Efficient deterministic multiple objective optimal control of (bio)chemical processes

Abstract

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.

Tuning of Predictive Controllers for Drinking Water Networked Systems

“…Efficient approaches to generate the Pareto front for multiobjective optimal control problems have been recently reported (see, e.g., Logist et al (2009). …”

Multi-objective dynamic optimisation of cyclic chemical reactors with distributed parameters

“…The case is based on the RFR by Eigenberger and Nieken (1988) to which a cooling jacket has been added (Logist et al, 2007(Logist et al, , 2009b) (see Figure 1). Based on the mass and energy balances the following nonlinear parabolic PDEs are obtained: (9) with spatial boundary conditions:…”

“…More specifically, NBI, NNC and ENNC are incorporated in a multiple shooting approach. For a fast and direct computation of the CSS in the resulting single objective optimisation problems, the model is reformulated as a periodic boundary value problem using a method of lines approach, i.e., the cyclic PDEs are discretised by finite difference schemes (Logist et al, 2009b), and solved using the simultaneous optimal control code MUSCOD-II (Leineweber et al, 2003a,b). The underlying integrator DAESOL automatically detects and exploits the sparsity in the ODEs.…”

“…Alternatively, a direct computation of the CSS as the solution of a boundary value problem in time has been exploited for SMB optimisation in combination with scalarisation (i.e., the ǫ-constraint method) (e.g., Kawajiri and Biegler (2007)) or interactive multiobjective methods (e.g., Hakanen et al (2007)). This paper extends the deterministic procedure by Logist et al (2009b) which allows a fast and efficient generation of Pareto fronts. The paper is structured as follows.…”

Optimization of Design Parameters of a Stirling Generator for Use With a Fluidized Bed Combustor

“…Then a point yY  is said to be 'Pareto optimal' (blue points in Fig. 3 From the computational point of view, the problem of multi-objective optimization can be faced through a number of evolutionary optimization algorithms based on genetic algorithms and neural networks (Eslick & Miller, 2012) as well as on traditional deterministic methods (Logist, et al, 2009). In order to approach optimization problems of different type and complexity, specific multi-objective software tools have been developed, among which modeFRONTIER being perhaps the most powerful (www.esteco.com).…”