The present study is an attempt to propose a mutation-based real-coded genetic algorithm (MBRCGA) for sizing and layout Optimization of planar and spatial truss structures. The Gaussian mutation operator is used to create the reproduction operators. An adaptive tournament selection mechanism in combination with adaptive Gaussian mutation operators are proposed to achieve an effective search in the design space. The standard deviation of design variables is used as a key factor in the adaptation of mutation operators. The reliability of the proposed algorithm is investigated in typical sizing and layout Optimization problems with both discrete and continuous design variables. The numerical results clearly indicated the competitiveness of MBRCGA in comparison with previously presented methods in the literature.

The optimized shape of trusses are found by presenting a new selection and reproduction operator. The stress, buckling an displacement constraints, consistent with design code, are used. Design variables are discrete size variables (member areas) and continuous shape variables (nodal coardinates). The proposed methods, is fast and has a stable convergence. In addition, it results in an optimized structure with low weight.

New penalty functions, which have better convergence properties, as compared to the commonly used exterior and interior penalty functions, have been proposed in this paper. The convergence behavior and accuracy of ordinary penalty functions depend on the selection of appropriate penalty parameters. The Optimization of ordinary penalty functions is accomplished after several rounds of Optimization where, at each round a different but fixed value of penalty parameter is used. While some useful hints and rules for the selection of suitable penalty parameter values have been provided by different authors, the objective of this paper has been to improve this procedure by including the penalty parameter in the design vector, so that it can be modified during the Optimization, automatically, in order to improve the convergence characteristics. This can also help accomplish Optimization in only one round, which is of considerable importance when it is desired to solve a constrained problem by using genetic algorithms. The proof of convergence to the optimum solution of the proposed functions is also included in the paper. Ten-bar and three-bar truss examples are used for illustration through which the convergence of ordinary and new functions are evaluated and compared. The results show that the new penalty functions can outperform the ordinary functions, especially in combination with genetic algorithms.

In this paper, the effect of angle between predictor and corrector surfaces on the Structural analysis is investigated. Two objective functions are formulated based on this angle and also the load factor. Optimizing these functions, and using the Structural equilibrium path’s geometry, lead to two new constraints for the nonlinear solver. Besides, one more formula is achieved, which was previously found by other researchers, via a different mathematical process. Several benchmark structures, which have geometric nonlinear behavior, are analyzed with the proposed methods. The finite element method is utilized to analyze these problems.The abilities of suggested schemes are evaluated in tracing the complex equilibrium paths.Moreover, comparison study for the required number of increments and iterations is performed. Results reflect the robustness of the authors’ formulations.