This supplementary material provides supporting methodological and numerical information for the study of uncertainty-aware fleet planning for heavy-duty freight. It expands on the construction of the case study, including the truck technologies, route characteristics, freight classes, operating scenarios, and economic and environmental assumptions used in the stochastic optimization model.
The document also provides additional formulation details, data tables, computational settings, and supporting analyses needed to interpret and reproduce the results. Together, these materials complement the main manuscript by documenting assumptions and calculations that could not be included in the article because of space limitations.

Recent research has introduced large language model (LLM)-based chatbots to help practitioners interpret solutions of optimization models. Existing chatbots primarily support the interpretation of a solution obtained from a single solve. In rolling horizon optimization, however, practitioners need to understand how and why solutions change across successive solves as the planning window advances and changes occur in model data and/or structure. We present an LLM-based agentic framework for this comparison task, works for time-indexed linear programming (LP) and mixed-integer linear programming (MILP) models represented in Pyomo. Four deterministic analytical modules detect model changes, quantify solution differences, assess whether prior decisions remain feasible under the updated model, and and links differences between successive plans to changes in model parameters and structure. LLM agents interpret user questions, select the corresponding module, and synthesize its numerical resu... [more]

This submission corresponds to the supplementary material for article submitted to FOCAPO titled:
"Privacy-Preserving Coordinated Operation of Multi-Player Industrial Network Using Secure Aggregation".

Supplementary material describing the refinery optimization problem used in the manuscript ``Physics Constrained Machine Learning for modeling of Chemical Refineries"

Chemical recycling has emerged as a promising pathway for increasing plastic circularity by re-covering value from mixed and contaminated waste streams that are unsuitable for mechanical recycling. Because chemically recycled products become indistinguishable from their fossil-derived counterparts, recycled-content (RC) certification relies on Chain-of-Custody (CoC) ac-counting frameworks, primarily Mass Balance (MB) and Book-and-Claim (BC). While these ac-counting approaches determine how recycled content is attributed to products, their implications for plastic supply chain design remain poorly understood. This work develops a mixed-integer optimization framework for the design of integrated plastic supply chains that explicitly incorporates alternative MB allocation methods and BC accounting for RC tracking while capturing competition between fossil and recycling pathways. The model simultaneously optimizes technology selection and capacity, facility location, transportation, and ma... [more]

The reliable identification of feasible and optimal operating conditions is a key challenge in the design and optimization of thermochemical conversion processes, where kinetics, limited data availability, and strict physical constraints coexist. In this work, a novel data-driven strategy based on Physics-Informed Neural Networks (PINNs) is proposed to explore the operability space of a bubbling fluidized bed (BFB) plastic pyrolysis process. The approach integrates mechanistic knowledge through explicit mass balance constraints with data-driven learning, enabling accurate prediction of and feasibility boundaries. An adaptive sampling framework is employed to iteratively augment the training dataset. The trained PINN surrogate is then used to predict feasible regions and perform constrained optimization aimed at minimizing tar production, which is one of the most problematic byproducts in plastic pyrolysis processes. Beyond classical optimality, a robustness-oriented uncertainty quantif... [more]

Digital supplementary information for the ESCAPE36 conference paper titled: High Performance HPs Using Tailored Refrigerants

SUPPORTING INFORMATION for the work "Particle Swarm Optimization for simultaneous design and optimization of heat pumps considering Mixed Integer problems", submited to ESCAPE 36.

This document provides the Supplementary Material for the study titled: Virtual Plant–Model Pair as a Step Towards Real-Time Optimization of a Simulated Moving Bed System. The work has been submitted to the peer-reviewed proceedings of the 36th European Symposium on Computer-Aided Process Engineering (ESCAPE 2026).

This document contains digital supplementary material for the article “An Extended Superstructure Formulation for Non-Isobaric Flowsheet Synthesis”, submitted to the peer-reviewed proceedings of the 36th European Symposium on Computer-Aided Process Engineering (ESCAPE 2026).

This document compiles the digital supplementary material associated with the article entitled “Optimizing Steam Flux for Energy Efficiency in Ammonia Recovery during Sodium Carbonate Production”, published in the peer-reviewed proceedings of the 36th European Symposium on Computer Aided Process Engineering (ESCAPE 36). It presents the effects of variations in steam pressure and temperature on the system’s temperature and mass flow rate.

This deterministic model formulation describes one root-to-leaf path in a scenario tree that describes the evolution of uncertainty for power grid capacity expansion planning problems. The main manuscript then extends this deterministic formulation to multi-stage and two-stage stochastic programs.

This document contains digital supplementary material (detailed model description, parameters for different case studies and additional figures) related to the article "Optimization of Site-wide Heat-Integrated Utility Systems with Heat Pumps using MILP" which is submitted to the peer reviewed conference proceeding of the 36th European Symposium on Computer Aided Process Engineering (ESCAPE 36).

This study presents a mixed-integer bilinear optimization model for the cost-optimal design of a Northern European hydrogen supply chain with integrated CCS, focusing on exports from Norway to Germany and CO2 sequestration in Norway. The model is formulated as a superstructure problem and implemented in Pyomo, considering multiple locations for infrastructure nodes and transport options for hydrogen, wood chips, and CO2.

This study presents a mixed-integer bilinear optimization model for the cost-optimal design of a Northern European hydrogen supply chain with integrated CCS, focusing on exports from Norway to Germany and CO2 sequestration in Norway. The model is formulated as a superstructure problem and implemented in Pyomo, considering multiple locations for infrastructure nodes and transport options for hydrogen, wood chips, and CO2.

