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The main bottleneck in using optimization at the industrial level is the presence of uncertainty in the form of model mismatch and disturbances. The way uncertainty can be handled constitutes the subject of this series of two papers. The first part dealt with the characterization of the nominal solution and proposed an approach to separate the constraint-seeking from the sensitivity-seeking components of the inputs. This second part reviews various strategies for optimization under uncertainty, namely the robust and measurement-based optimization schemes. A novel scheme is proposed, where optimality is achieved by tracking the necessary conditions of optimality. The different approaches are compared via the simulation of a bioreactor for penicillin production.