Limit-behavior of a hybrid evolutionary algorithm for the Hasofer-Lind reliability index problem
Abstract
In probabilistic structural mechanics, the Hasofer-Lind reliability index problem is a paradigmatic equality constrained problem of searching for the minimum distance from a point to a surface. In practical engineering problems, such surface is defined implicitly, requiring the solution of a boundary-value problem. Recently, it was proposed in the literature a hybrid micro-genetic algorithm (HmGA), with mixed real-binary genotype and novel deterministic operators for equality-constraint handling, namely the Genetic Repair and Region Zooming mechanisms (G. das Neves Carneiro and C. Concei\c{c}\~ao Ant\'onio, "Global optimal reliability index of implicit composite laminate structures by evolutionary algorithms", Struct Saf, vol. 79, pp. 54-65, 2019). We investigate the limit-behavior of the HmGA and present the convergence theorems for the algorithm. It is proven that Genetic Repair is a conditionally stable mechanism, and its modes of convergence are discussed. Based on a Markov chain analysis, the conditions for the convergence with probability 1 of the HmGA are given and discussed.
Cite
@article{arxiv.2305.09511,
title = {Limit-behavior of a hybrid evolutionary algorithm for the Hasofer-Lind reliability index problem},
author = {Gonçalo das Neves Carneiro and Carlos Conceição António},
journal= {arXiv preprint arXiv:2305.09511},
year = {2023}
}