Journal ID : AMA-29-08-2021-10660
[This article belongs to Volume - 52, Issue - 01]
Total View : 473

Title : Analysis on the Entropy Characters of Population Diversity and Strong Convergence (a.s.) in Gene Expression Programming

Abstract :

BS-GEP (Gene Expression Programming (GEP) based on Block Strategy) is an improved GEP in time series prediction proposed in our previous work, in which the population is divided into several blocks according to the individual fitness of each generation and the mutation operators are reset differently in each block to guarantee the population diversity. To confirm the influence of our opinion on population diver- sity, and eventually reveal the evolutionary direction of the population diversity, by employing Shannon entropy to measure diversity, the entropy characters of gene-bit mutation are investigated theoretically, and the features of diversity in the evolution are analyzed. It is shown that the entropy of gene sequences adjusts with the mutation rate in BS-GEP, so that the population diversity tends to its maximum swiftly and then lower gently. Thus BS-GEP maintains more rich population diversity than the stand- ard GEP. In addition, to verify convergence of BS-GEP is not weaker 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.

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