Structural optimization has been widely studied over the last forty years. Although Mathematical Programming has been the main tool during the first twenty years, it ran out of steam in front of a new group metaheuristic techniques based in Evolutionary Computation. Among them, Genetic Algorithms are meaningfully highlighted.
During the last years structural optimization has evolved from mere size optimization, to number of bars and joints placement (topology) optimization, and finally to simultaneous optimization.
The irruption of these new techniques in the field of structural optimization is owed, to a large extent, to mathematical programming lack of capacity to manage the simultaneous optimization owed to constraint and design variables high nonlinearities.
However, metaheuristic techniques are mathematically simpler and computationally easier because it is not required any extra information, aside from the objective function, to evaluate the solution fitness. Therefore, there are not required any linearization process neither function derivatives.
The main aim of present work is to go further a little in the simultaneous optimization of design variables, defining a new algorithm that does not need a predefined structure and covers the geometry parameters. Unlike current methods, the developed algorithm does not require any initial structure neither another type of additional information, apart from the load and support keypoints and support class definition.
The new algorithm lays assuming the following hypothesis: The previous definition of the form, geometry, rule or preconceived model implies a design constraint by themselves and so such algorithm, which is not subjected to that constraint must generate better designs, or at least as good as the previous ones.
A new algorithm was developed using this hypothesis, using a mixed code, adapted to each group of design variables, defining different operators who act independently on each group. The algorithm incorporates, in addition, some operators to ensure the solution's legality before being evaluated, as well as a group of strategies oriented to keep the solution diversity and to reduce the computational effort, the Achilles' heel of metaheuristics techniques.
Later, the algorithm was proven by a classical structural optimization problem: the ten-bar and six nodes cantilever structure, considering displacement and stress constraints. Using this structure as a benchmark, the different strategies implemented in the algorithm, for each operator over each group of design variables, were individually evaluated. As a result, the lower weight design reported, until now, was obtained, considering until sixty scientific papers where the structure was used as a benchmark.
Through the study of the evolutionary process developed during the benchmarking, and by comparison between the previously reported designs, it can be concluded that the previous reported algorithms were constrained by their own definition, conditioning so their results, so the initial hypothesis was proven. Moreover, the theorems of Fleron were proven, and also it was possible to generalize the optimum topology because it remained unchanged during all runs.
Between the main contributions of the present work, apart from the algorithm development, it can be stood: the new genetic operators, the penalty function, the possibility of acquire new information by the evolutionary process (owed to the algorithm definition) and finally obtaining a new minimum weight for the benchmark structure, a 10,92 lower than any other reported before.