In this paper we address the problem of approximating the 'knee' of a bi-objective optimization problem with stochastic search algorithms. Knees or entire knee-regions are of particular interest since such solutions are often preferred by the decision makers in many applications. Here we propose mid investigate two update strategies which can he used in combination with stochastic multi-objective search algorithms (e.g., evolutionary algorithms) and aim for the computation of the knee mid the knee-region, respectively. Finally, we demonstrate the applicability of the approach on two examples.