Abstract
Abstract This paper discusses an improved method for solving multiple objective optimal control (MOOC) problems, and efficiently obtaining the set of Pareto optimal solutions. A general MOOC procedure has been introduced in Logist et al. [2007], to derive optimal generic temperature profiles for a steady-state tubular plug flow reactor. This procedure is based on a weighted sum of the different costs, and combines analytical and numerical optimal control techniques. By varying the weights, the exact Pareto set has been obtained. However, it is known for the weighted sum approach that a uniform variation of the weights, not necessarily leads to an even spread on the Pareto front (and thus an accurate representation). In addition, the analytical derivations in the proposed procedure become intractable for large-scale systems. Therefore, this paper introduces two modifications: the use of (i) the normal constraint method (Messac and Mattson [2004]) instead of the weighted sum, and (ii) piecewise linear approximations instead of the analytical relations. Two examples, i.e., (i) a classic minimum time, minimum control effort problem, and (ii) a more real-life determination of optimal temperature profiles for tubular reactors, illustrate the enhanced performance and the general applicability of the procedure.
Published Version
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