Continuous and Discrete Composite Adjoints for the Hessian of the Lagrangian in Shooting Algorithms for Dynamic Optimization

Expert Systems with Applications

Hufkens

Impe

et al. 2015

Please cite this article as: Vallerio, M., Hufkens, J., Impe, J.V., Logist, F., An interactive decision-support system for multi-objective optimization of nonlinear dynamic processes with uncertainty, Expert Systems with Applications (2015), doi: http://dx. AbstractThe manufacturing industry is faced with the challenge to constantly improve its processes, e.g., due to lower profit margins, more strict environmental policies and increased societal awareness. These three aspects are considered as the pillars of sustainable development and typically give rise to multiple and conflicting objectives. Hence, any decision made will require trade-offs to be evaluated and compromises to be made. To support decision making an interactive multi-objective framework is presented to optimize dynamic processes based on mathematical models. The framework includes a numerically efficient strategy to account for parametric uncertainty in the models and it allows to directly minimize the operational risks arising from this uncertainty. Hence, for the first time expert knowledge on the trade-offs between traditional objective functions and operational risks is readily and interactively available for the practitioners in the field of dynamic systems. The introduced interactive framework for multi-objective dynamic optimization under uncertainty is successfully tested for a three and five-objective fed-batch reactor case study with uncertain feed temperature and heat transfer parameters.

Section: Case Study: a Fed-batch Reactor With Uncertain Parametersmentioning

confidence: 99%

An interactive decision-support system for multi-objective optimization of nonlinear dynamic processes with uncertainty

Expert Systems with Applications

Hufkens

Impe

et al. 2015

“…The case study described in this section is the Williams-Otto fedbatch reactor (e.g., Hannemann and Marquardt [12]; Logist et al [27]). The following reactions take place in the reactor: A + B → C, B + C → P + E and C + P → G. Reactant A is initially present while reactant B is added continuously.…”

Section: The Williams-otto Fed-batch Reactormentioning

confidence: 99%

Approximate robust optimization of nonlinear systems under parametric uncertainty and process noise

Telen

Journal of Process Control

Cabianca

et al. 2015

a b s t r a c tDynamic optimization techniques for complex nonlinear systems can provide the process industry with sustainable and efficient operating regimes. The problem with these regimes is that they usually lie close to the limits of the process. It is therefore paramount that these operating conditions are robust with respect to the parameter uncertainties and to the process noise such that critical constraints are not violated. Besides the uncertainty in the constraints, also the uncertainty in the objective function needs to be taken into account. However, including robustness in an optimization problem typically leads to semi-infinite optimization problems that are challenging to solve in practice. In the current manuscript several computationally tractable methods are exploited to approximately solve the robust dynamic optimization problem. These methods allow the use of fast deterministic gradient based optimization techniques. The first type of methods are based on a linearization approach while the second method exploits the unscented transformation to construct an estimation of the uncertainty propagation. Both types provide the user with an approximation of the variance-covariance matrix of the critical constraints and of the objective function. This allows the user to easily take them into account in the dynamic optimization routine in a stochastic setting without the need of using computationally expensive Monte Carlo simulations in the optimization procedure. Moreover, an iterative scheme is mentioned to evaluate the approximate results and to improve them if necessary. Two illustrative case studies are discussed, a jacketed tubular reactor and the Williams-Otto reactor.

“…All the model parameters, their values, the initial condition and additional constraints are reported in literature (Hannemann & Marquardt (2010); Logist et al…”

Section: Case V: Multi-objective Optimal Control Of a Batch Reactormentioning

confidence: 99%

Interactive NBI and (E)NNC methods for the progressive exploration of the criteria space in multi-objective optimization and optimal control

Computers & Chemical Engineering

Vercammen

Impe

et al. 2015

A wide range of problems arising from real world applications present multiple and conflicting objectives to be simultaneously optimized. However, this multi-objective nature is too often neglected. Multi-objective optimization proved to be a powerful tool to correctly describe the trade-o↵s among conflicting objectives in a set of optimal solutions known as the Pareto set. This paper introduces an interactive method to solve multi-objective problems based on geometric considerations. The method returns a wider Pareto set, at a negligible computational cost, when compared to existing methods. The interactivity also allows the decision-maker to explore only relevant parts of the Pareto set. The extreme solutions yield insightful considerations on the generation of the scalarization parameters for the Normal Boundary Intersection and the Enhanced Normalized Normal Constraints methods. The proposed method is applied to: (i) three scalar multi-objective problems, (ii) the multi-objective optimal control of a tubular and (iii) a fed-batch reactor.