Bounding NBLM neighbourhood's adequate sizes

Abstract

We try to address the problem of a priori selection of the adequate size for NBLM neighbourhoods. The application of the concept of neural neighbourhood to the Levenberg-Marquardt optimization method led us to the development of the NBLM algorithm. When this algorithm is used, there can be neighbourhoods that, not only produce significant reductions in memory requirements, but that also achieve better time performance than that of the Levenberg-Marquardt method. However, as long as the problem of choosing an appropriate neighbourhood size is not solved, the NBLM algorithm will not be able to offer the best possible performance.