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]

Process synthesis is a fundamental step in process design. The aim is to determine the optimal configuration of unit operations and stream flows to enhance key performance metrics. Traditional methods provide just one optimal solution and are strongly dependent on user-defined technologies, stream connections, and initial guesses for unknown variables. Usually, a single solution is not sufficient for adequate decision-making, especially, when properties such as flexibility or reliability are considered in addition to the process economics. Wastewater Treatment network synthesis and design is a complex problem that demands innovative approaches in design, retrofits, and maintenance strategies. Considering this, an enhanced framework for improving reliability in wastewater transportation networks based on graph theory and machine learning is presented. Machine learning models were developed to predict failure probability, where the XGBoost model provided the best predictions. To select t... [more]

While bilevel optimization is gaining prominence across various domains, the field lacks standardized tools for generating test problems that can effectively evaluate and guide the development of efficient solution algorithms. We define the term "trivial bilevel optimization problem" as a bilevel problem whose high-point relaxation solution is also feasible. These easy-to-solve problems frequently arise in naïve implementations of random bilevel optimization problem generators, significantly impacting the evaluation of bilevel solution algorithms. However, this problem has not been addressed in the literature to our best knowledge. This work introduces a non-trivial mixed-integer bilevel optimization problem generator, NT-BMIPGen, and a problem library, designed to eliminate the generation of trivial bilevel problems. Through analysis of the bilevel problem structure, we identify key factors contributing to problem triviality. Particularly, the upper to lower variable ratios and the nu... [more]

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]

Second-order optimization algorithms that leverage the exact Hessian or its approximation have been proven to achieve a faster convergence rate than first-order methods. However, their applications on training deep neural networks models, partial differential equations-based optimization problems, and large-scale non-convex problems, are hindered due to high computational cost associated with the Hessian evaluation, Hessian inversion to find the search direction, and ensuring its positive-definiteness. Accordingly, we propose a new search direction based on an interval Hessian and incorporate it into a line-search framework. We apply our algorithm to a set of 210 problems and show that it converges to a local minimum for 70% of the problems. We also compare our algorithm with other approaches. We illustrate that our algorithm is competitive to other methods in finding a local minimum using a smaller number of O(n3) operations.

Heuristic decomposition schemes like moving horizon schemes are a common approach to approximately solve large-scale mixed-integer programs. The authors propose Bayesian optimization as a methodological approach to systematically tune parameters of decomposition schemes for mixed-integer programs. This paper discusses detailed results of three studies of the Bayesian optimization-based approach using hoist scheduling as a case study: Firstly, two objectives of the tuning problem are examined considering sequences of incumbent solutions found by the Bayesian optimization. Secondly, the Bayesian optimization is applied to a set of test instances of the hoist scheduling problem using four types of acquisition functions; they are compared with respect to the convergence of the tuning problem solutions. Thirdly, the scaling behaviour of the Bayesian optimization is studied with respect to the dimension of the space of tuning parameters. The results of the three studies show that the solutio... [more]

Sustainability is increasingly recognized as a critical global issue. Multi-objective optimization is an important approach for sustainable decision-making, but problems with four or more objectives are hard to interpret due to its high dimensions. In our group’s previous work, an algorithm capable of systematically reducing objective dimensionality for (mixed integer) linear Problem has been developed. In this work, we will extend the algorithm to tackle nonlinear many-objective problems. An outer approximation-like method is employed to systematically replace nonlinear objectives and constraints. After converting the original nonlinear problem to linear one, previous linear algorithm can be applied to reduce the dimensionality. The benchmark DTLZ5(I, M) problem set is used to evaluate the effectiveness of this approach. Our algorithm demonstrates the ability to identify appropriate objective groupings on benchmark problems of up to 20 objectives when algorithm hyperparameters are app... [more]

Artificial neural networks are widely used as data-driven models for capturing complex, nonlinear systems. However, suboptimal training remains a significant challenge due to the nonlinearity of activation functions and the reliance on local solvers, which makes achieving global solutions difficult. One solution involves reformulating activation functions as piecewise linear approximations to convexify the problem, though this approach often requires substantial CPU time. This study demonstrates that a tailored branch-and-bound algorithm can effectively address these challenges by efficiently navigating the solution space using linear relaxations. The proposed method achieves minimal training error, offering a robust solution to the training bottleneck. Unlike traditional mixed-integer programming approaches, which often struggle to converge within reasonable CPU times, the SOSX algorithm shows superior scalability, with computational demand growing almost linearly rather than exponent... [more]

Surrogate models are widely used to improve the tractability of process optimization. Some commonly used surrogate models are obtained via machine learning such as multi-layer perceptrons (MLPs), Gaussian processes, and decision trees. Recently, a new class of machine learning models named Kolmogorov Arnold Networks (KANs) have been proposed. Broadly, KANs are similar to MLPs, yet they are based on the Kolmogorov representation theorem instead of the universal approximation theorem for the MLPs. Compared to MLPs, it was reported that KANs require significantly fewer parameters to approximate a given input/output relationship. One of the bottlenecks preventing the embedding of MLPs into optimization formulations is that MLPs with a high number of parameters (larger width or depth) are more challenging to globally optimize. We investigate whether the parameter efficiency of KANs relative to MLPs can be translated to computational benefits when embedding them into optimization problems an... [more]

