Discrete Sizing and Continuous Shaping Optimisation of Space Trusses using a Hybrid Metaheuristic Method

In this paper, a hybrid metaheuristic method is presented for discrete sizing and continuous shaping truss optimization problems where the structural response variables are implicit functions of the design variables. The proposed hybrid method ANGEL, which has been already introduced for continuous shaping-sizing truss optimization problems combines ant colony optimization (ACO), genetic algorithm (GA), and local search strategy (LS). ACO and GA search alternately and cooperatively in the solution space. The powerful LS algorithm, which is based on the local linearization of the constraint set and the objective function, is applied to yield a better feasible or less unfeasible solution when ACO or GA obtains a solution. According to the discrete nature of the sizing variables, in the LS process a local improvement step is formulated as a mixed integer linear programming problem (MILP). The geometrically nonlinear space structure is formulated as a large displacement structural model. The minimal weight design is subjected to stress, local buckling, and displacement constraints. The combined sizing-shaping truss optimization problems are formulated as geometrically linear and nonlinear discrete optimization problems in terms of cross-sectional design variables, and continuous in terms of shifting variables. The verification of the method is presented trough of a middle size truss bridge optimization problem under moving loads.