An Application of Analytical Multi-Objective Optimizationto Truss Structures

The Fritz John necessary condition for Pareto-optimality has been set into matrix form and used for introducing a method for the analytical derivation of the Paretooptimal set. The procedure for the analytical derivation of the Pareto-optimal set depends on the number of design variables n, of objective functions k and of constraints m. Some relevant cases are discussed in the paper. A simple formula for deriving the Pareto-optimal set is presented for a bi-objective unconstrained problem. The new formula has been applied to the optimization (minimization of mass and compliance) of topology, geometry and size of a truss structure under single and multiple loads conditions.