  We suggest a novel approach for the efficient and reliable approximation of
the Pareto front of sufficiently smooth unconstrained bi-criteria optimization
problems. Optimality conditions formulated for weighted sum scalarizations of
the problem yield a description of (parts of) the Pareto front as a parametric
curve, parameterized by the scalarization parameter (i.e., the weight in the
weighted sum scalarization). Its sensitivity w.r.t. parameter variations can be
described by an ordinary differential equation (ODE). Starting from an
arbitrary initial Pareto optimal solution, the Pareto front can then be traced
by numerical integration. We provide an error analysis based on Lipschitz
properties and suggest an explicit Runge-Kutta method for the numerical
solution of the ODE. The method is validated on bi-criteria convex quadratic
programming problems for which the exact solution is explicitly known, and
numerically tested on complex bi-criteria shape optimization problems involving
finite element discretizations of the state equation.
