Many practical engineering problems involve the determination of optimal control trajectories for given multiple and conflicting objectives. These conflicting objectives typically give rise to a set of Pareto optimal solutions. To enhance real-time decision making efficient approaches are required for determining the Pareto set in a fast and accurate way. Hereto, the current paper integrates efficient multiple objective scalarisation strategies (e.g., Normal Boundary Intersection and Normalised Normal Constraint) with fast deterministic approaches for dynamic optimisation (e.g., Single and Multiple Shooting). All techniques have been implemented as an easy-to-use add-on module of the automatic control and dynamic optimisation toolkit A-CADO (both freely available at www.acadotoolkit.org). Several algorithmic synergies (e.g., hot-start initialisation strategies) are exploited for an additional speed-up. The features of ACADO Multi-Objective are discussed and its use is illustrated on different multiple objective optimal control problems arising in several engineering disciplines.
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 document contains the post-print pdf-version of the refereed paper: "Optimal experiment design for dynamic bioprocesses: a multiobjective approach" by Dries Telen, Filip Logist, Eva Van Derlinden, Ignace Tack and Jan Van Impe which has been archived in the university repository Lirias (https://lirias.kuleuven.be/) of the Katholieke Universiteit Leuven. The content is identical to the content of the published paper, but without the final typesetting by the publisher.
BackgroundMicro-organisms play an important role in various industrial sectors (including biochemical, food and pharmaceutical industries). A profound insight in the biochemical reactions inside micro-organisms enables an improved biochemical process control. Biological networks are an important tool in systems biology for incorporating microscopic level knowledge. Biochemical processes are typically dynamic and the cells have often more than one objective which are typically conflicting, e.g., minimizing the energy consumption while maximizing the production of a specific metabolite. Therefore multi-objective optimization is needed to compute trade-offs between those conflicting objectives. In model-based optimization, one of the inherent problems is the presence of uncertainty. In biological processes, this uncertainty can be present due to, e.g., inherent biological variability. Not taking this uncertainty into account, possibly leads to the violation of constraints and erroneous estimates of the actual objective function(s). To account for the variance in model predictions and compute a prediction interval, this uncertainty should be taken into account during process optimization. This leads to a challenging optimization problem under uncertainty, which requires a robustified solution.ResultsThree techniques for uncertainty propagation: linearization, sigma points and polynomial chaos expansion, are compared for the dynamic optimization of biological networks under parametric uncertainty. These approaches are compared in two case studies: (i) a three-step linear pathway model in which the accumulation of intermediate metabolites has to be minimized and (ii) a glycolysis inspired network model in which a multi-objective optimization problem is considered, being the minimization of the enzymatic cost and the minimization of the end time before reaching a minimum extracellular metabolite concentration. A Monte Carlo simulation procedure has been applied for the assessment of the constraint violations. For the multi-objective case study one Pareto point has been considered for the assessment of the constraint violations. However, this analysis can be performed for any Pareto point.ConclusionsThe different uncertainty propagation strategies each offer a robustified solution under parametric uncertainty. When making the trade-off between computation time and the robustness of the obtained profiles, the sigma points and polynomial chaos expansion strategies score better in reducing the percentage of constraint violations. This has been investigated for a normal and a uniform parametric uncertainty distribution. The polynomial chaos expansion approach allows to directly take prior knowledge of the parametric uncertainty distribution into account.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-016-0328-6) contains supplementary material, which is available to authorized users.
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