple greedy algorithms for solving variants of permanent magnet optimization, and demonstrate their capabilities by designing magnets for stellarator plasmas. The algorithms can a-priori produce sparse, grid-aligned, binary solutions. Despite its simple design and greedy nature, we provide an algorithm that compares with or even outperforms the state-of-the-art algorithms while being substantially faster, more flexible, and easier to use.