On Uncensored Mean First-Passage-Time Performance Experiments with Multi-Walk: a New Stochastic Optimization Algorithm

Abstract

A rigorous empirical comparison of two stochastic solvers is important when one of the solvers is a prototype of a new algorithm such as multi-walk (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 $m\ast(m - 2)$, 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 $r_{n} < = m - 2$. 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. This 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.