Latin Hypercube Sampling and Pattern Search in Magnetic Field Optimization Problems

Latin hypercube is a sampling technique for searching n dimensional space. Like Monte Carlo methods, it retains random qualities, and yet Latin hypercube is consistently more effective than Monte Carlo. Despite this fact, not a single paper has been published in IEEE Transactions on Magnetics on its use. Field analysis is a long way from delivering vectorized solutions where a vector of inputs can be processed. Stochastic algorithms are exceptionally inefficient compared to their deterministic counterparts. The best optimization tool would be a deterministic method which quickly and effectively interrogates the search space. Latin hypercube sampling, combined with pattern search solutions, comes close to achieving that objective. An improved solution for the magnetic TEAM Workshop problem 22 is presented using these tools.