论文标题
贪婪的永久磁铁优化
Greedy permanent magnet optimization
论文作者
论文摘要
许多科学领域都依赖于放置永久磁铁以产生所需的磁场。我们在最近的工作中表明，放置过程可以作为稀疏回归。但是，对于逼真的工程设计，需要二进制网格一致的解决方案。 We now show that the binary permanent magnet problem can be formulated as a quadratic program with quadratic equality constraints (QPQC), the binary, grid-aligned problem is equivalent to the quadratic knapsack problem with multiple knapsack constraints (MdQKP), and the single-orientation-only problem is equivalent to the unconstrained quadratic binary problem (BQP).然后，我们提供了一组简单的贪婪算法，用于求解永久磁铁优化的变体，并通过设计恒星等离子体的磁铁来证明它们的功能。该算法可以产生稀疏的，网格对准的二元溶液。尽管设计简单和贪婪的性质，但我们提供了一种算法，该算法的表现优于最先进的算法，同时实质上更快，更灵活且易于使用。
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 (QPQC), the binary, grid-aligned problem is equivalent to the quadratic knapsack problem with multiple knapsack constraints (MdQKP), and the single-orientation-only problem is equivalent to the unconstrained quadratic binary problem (BQP). 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 outperforms the state-of-the-art algorithms while being substantially faster, more flexible, and easier-to-use.
