For the complex ocean engineering structures, most of the functions of limit state are implicit. It is very difficult to calculate the reliability by using genetic algorithms when the penalty function is applied. An improved genetic algorithms is proposed in this article. Firstly, two group initial populations are generated in the space of G>0 (the safe domain) and G<0 (the failure domain), respectively, and then a bisection method is applied iteratively to generate a new population on the lines between a population located in G>0 and another population located in G<0. In this way, the new population will approach to the limit state function gradually. So, the constraints in optimization model will be released, which can be solved by GAs easily. Furthermore, the sensitivity analysis of the reliability to changes in distribution parameters is also made.


In the independent multidimensional standard normal space, reliability index β is the minimum distance from the curve surface of limit state to origin (Schuëller, 1989). So, the solving process of reliability becomes the solving process of optimization with constraints. When the constraints of the optimization model to solve reliability are explicit, the model can be solved with genetic algorithms (GAs) through which the optimal solution or approximately optimal solution in the whole space could be searched rapidly (Xu, 2000). But for the complex ocean engineering structures, most of the functions of limit state are implicit. For handling the nonlinear programming problems with implicit constraints by GAs, most of them are based on the concept of penalty functions, by which infeasible solutions are penalized (Joines, 1994). Although several ideas have been proposed about how the penalty function is designed and applied to infeasible solutions, penalty-based methods still have some shortcomings, and the experimental results are disappointed in many test case (Michalewicz, 1996).

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