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Describes the parameter estimation procedures for the non‐linear finite element analysis using the hierarchical neural network. These procedures can be classified as the neural network based inverse analysis, which has been investigated by the authors. The optimum values of the parameters involved in the non‐linear finite element analysis are generally dependent on the configuration of the analysis model, the initial condition, the boundary condition, etc., and have been determined in a heuristic manner. The procedures to estimate such multiple parameters consist of the following three steps: a set of training data, which is produced over a number of non‐linear finite element computations, is prepared; a neural network is trained using the data set; the neural network is used as a tool for searching the appropriate values of multiple parameters of the non‐linear finite element analysis. The present procedures were tested for the parameter estimation of the augmented Lagrangian method for the steady‐state incompressible viscous flow analysis and the time step evaluation of the pseudo time‐dependent stress analysis for the incompressible inelastic structure.

In an attempt to solve multiobjective optimization problems, many traditional methods scalarize an objective vector into a single objective by a weight vector. In these cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands a user to have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto‐optimal points, instead of a single point. In this paper, Pareto‐based Continuous Evolutionary Algorithms for Multiobjective Optimization problems having continuous search space are introduced. These algorithms are based on Continuous Evolutionary Algorithms, which were developed by the authors to solve single‐objective optimization problems with a continuous function and continuous search space efficiently. For multiobjective optimization, a progressive reproduction operator and a niche‐formation method for fitness sharing and a storing process for elitism are implemented in the algorithm. The operator and the niche formulation allow the solution set to be distributed widely over the Pareto‐optimal tradeoff surface. Finally, the validity of this method has been demonstrated through some numerical examples.