Multi-objective optimization for prestress design of cable-strut structures

Load bearing capacity of a cable-strut structure is dependent on the level and distribution of prestress. Although a higher prestress level enhances overall stiffness of the structure, this condition may demand larger member sectional areas and material cost. The effect of fabrication and installation error should also be incorporated in the prestress design. This paper presents a new optimization method for prestress design of cable-strut structures. A multi-objective optimization problem is formulated and solved to obtain preferred coefficient vectors of prestress modes with the following four objective functions: (1) minimize average area of members; (2) maximize minimum eigenvalue of stiffness matrix; (3) minimize prestress variance of cables; and (4) minimize maximum eigenvalue of error sensitivity matrix. Pareto optimal solutions are obtained by NSGA-II. Among the Pareto optimal solutions, the most preferred solution is selected using PROMETHEE-II. Two examples are presented to illustrate the proposed process. The results are compared with those by existing methods of optimization with a single objective function. Significance of each objective function is also evaluated by the number of remaining Pareto optimal solutions after removal of the objective function