Mathematically, the notion of an optimal trade-off is formalized by the concept of Pareto optimality (see SI for an extended description) . The Pareto theory tells us that a combination of target values constitutes an optimal trade-off, if an improvement in one target is always detrimental to at least one other target. Consider, for instance, the lignin yield and the number of β-O-4 linkages. If we are interested in achieving both high yield and a high β-O-4 content, we have an optimal trade-off for fixed processing conditions (P f , T ) if an increase in the yield always leads to a decrease in the β-O-4 content and vice versa. We refer to an optimal trade-off as a Pareto point, and to the set of all Pareto points as the Pareto front. Similarly, the lignin extraction conditions corresponding to the Pareto points are known as the Pareto optimal solutions. Once the Pareto front is known, a particular Pareto point can be chosen as the preferred solution to the optimization problem based on some additional design criteria, e.g., a minimum required yield.