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A hybrid stochastic−deterministic method, based on the control vector parameterization (CVP) approach, is presented as a reliable and efficient alternative for the solution of dynamic optimization (or open loop optimal control) problems.The problems under consideration are related to free final time single-stage systems and more general multi-stage procecesses that are described by different sets of differential and algebraic equations (DAEs), one for each stage. The operating conditions and the duration of each stage must be computed in order to achieve an overall optimal result for the process subject to constraints in the state and control variables. The solution of three challenging dynamic optimization problems is presented, including a large-scale case study, showing the capabilities of this new strategy.

The dynamic optimization of combined lumped and distributed process systems, governed by nonlinear ordinary and partial differential equations (ODEs and PDEs), is considered in this work. The application of a recently developed method based on the combination of the control vector parametrization approach with the calculation of exact gradients and projected Hessians (Hp's), is presented as an alternative for the efficient computation of the control policies needed to optimize a specific performance criterion. The exact first- and second-order information is calculated by means of the solution of an extended initial value problem (IVP) whose particular time-varying Jacobian structure is exploited by a sparse implicit solver to increase efficiency. Finally, the applicability of this method is shown through the solution of a number of case studies demonstrating that a significant speed-up can be obtained through the use of exact second-order information.

A novel list-based threshold-accepting (LBTA) algorithm is proposed for solving the zero-wait (ZW) scheduling problem. The LBTA algorithm belongs to the class of threshold-accepting algorithms, but the acceptance probability decreases based on a list that is rejuvenated and adapted according to the topology of the solution space of the problem. A probabilistic steepest optimization strategy was adapted to search the solution space effectively. The effectiveness of the LBTA method is illustrated through case studies from scheduling literature which were formulated as mixed-integer linear programming and mixed-integer nonlinear programming models. The performance of the LBTA algorithm is also compared with that of the simulated annealing (SA) algorithm for a large number of various problem sizes. The proposed algorithm gives optimal solutions for small- to moderate-size ZW scheduling problems within a very short time and shows much superior computational performance compared to SA for large-size problems.

The dynamic optimization (open-loop optimal control) of bioprocesses is considered. It is shown how these problems can be solved using a recently developed method, based on the control vector parametrization concept, which makes use of second-order sensitivities to obtain exact gradients and Hessians for the objective function of the underlying dynamic process model. A further extension of this scheme, which makes use of restricted second-order information, is also presented. This extension results in an efficient way to solve general dynamic optimization problems, even for high levels of control discretization. This new approach allows the efficient and robust solution of two challenging case studies regarding the optimal control of fed-batch bioreactors taken from the open literature.

This is the second part of the study in the identification and manipulation of biochemical reaction limiting steps. The first part (Analysis and Optimization of Biochemical Process Reaction Pathways. 1. Pathway Sensitivities and Identification of Limiting Steps) establishes a link between biochemical reactions and the macroscopic fermentation process by using a set of amplification/attenuation factors which influence individually each reaction step. A sensitivity analysis uses these factors to establish the influence of each step on the process objective function for any processing mode. In this paper the optimal selection of the amplification/attenuation factors is examined, in formulations resulting in nonlinear programming.

This work focuses on establishing a link between biochemical reactions and the macroscopic fermentation process by using a set of amplification/attenuation factors which influence individually each reaction step. A sensitivity analysis based on these factors yields a novel measure of reaction step influence on the overall process objective. These measures are generalized to any type of processing mode, primarily focusing on dynamic processes, for which it is shown how the sensitivities can be used to identify reaction network bottlenecks.