Research And Application Of Gene Expression Programming In Software Reliability Modeling

In the study of software reliability, reliability model is the key matter. A suitable reliability model of a software system can support reliability quantitative analysis technologies, in order to guide the development process. There are not less than one hundred kinds of software reliability models; however, all of them are generally limited in a certain application range, also say, their universality is poor. Seeking out a software reliability model with excellent universality and prediction accuracy is of great significance.At present, research focuses on software reliability models based on Computational Intelligence (CI), of which models based on Genetic Programming (GP) and Back Propagation (BP)(a kind of Artificial Neural Networks (ANN)) are two representatives. But prediction accuracy of the two is impacted by their inherent defects. Gene Expression Programming (GEP) is a kind of high efficient evolutionary algorithm, with a brand new information expression approach, suitable for processing in a highly nonlinear system. GA has difficulty in complicated problems, while GP owns a low efficiency. But GEP can overcome them both. Compared with ANN, it is easy to apply because there is no need for division level and training various samples. GEP is now a research hot spot in CI.The basic technologies of GEP are described in detail. On analysis of characteristics of GA and GP technologies, the root cause of GEP high efficiency is revealed. But GEP also has an inherent limitation, called premature convergence. For this, from the perspective of population diversity, an improved algorithm, Gene Expression Programming based on Block Strategy (BS-GEP) is proposed in this paper, adjusting genetic operators dynamically, to avoid the algorithm into a local convergence. To confirm the validity of the new strategy, by employing Shannon entropy as a diversity measure, the entropy characters of gene-bit mutation are investigated theoretically, and the features of population diversity in the evolution are analyzed. In addition, to verify convergence of BS-GEP is not weak than of GEP, which is proved as Strong Convergence in Probability, martingale theory is adopted to demonstrate BS-GEP with Almost Everywhere Strong Convergence (a.s.) in its Markov chain analysis, to complement the convergence theory of BS-GEP. Taking software failure series as samples, GEP and its improved algorithm are adopted to research comprehensive efforts of all underlying factors influencing software failure, and evolve to obtain an optimal software failure characteristic function, to build mathematical models. Simulations results show that the modeling approaches based on both GEP and BS-GEP are able to model on failure interval series, as well as failure cumulative time series, thus they can lower requirements of failure data collection. BS-GEP can find an optimal model owning excellent fitting and prediction capabilities with higher efficiency. It is more suitable for reliability modeling. Consequently, it makes significant progress in software reliability modeling theories.