On Uncensored Mean First-Passage-Time Performance Experiments with Multiwalk in R p : a New Stochastic Optimization Algorithm Franc Brglez Computer Science, NC State University Raleigh, NC 27695, USA brglez@ncsu.edu 0 20 40 60 80 100 total number of steps (walklength) under restarts = 1 absolute errors based on best-known-value of function trefethen1 5e-09 5e-07 5e-05 5e-03 5e-01 5e+01 solver DEsFR1: symbol for error value = 0 plateauLmt=16 solver DEsFR1: restarts = 1 agentId=7 agentId=7 agentId=7 agentId=13 agentId=11 solver MWR04: symbol for error value = 0 plateauLmt=16 solver MWR04: restarts = 1 agentId=32 agentId=32 agentId=32 agentId=9 agentId=31 agentId=18 Summary. 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 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 <= 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 uncen- sored 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. NOTE: Unlike the original IEEE publication, this reprint has been typeset in L A T E X using the vanilla document class ‘article’. This class generates more pages when compared to the 6-page limit of the IEEE original. Please cite the paper as follows: Franc Brglez. On Uncensored Mean First-Passage-Time Performance Experiments with Multiwalk in R p : a New Stochastic Optimization Algorithm. Invited talk, IEEE Proc. 7th Int. Conf. on Reliability, InfoCom Technologies and Optimization (ICRITO’2018); Aug. 29–31, 2018, Amity University, Noida, India, 2018. For the 6-page download, see https: // people. engr. ncsu. edu/ brglez/ publications/ OPUS2-2018-mwR-ICRITO-Brglez. pdf For on-going work and additional context, see On Uncensored Global Stochastic Optimization in R p /D p and Multi-Walk Algorithms under Problem-Specific Tableau Formulations https://people.engr.ncsu.edu/brglez/publications/OPUS2-2018-mwRD-Brglez-talk.pdf Throwing Darts and Needles under Four Configurations: the Uncensored Mean First-Passage-Time of Hitting the k Decimal Digits Value of π https://people.engr.ncsu.edu/brglez/publications/OPUS2-2018-pi-tufte-Brglez.pdf arXiv:1812.03075v1 [cs.AI] 6 Dec 2018