Bi-objective Optimization of Truss Structure with Discrete Variables via Genetic Algorithm

This work presents an integrated method for the bi-objective optimization of truss structures with discrete variables using a Genetic Algorithm. The problem consists of simultaneously minimizing the total mass of the structure and the nodal displacement at a critical point under external loading. The structural analysis is performed analytically by the method of joints combined with the principle of virtual work, coupled directly to the fitness function of the genetic algorithm. The accuracy of the displacement calculation was verified by comparison with the Ftool software. The approximate Pareto front is systematically generated by varying the weights of the objective function. The stability of the algorithm is assessed through 30 independent runs, whose results reveal high consistency and identify two distinct attractors in the search space.