Approximating the Pareto curve to help solve biobjective design problems

When faced with multiple objectives, designers have to find ways to combine these objectives to find the solution that satisfies acceptable trade-off levels. In this paper, we present a methodology based on approximating the Pareto set of biobjective problems and presenting these trade-off graphs to the designer to facilitate decisions on trade-off. Once a solution is selected from the approximated set, the designer can select to either set a target on one or both objectives and use one of two methods to find the sought after solution. The paper details the methodology and applies it to three structural problems of increasing complexity. showing that the procedure provides also useful feedback even in the case of nonconvex Pareto sets.