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A rigorous empirical comparison of two stochastic solvers is important whenone 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 ofMWA 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 representsabsolute values of pairwise differences between $m$ marks. Before taking thenext step, a controller links the tableau of neighborhood matrices and computesnew and improved positions for each of the $m$ marks. The number of columns ineach neighborhood matrix is denoted as the neighborhood radius $r_n \le m-2$.Any variant of the DEA (differential evolution algorithm) has an effectivepopulation neighborhood of radius not larger than 1. Uncensoredfirst-passage-time performance experiments that vary the neighborhood radius ofa 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) significantvariability in convergence rate for seven DE-based solver configurations, and(2) consistent, monotonic, and significantly faster rate of convergence for theMW-solver prototype as we increase the neighborhood radius from 4 to itsmaximum value.

On Uncensored Mean First-Passage-Time Performance Experiments with Multiwalk in $\mathbb{R}^p$: a New Stochastic Optimization Algorithm