Efficient deterministic multiple objective optimal control of (bio)chemical processes

In practical optimal control problems multiple and conflicting objectives are often present, giving rise to a set of Pareto optimal solutions. Although combining the different objectives into a convex weighted sum and varying the weights is the most common approach to generate the Pareto front (when deterministic optimisation routines are exploited), it suffers from several intrinsic drawbacks. A uniform variation of the weights does not necessarily lead to an even spread on the Pareto front, and points in non-convex parts of the Pareto front cannot be obtained [Das, I., Dennis, J.E., 1997. A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems. Structural Optimization 14, 63–69]. Therefore, this paper investigates alternative approaches based on novel methods as normal boundary intersection [Das, I., Dennis, J.E., 1998. Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM Journal on Optimization 8, 631–657] and normalised normal constraint [Messac, A., Ismail-Yahaya, A., Mattson, C.A., 2003. The normalized normal constraint method for generating the Pareto frontier. Structural and Multidisciplinary Optimization 25, 86–98] to mitigate these drawbacks. The resulting multiple objective optimal control procedures are successfully used in (i) the design of a chemical reactor with conflicting conversion and energy costs, and (ii) the control of a bioreactor with a conflict between yield and productivity.