On Uncensored Mean First-Passage-Time Performance Experiments with
  Multiwalk in $\mathbb{R}^p$: a New Stochastic Optimization Algorithm
  A rigorous empirical comparison of two stochastic solvers is important when
one of the solvers is a prototype of a new algorithm such as multiwalk (MWA).
When searching for global minima in $\mathbb{R}^p$, the key data structures of
MWA include: $p$ rulers with each ruler assigned $m$ marks and a set of $p$
neighborhood matrices of size up to $m(m-2)$, where each entry represents
absolute values of pairwise differences between $m$ marks. Before taking the
next step, a controller links the tableau of neighborhood matrices and computes
new and improved positions for each of the $m$ marks. The number of columns in
each neighborhood matrix is denoted as the neighborhood radius $r_n \le m-2$.
Any variant of the DEA (differential evolution algorithm) has an effective
population neighborhood of radius not larger than 1. Uncensored
first-passage-time performance experiments that vary the neighborhood radius of
a MW-solver can thus be readily compared to existing variants of DE-solvers.
The paper considers seven test cases of increasing complexity and demonstrates,
under uncensored first-passage-time performance experiments: (1) significant
variability in convergence rate for seven DE-based solver configurations, and
(2) consistent, monotonic, and significantly faster rate of convergence for the
MW-solver prototype as we increase the neighborhood radius from 4 to its
maximum value.
