Meik Bernhard Franke

Large-scale mixed-integer programs (MIPs) typically cannot be solved by standard solvers with reasonable computational cost. MIP-heuristics decompose large-scale monolithic mixed-integer programs into polylithic programs such that they can be solved with reasonable computational cost at the price of loosing their optimality certificate. The decomposition is steered by hyperparameters that impact the solution quality and the computational cost diametrically. The proper selection of the hyperparameter values is a black-box optimization problem which is mostly solved by grid search or random search. In previous publications the authors proposed a novel hyperparameter optimization method based on Bayesian optimization and studied a use case from the PSE domain. Computational studies showed that the BO-based algorithm is superior for objective functions with few optimal solutions.This contribution generalizes the description of the MIP-Heuristic Optimization Problem (MIP-HOP) and the computer implementation of the solution-method. It supports the transferability of the method to other use cases. The general mathematical description of the MIP-HOP comprises eight expressions covering the monolithic and the polylithic MIP-model, the heuristic decomposition and composition operator, and the MIP-HOP. The formulation is explained and linked to the computer implementation of the solution method. The Python-code integrates state-of-the-art tools for mathematical programming (Pyomo and CPLEX) and Bayesian optimization (SMAC3) and will be published on GitHub.

Improving energy efficiency and reducing carbon emissions have become critical challenges in urea production, motivating increased interest in recovering mechanical energy within the process. This study develops a superstructure-based work exchange network with direct work exchangers to analyze mechanical energy recovery in urea synthesis. The work integration (WI) method is evaluated for single-, double-, and triple-stage configurations across different production capacities and compared with a conventional HPRT-based system. Results show that WI consistently outperforms HPRT in both energy recovery and CO₂ reduction. The single-stage configuration achieves the highest energy recovery, reaching 8448 MWh/year at 3710.83 t/day, an 18.8% improvement over HPRT. Wind power has the lowest carbon intensity, and emission reduction increases with production capacity. The largest absolute CO₂ reduction occurs in the single-stage case, while the greatest relative improvement (up to 41.1%) is observed in the three-stage configuration. Overall, WI significantly enhances energy efficiency and environmental performance in urea production.

Real-world flowshop problems which are very common in the chemical industry are often difficult to solve in a reasonable time with allocation, sequencing, and lot-sizing decisions. Although great progress has been made in the last 20 years regarding MILP model formulations and solution algorithms, realistically-sized flowshop problems with resource and buffer constraints are still difficult to solve. On the other hand, discrete-event simulation (DES) allows for very detailed modelling of process plants, but lacking of optimization capabilities. Simulation Optimization (SO) combines the high-detail DES with mathematical optimization. We show that is possible to integrate MILP and DES using Benders decomposition. We explain the Benders-DES (BDES) approach with a small motivation example with makespan minimization objective and apply it to a real-world case study of a formulation plant with seven formulation and filling lines with sequencing, allocation, and lot-sizing decisions. We show that the BDES approach performs comparably to the original monolithic-sequential MILP-DES approach. However, the key advantage of this method is the ability to leverage MILP optimization power without requiring a detailed model description.

A reinforcement learning framework is developed for the synthesis of distillation trains. The rigorous Naphtali-Sandholm algorithm for equilibrium separation modeling was implemented in JAX and coupled with the benchmarking Jumanji RL library. The vanilla actor-critic agent was successfully trained to build distillation trains for a seven-component hydrocarbon mixture. A transformer encoder structure was used to apply self-attention over the agent's observation. The agent was trained on minimal data representation containing quantitative component flows and relative volatility parameters between present components. Training sessions involving 5•10 4 episodes (3•10 5 column designs) were typically run in under 60 minutes. While training was fast and reliable with appropriate tuning of the hyperparameters, further improvements are needed in the generalizability performance for similar separation problems.

Digitalization plays a crucial role in improving the performance of chemical companies. In this context, different modeling, simulation, and optimization techniques such as MILP, discrete-event simulation (DES), and data-driven (DD) models are being used. Due to their heterogeneity, these techniques must be executed individually, and holistic optimization is manual and time-consuming. We propose Benders decomposition to combine these techniques into one rigorous optimization procedure. The main idea is that heterogeneous models can simultaneously be optimized as Benders subproblems. We illustrate this concept with the distributed permutation flow shop scheduling problem (DPFSP) and assume that a MILP, DES, and DD model exist for three flow shops. Our approach can compute bounds and report gap information on the optimal makespan for five medium-sized literature instances. The approach is promising because it enables the optimization of heterogeneous models and makes it possible to build optimization capabilities on an existing model and tool landscape in chemical companies.

Digitalization plays a crucial role in improving the performance of chemical companies. In this context, different modeling, simulation, and optimization techniques like MILP, discrete-event simulation (DES), and data-driven (DD) models are being used. Due to their heterogeneity, these techniques must be executed individually, and holistic optimization is a manual and time-consuming process. We propose Benders decomposition to combine these techniques into one rigorous optimization procedure. The main idea is that heterogeneous models can simultaneously be optimized as Benders subproblems. We illustrate this concept with the distributed permutation flow shop scheduling problem (DPFSP) and assume that a MILP, DES, and DD model exist for three flow shops. Our approach can compute bounds and report gap information on the optimal makespan for five medium-sized literature instances. The approach is promising because it enables the optimization of heterogeneous models and makes it possible to build optimization capabilities on an existing model and tool landscape in chemical companies.