What are the advantages of using a genetic algorithm in optimization of structural members over traditional gradient search methods?
Gradient-based methods can get stuck in local minimum and their performance are dependent on initial values of design variables.
Your question is specific to optimal design of steel structures and as a structural engineer, I can say the following:
In structural optimization problems,the variables are often discrete and moreover the constraints (stress, displacement, etc) are not explicit. Constraints are only available in an implicit form and must be obtained from FEM analysis. That is why evolutionary algorithms (GA, PSO, ACO, DE, ...) are more suitable for the optimization.
I hope that answers your question.
GA are part of metaheuristic algorithms, ie, they can find a good near-optimal feasible solution in a reduced computational time, but it is not usually the global optimal solution. Specifically, in GA you need to know the objective function and make a smart representation of solutions using binary strings. Also, a crossover function have to be provided. The most critical things of GA are a faster computation of objective function and how to do good crossover operation in order to avoid unfeasible solutions.