Guided genetic algorithm for dome optimization against instability with discrete variables

Stability is a decisive factor in the design of domes. The relative gradient of joint well-formedness (gra_r) is defined in the present paper to represent the stability of domes from the perspective of joint well-formedness. The lowest value of gra_r (gra_rmin) functions as an indicator of the buckling capacity. The gra_r and gra_rmin, numerical representations of dome stability, lay the mathematical groundwork for optimization against instability. Characterized by clarity in physical meaning and simplicity of calculation, gra_r is suitable for a high-performance optimum algorithm. To improve the buckling capacity of space domes, an optimization model against instability, which takes the maximization of gra_rmin as the objective and the member sections as discrete variables, is formulated subject to the constraints on design specifications and steel consumption. Subsequently, a guided genetic algorithm (GGA) is proposed for the stability optimization of large-scale space domes. Information on joint well-formedness that is calculated for a fitness function is re-used to identify stability-vulnerable elements and stiffness-redundant members. Mutation then operates on these members under the guidance of an instability mechanism. The GGA works on guided mutation rather than stochastic mutation of the canonical genetic algorithm, to realize oriented evolution for rapid search. The performance of the proposed method is validated on two large-scale domes. For real-life space domes, the GGA presented shows advantages in computational efficiency, robustness and engineering application, particularly for real-life large-scale domes.