Process systems engineering optimization problems may be challenging. These problems often exhibit nonlinearity, non-convexity, discontinuity, and uncertainty, and often only the values of objective and constraint functions are accessible. Additionally, some problems may be computationally expensive. In such scenarios, black-box optimization methods may be appropriate to tackle such problems. A general-purpose multi-agent framework for optimization has been developed to automate the configuration and use of hybrid optimization, allowing for multiple optimization solvers, including different instances of the same solver. Solvers can share solutions, leading to better outcomes with the same computational effort. Alongside cooperation, competition is introduced by dynamically allocating more computational resource to solvers best suited to the problem. Each solver is assigned a priority that adapts to the evolution of the search. The scheduler is priority-based and uses similar algorithms... [more]

Bayesian optimization is known to be able to search for the optimal conditions based on a small number of experiments. However, these experiments are insufficient to understand the experimental condition space. In contrast, we report the development of an algorithm that combines a low-confounding definitive screening design with Bayesian optimization, allowing for rapid optimization and ensuring sufficient experiments to understand the experimental condition space with a low confounding.

This paper introduces the Updated Absolute Expected Value Solution, U-AEEV, a heuristic for solving multi-stage stochastic programming (MSSP) problems with type 2 endogenous uncertainty. U-AEEV is an evolution of the Absolute Expected Value Solution, AEEV [1]. This paper aims to show how U-AEEV overcomes the drawbacks of AEEV and performs better than AEEV. To demonstrate the performance of U-AEEV, we solve 6 MSSP problems with type 2 endogenous uncertainty and compare the solutions and computational resource requirements.

Reaction processes require optimization to enhance key performance indicators (KPIs) such as yield, conversion, and selectivity. Techniques like Bayesian Optimization (BO), Model-Based Design of Experiments (MBDoE), and Goal-Oriented Optimal Experimental Design (GOOED) play pivotal roles in achieving these objectives. BO efficiently explores the design space to identify optimal conditions, while MBDoE maximizes the information gain by reducing kinetic model uncertainty. In contrast, GOOED focuses solely on maximizing the KPIs without considering the system uncertainty, identifying reactor conditions in the design space guaranteeing optimal performance. This study compares BO, MBDoE, and GOOED in optimizing methane oxidation in an automated flow reactor. Performance is assessed based on optimal methane conversion, reduced system uncertainty and minimal experimental efforts to achieve maximum conversion. BO quickly identifies high-conversion conditions, MBDoE minimizes experimental runs... [more]

This study presents a deterministic optimization methodology for the design of shell-and-tube heat exchangers with twisted tape turbulence promoters, focusing on minimizing the total annualized cost (TAC) while balancing thermal performance and energy consumption. A sensitivity analysis was carried out as Case I (Methanol-Water), it reveals that increasing the twist ratio (TR) reduces flow turbulence, resulting in lower fluid velocity, pressure drop (?Pi), and overall heat transfer coefficient (U). Among the turbulence promoters evaluated, twisted tapes with V-cuts achieved a 21.1% increase in U with a 52.27% increase in pressure drop, demonstrating an optimal balance between thermal enhancement and energy cost. In contrast, promoters with circular rings and multiple perforations showed the highest U improvements (26.7% and 25.8%, respectively) but incurred significant pressure drops (93.5% and 97.9%). The optimization problem has been stated as a nonlinear programming (NLP) problem an... [more]

Real-time optimization (RTO) is a model-based technique that drives plants to optimal operating conditions. Modifier Adaptation (MA) is a class of methods that adjusts the optimization problem using gradient information. This enables the plant to reach the optimum operating point or batch trajectory without the need of a precise model which reduces the necessary modeling efforts. However, computing the gradients of the cost function or of the plant outputs with respect to the inputs online is a challenging task. Modifier Adaptation with Quadratic Approximation (MAWQA) integrates MA with Quadratic Approximation (QA), which helps mitigate the challenges of estimating gradients from noisy measurements by utilizing historical operating data. However, the distribution of these past operating points significantly affects the effectiveness of the MAWQA strategy. To address this issue in this contribution, new methods to compute probing points which lead to fast convergence to the optimum are... [more]

The optimization of shell-and-tube heat exchangers (STHEs) is critical for improving energy efficiency, reducing operational costs, and mitigating environmental impacts in industrial applications. This study evaluates the performance of the Success-Based Optimization Algorithm (SBOA), a novel metaheuristic strategy inspired by behavioral patterns in success perception, against seven established algorithms—Cuckoo Search, Differential Evolution (DE), Grey Wolf Optimization (GWO), Jaya Algorithm, Particle Swarm Optimization, Teaching-Learning Based Optimization, and Whale Optimization Algorithm—for minimizing the total annual cost (TAC) of STHE designs. Using the Bell-Delaware method, the optimization framework incorporates eleven decision variables, including geometric and operational parameters, subject to thermo-hydraulic constraints. A penalty function method enforces feasibility by dynamically adjusting constraint weights. Statistical analysis of 30 independent runs reveals that DE a... [more]