Statistical Distribution of Generation-to-Success in GP: Application to Model Accumulated Success Probability

Abstract

Esta es la versión de autor de la comunicación de congreso publicada en: This is an author produced version of a paper published in: Abstract. Many different metrics have been defined in Genetic Programming. Depending on the experiment requirements and objectives, a collection of measures are selected in order to achieve an understanding of the algorithm behaviour. One of the most common metrics is the accumulated success probability, which evaluates the probability of an algorithm to achieve a solution in a certain generation. We propose a model of accumulated success probability composed by two parts, a binomial distribution that models the total number of success, and a lognormal approximation to the generation-to-success, that models the variation of the success probability with the generation.

Effects of the lack of selective pressure on the expected run-time distribution in genetic programming

“…In order to give an analytic model, we performed a run-time analysis of some common GP problems, finding that the expected run-time, measured in generations, fits well a lognormal distribution. This paper extends [8] and addresses a new research question: The relationship between the expected run-time distribution and the lack of selective pressure. In contrast to [8] , this study includes two new problem instances to study their run-time lognormality in a standard parameter setting and analyzes the influence of the selective pressure to the expected run-time distribution.…”

“…This paper extends [8] and addresses a new research question: The relationship between the expected run-time distribution and the lack of selective pressure. In contrast to [8] , this study includes two new problem instances to study their run-time lognormality in a standard parameter setting and analyzes the influence of the selective pressure to the expected run-time distribution. The results draw a richer -and more complex-scenario.…”

“…The resulting run-time distribution was compared to several distributions (normal, lognormal, Weibull and logistic), finding that the closest one is the lognormal [8], which can be converted into normal just by taking logarithms. With this relationship in mind, we tested the normality of the six empirical distributions by representing the quantile plots of their logarithm, the result is in Fig.…”

“…The term that is probably most widely used is Run-Time Distribution, which is the cumulative distribution function of the run-time [6]; in case that time is measured in an architecture-independent way the term Run-Length Distribution is preferred [7]. Some authors prefer constraining the run-time analysis to those runs that found a solution, using different terms to name it, such as expected run-time [3] or time-to-target [1] or generation-tosuccess [8].…”

“…In [8], we proposed a model of success probability based on its decomposition on two components, the expected run-time distribution and the success rate. In order to give an analytic model, we performed a run-time analysis of some common GP problems, finding that the expected run-time, measured in generations, fits well a lognormal distribution.…”