Optimization

One of the main applications of CADET-Process is performing optimization studies. Optimization refers to the selection of a solution with regard to some criterion. In the simplest case, an optimization problem consists of minimizing some function \(f(x)\) by systematically varying the input values \(x\) and computing the value of that function.

\[ \min_x f(x) \]

In the context of physico-chemical processes, examples for the application of optimization studies include scenarios such as process optimization (see Optimize Batch Elution Process (Single Objective)) and parameter estimation (see Fit Column Transport Parameters). Here, often many variables are subject to optimization, multiple criteria have to be balanced, and additional linear and nonlinear constraints need to be considered.

\[ \begin{align}\begin{aligned}\begin{split} \min_x f(x) \\\end{split}\\\begin{split}s.t. \\ &g(x) \le 0, \\ &h(x) = 0, \\ &x \in \mathbb{R}^n \\ \end{split}\end{aligned}\end{align} \]

where \(g\) summarizes all inequality constraint functions, and \(h\) equality constraints.

In the following, the optimization module of CADET-Process is introduced. To decouple the problem formulation from the problem solution, two classes are provided: An OptimizationProblem class to specify optimization variables, objectives and constraints. And an OptimizerBase class which allows interfacing different external optimizers to solve the problem.

• Optimization Problem
  • Optimization Variables
  • Objectives
  • Linear constraints
  • Nonlinear constraints
  • Initial Values
  • Callbacks
• Optimizer
  • Initial values
  • Checkpoint
  • Optimization Results

Installation of different Optimizers

To maintain the manageability and efficiency of CADET-Process, some optimizers that come with a substantial number of dependencies are made optional. This approach ensures that the core package remains lightweight, while providing users the flexibility to install additional optimizers if needed. By default, scipy and pymoo are installed. Below, we provide instructions on how to install these optional dependencies.

Ax/BoTorch

Ax is an adaptable machine learning optimization library developed by Facebook. At its core, it uses BoTorch, a Bayesian optimization framework also developed by Facebook. Ax/BoTorch leverages Gaussian Processes to model the objective function and applies Bayesian optimization techniques to find the optimal parameters.

To install Ax as an optional dependency of CADET-Process, use the following command:

pip install cadet-process[ax]

Advanced Configuration

• Parallel Evaluation
• Evaluation Toolchains
  • Evaluation Objects
  • Evaluators
• Multi-Objective Optimization
  • Multi-criteria decision making (MCDM)
  • Meta Scores
• Specifying indices of multidimensional parameters for Optimization Variables
  • Specifying indices for (multidimensional) arrays
  • Specifying Indices of Multidimensional Event States
• Variable Normalization
  • Linear Normalization
  • Log Normalization
  • Auto Transform
• Variable Dependencies
  • Adsorption rates example