Text entry user interfaces have been a bottleneck of nontraditional computing devices.One of the promising methods is the virtual keyboard on touch screens.Various layouts have been manually designed to replace the dominant QWERTY layout.This paper presents two computerized quantitative design techniques to search for the optimal virtual keyboard.The first technique simulated the dynamics of a keyboard with "digraph springs" between keys, which produced a "Hooke's" keyboard with 41.6 wpm performance.The second technique used a Metropolis random walk algorithm guided by a "Fitts energy" objective function, which produced a "Metropolis" keyboard with 43.1 wpm performance.The paper also models and evaluates the performance of four existing keyboard layouts.We corrected erroneous estimates in the literature and predicted the performance of QWERTY, CHUBON, FITALY, OPTI to be in the neighborhood of 30, 33, 36 and 38 wpm respectively.Our best design was 40% faster than QWERTY and 10% faster than OPTI, illustrating the advantage of quantitative user interface design techniques based on models of human performance over traditional trial and error designs guided by heuristics.