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 and Dennis, 1997). Therefore, this paper investigates alternative approaches based on novel methods as Normal Boundary Intersection (Das and Dennis, 1998) and Normalised Normal Constraint (Messac et al., 2003;Messac and Mattson, 2004) 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.
This paper studies the design of optimal temperature profiles for a class of exothermic, jacketed dispersive tubular reactors under steady-state conditions and subject to maximum temperature constraints. The studied class ranges from perfectly mixed continuous stirred tank reactors to plug flow reactors. The aim is to derive the Pareto optimal set of temperature profiles for conflicting conversion and energy costs, while extracting generic features from the obtained solutions. Hereto, a four step procedure which is based on a weighted sum of both costs and which combines indirect, analytical and direct, numerical optimal control techniques, is employed. The generic features are studied (i ) along the Pareto set by varying the weights and (ii ) along the reactor class by adapting the dispersion level.
This document contains the post-print pdf-version of the refereed paper: "Detailed steady-state simulation of tubular reactors for LDPE production: influence of numerical integration accuracy."
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