Supply chain superstructure optimization model for export of either wood chips or compressed hydrogen from Norway to Germany

Optimization under uncertainty is inherent to many PSE applications ranging from process design to RTO. Reaching process true optima often involves learning from experimentation, but actual experiments involve a cost (economic, resources, time) and a budget limit usually exists. Finding the best trade-off on cumulative process performance and experimental cost over a finite budget is a Partially Observable Markov Decision Process (POMDP), known to be computationally intractable. This paper follows the nonmyopic Bayesian optimization (BO) approximation to POMDPs developed by the machine-learning community, that naturally enables the use of hybrid plant surrogate models formed by fundamental laws and Gaussian processes (GP). Although nonmyopic BO using GPs may look more tractable, evaluating multi-step decision trees to find the best first-stage candidate action to apply is still expensive with evolutionary or NLP optimizers. Hence, we propose modelling the value function of the first-st... [more]

The pharmaceutical industry is a highly specialized field where strict quality control and accelerated time-to-market are essential for maintaining competitive advantage. Spherical crystallization has emerged as a promising approach in pharmaceutical manufacturing, offering significant potential to reduce equipment and operating costs, enhancing drug bioavailability, and facilitating compliance with product quality regulations. Emulsions, as an enabling technology for spherical crystallization, present unique advantages. However, the quality of spherical crystallization products derived from emulsions is significantly influenced by the intricate interactions between crystallization phenomena, formulation variables, and solution hydrodynamics. These complexities pose substantial challenges in determining optimal operational conditions to achieve the desired product characteristics. In this study, Bayesian optimization (BO) is employed to refine and optimize the operational conditions fo... [more]

Soybean is a highly valuable global commodity due to its versatility and numerous derivative products. During harvest, all non-seed materials become “straw”. Currently, this waste is primarily used for low-value purposes such as animal feed, landfilling, and incineration. To address this, the present work proposes a conceptual biorefinery aimed at converting soybean straw into higher-value products. The study began with data collection to identify potential conversion routes. Based on this information, a superstructure was developed, comprising seven conversion routes: four thermochemical routes (pyrolysis, combustion, hydrothermal gasification, and liquefaction), two biological routes (fermentation and anaerobic fermentation), and one chemical route (alkaline extraction). Each process was evaluated based on product yields, conversion times, and associated capital and operating costs. Using this data, an MILP (Mixed-Integer Linear Programming) optimization model was built in Pyomo usin... [more]

Rare earth elements (REE) and many other critical minerals are necessary for the manufacturing of modern everyday technologies, including microchips, batteries and electric motors. Recovery of these materials typically involves aqueous systems which can be modeled as chemical equilibrium problems. One common method for solving these problems is the law of mass action approach (LMA), where a system of non-linear equations involving the equilibrium constants is solved. However, despite being theoretically simple, these problems are in practice very difficult to solve. Currently, the use of iterative heuristics based on saturation indices to decide on which species and reactions to include in the calculations is the state of the art to arrive at a solution. Here, we present an optimization-based alternative to solve chemical equilibria problems involving precipitation/dissolution reactions without the need for such heuristics. Our approach is first validated against the LMA software MINTE... [more]

The transition to renewable energy sources, such as biogas, requires purification processes to separate methane from carbon dioxide, with adsorption-based methods being widely employed. Accurate simulations of these systems, governed by coupled PDEs, ODEs, and algebraic equations, critically depend on precise parameter determination. While traditional approaches often result in significant errors or complex procedures, optimization algorithms provide a more efficient and reliable means of parameter estimation, simplifying the process, improving simulation accuracy, and enhancing the understanding of these systems. This work introduces an Artificial Intelligence-based methodology for estimating the isotherm parameters of a mathematical phenomenological model for fixed-bed experiments. The separation of CO2 and CH4 is used as case study. This work develops an algorithm for parameter estimation for the system's mathematical model. The results show that the validated model has a close fit... [more]

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 5·104 episodes (3·105 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.

Operational decision-making in Process Systems Engineering (PSE) has achieved high proficiency at specific levels, such as supply chain optimization and unit-operation optimization. However, a critical challenge remains: integrating these layers of optimization into a cohesive, hierarchical decision-making framework that enables sustainable and automated operations. Addressing this challenge requires systems capable of coordinating multi-level decisions while maintaining interpretability and adaptability. Multi-agent frameworks based on Large Language Models (LLMs) have demonstrated significant promise in other domains, successfully simulating traditional human decision-making tasks and tackling complex, multi-stage problems. This paper explores their potential application within operational decision-making for PSE, focusing on sustainability-driven objectives. A realistic Gas-Oil Separation Plant (GOSP) network is used as a case study, mimicking a hierarchical workflow that spans from... [more]

This work presents a model for optimizing shell-and-tube heat exchanger design using Q-learning, a reinforcement learning technique. An agent is trained to interact with a simulated environment of a heat exchange model, iteratively refining design configurations to maximize a reward function. This reward function balances heat exchanger effectiveness and pressure drop, emphasizing designs that minimize pressure drop. Results showed that simpler configurations consistently achieved higher rewards, despite complex designs offering better heat transfer efficiency.

Understanding data with complex patterns is a significant part of the journey toward accurate data prediction and interpretation. The relationships between input and output variables can unlock diverse advancement opportunities across various processes. However, most AI models attempting to uncover these patterns are not explainable or remain opaque, offering little interpretation. This paper explores an approach in explainable AI by introducing a multi-agent system (MaSR) for extracting equations between features using data. We developed a novel approach to perform symbolic regression by discovering mathematical functions using a multi-agent system of LLMs. This system addresses the traditional challenges of genetic optimization, such as random seed generation, complexity, and the explainability of the final equation. We utilize the in-context learning capabilities of LLMs trained on vast amounts of data to generate accurate equations more quickly. This study presents research on expa... [more]