The gradient projection algorithm with adaptive mutation step length for non-probabilistic reliability index

Ciljajući na probleme odabira parametra korak-veličina i prerane konvergencije koja se dogodila kod pretraživanja na lokalnom optimalnom području u dizajnu adaptivnog gradijenta projekcijskog algoritma u ovom radu, uspostavljena je strategija mehanizma prilagodljive varijable korak-veličina i mehanizma prilagodljive promjenljive varijable korak-veličina. Uvedene su u algoritam gradijenta projekcije i upotrebljene za reguliranje duljine koraka iteracije. Kroz primjere indeksa nevjerojatnosne pouzdanosti može se pokazati da se tom metodom može brzo i točno izračunati indeks pouzdanosti kad model ima višestruke varijable i složenu funkciju graničnog stanja. Kod komparacije i kontrastiranja ovog algoritma s algoritmom gradijenta projekcije, taj algoritam nije osjetljiv na položaj polazne točke. Tako on ne samo da uzima u obzir i lokalnu performansu i globalnu sposobnost pretraživanja već posjeduje i veliku brzinu konvergencije i visoku preciznost. Stoga je to učinkovit i praktičan algoritam optimizacije.Aiming at the problems of selection parameter step-size and premature convergence that occurred when searching the local area in the optimal design of adaptive gradient projection algorithm in this paper, adaptive variable step-size mechanism strategy and adaptive variable step-size mechanism were established. They were introduced into the gradient projection algorithm, and were used to control iteration step length. Through the examples of non-probabilistic reliability index, it can be showed that the method could quickly and accurately calculate the reliability index when the model had multiple variables and complex limit state function. To compare and contrast this algorithm with the simple gradient projection algorithm, this algorithm is not sensitive to the initial point position. And it not only takes into account both local performance and global search ability, but also has fast convergence speed and high precision. So it is an efficient and practical optimization algorithm