Interval analysis based robust truss optimization with continuous and discrete variables using mix-coded genetic algorithm

Abstract

The problem of optimizing truss structures in the presence of uncertain parameters considering both continuous and discrete design variables is studied. An interval analysis based robust optimization method combined with the improved genetic algorithm is proposed for solving the problem. Uncertain parameters are assumed to be bounded in specified intervals. The natural interval extensions are employed to obtain explicitly a conservative approximation of the upper and lower bounds of the structural response, and hereby the bounds of the objective function and the constraint function. This way the uncertainty design may be performed in a very efficient manner in comparison with the probabilistic analysis based method. A mix-coded genetic algorithm (GA), where the discrete variables are coded with binary numbers while the continuous variables are coded with real numbers, is developed to deal with simultaneously the continuous and discrete design variables of the optimization model. An improved differences control strategy is proposed to avoid the GA getting stuck in local optima. Several numerical examples concerning the optimization of plane and space truss structures with continuous, discrete or mixed design variables are presented to validate the method developed in the present paper. Monte Carlo simulation shows that the interval analysis based optimization method gives much more robust designs in comparison with the deterministic optimization method.