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]

Maintenance is critical for industrial plants to ensure operational reliability and worker safety. In process industries, fouling, the accumulation of solid residues in equipment, poses a significant challenge, causing inefficiencies and productivity losses. Effective modeling of fouling evolution over time is essential for maintenance planning to prevent equipment from operating under suboptimal conditions. Traditional approaches to fouling prediction include equation-based models, which offer high precision but may struggle with continuously changing process bound-aries, and machine learning techniques, which are more adaptable but less effective at capturing rapidly evolving trends driven by complex underlying physics. This study introduces an innova-tive hybrid machine learning approach for predictive maintenance, combining the strengths of both methods. Pressure differential is modeled using an equation-based approach that links pressure data with fouling thickness, while the foul... [more]

This study proposes a model-based approach utilizing a hybrid population balance model (PBM) to optimize temperature profiles for minimizing agglomeration and enhancing crystal growth. The PBM incorporates key mechanisms—nucleation, growth, dissolution, agglomeration, and deagglomeration—and is applied to the crystallization of an industrial active pharmaceutical ingredient (API), Compound K. Parameters were estimated through prior design of experiments (DoE) and refined via additional thermocycle experiments. In-silico DoE simulations demonstrate that the hybrid PBM outperforms traditional methods in assessing process performance under agglomeration-prone conditions. Results confirm that thermocycles effectively reduce agglomeration and promote bulk crystal formation, though their efficiency plateaus beyond a certain cycle number. This model-based approach provides a more robust strategy for agglomeration control compared to conventional methods, offering valuable insights for industr... [more]

The Fourth Industrial Revolution (Industry 4.0) brings a new chapter at dairy sector. Dairy 4.0 technologies are based on Big Data Analysis, Internet of Things, Robotics and Machine Learning. The usage of smart technologies to processing and analyzing complicated massive data has a significant impact in automation, optimization, functional costs and innovation. Artificial Intelligence tools are applied from dairy farms and production lines – including packaging- to supply chain. The aim of this paper is to demonstrate the most used applications of Machine Learning in dairy production so as to enhance the sustainability and the quality of dairy products. The most significant Machine Learning applications integrate machine vision, smart environmental sensors, activity collars, thermal imaging cameras, and digitized supply chain systems to facilitate inventory management. Challenges like milk adulteration, animal diseases, mastitis, traceability and supply chain losses are also addressed... [more]

Physics-Informed Symbolic Regression (PISR) offers a pathway to discover human-interpretable solutions to partial differential equations (PDEs). This work investigates three fitness metrics within a PISR framework: PDE fitness, Bayesian Information Criterion (BIC), and a fitness metric proportional to the probability of a model given the data. Through experiments with Laplace’s equation, Burgers’ equation, and a nonlinear wave equation, we demonstrate that incorporating information theoretic criteria like BIC can yield higher fidelity models while maintaining interpretability. Our results show that BIC-based PISR achieved the best performance, identifying an exact solution to Laplace’s equation and finding solutions with R2-values of 0.998 for Burgers’ equation and 0.957 for the nonlinear wave equation. The inclusion of the Bayes D-optimality criterion in estimating model probability strongly constrained solution complexity, limiting models to 3-4 parameters and reducing accuracy. Thes... [more]

Maintenance is critical for industrial plants to ensure operational reliability and worker safety. In process industries, fouling, the accumulation of solid residues in equipment, poses a significant challenge, causing inefficiencies and productivity losses. Effective modeling of fouling evolution over time is essential for maintenance planning to prevent equipment from operating under suboptimal conditions. Traditional approaches to fouling prediction include equation-based models, which offer high precision but may struggle with continuously changing process boundaries, and machine learning techniques, which are more adaptable but less effective at capturing rapidly evolving trends driven by complex underlying physics. This study introduces an innovative hybrid machine learning approach for predictive maintenance, combining the strengths of both methods. Pressure differential is modeled using an equation-based approach that links pressure data with fouling thickness, while the foulin... [more]

The analysis of large chemical reaction space sheds light on reaction patterns between molecules and can inform subsequent reaction pathway planning. With the aim to discover more sustainable production systems, it became worthwhile to explicitly model the reaction space reachable from biobased feedstocks. In particular, the space that reactions in integrated biorefineries span for optimised biorefinery planning is of interest. In this work we show a network-theoretical analysis of biorefinery reaction data. We utilise the directed all-to-all mapping between reactants and products to compare the reaction space obtained from biorefineries with the entire network of organic chemistry (NOC). In our results, we find that despite having 1000 times fewer molecules, the constructed network resembles the NOC in terms of its scale-free nature and shares similarities regarding its small-world property. Additionally, we analyse the coverage rate of the biorefinery reaction data and find that many... [more]

Robust optimisation is a powerful approach for addressing uncertainty ensuring constraint satisfaction for all uncertain parameter realisations. While convex robust optimisation problems are effectively tackled using robust reformulations and cutting plane methods, extending these techniques to non-convex problems remains largely unexplored. In this work we propose a method that is based on a parallel robustness and optimality search. We introduce a novel spatial Branch-and-Bound algorithm integrated with robust cutting-planes for solving non-convex robust optimisation problems. The algorithm systematically incorporates global and robust optimisation techniques, leveraging McCormick relaxations. The proposed algorithm is evaluated on benchmark pooling problems with uncertain feed quality, demonstrating algorithm stability and solution robustness. The computational time for the examined case studies is within the same order of magnitude as state-of-the-art. The findings of this work hig... [more]

Currently, state-of-the-art approaches to solving complex optimization problems have focused solely on methods requiring high computational time and unable to find the global optimal solution. In this work, a methodology based on quantum computing is presented to overcome these drawbacks. The novelty of this framework stems from the quantum computer’s architecture and taking into consideration the quantum phenomena that take place to solve optimization problems with specific structure. The proposed methodology includes steps for the transformation of the initial optimization problem into an unconstrainted optimization problem with binary variables and its embedding onto a quantum device. Moreover, different resolution levels for the transformation step and different architectures for the embedding process are utilized. To illustrate the procedure, a case study based on Haverly’s pooling and blending problem is examined while demonstrating the potential of the proposed approach. The res... [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]

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.

The definition of strategies for operation of process networks is a key research focus in process systems engineering. This challenge is commonly formulated as a numerical constraint satisfaction problem, where most practical algorithms are limited to identifying inner approximations to the feasible operational envelope. Sampling-based approaches so far have only been developed for formulations that required coordinated operation of the units within the network. We propose a decomposition approach that enables decentralized operation for acyclic muti-unit processes by sampling. Our methodology leverages problem structure to decompose unit-wise and deploys surrogate models to couple the resultant subproblems. We demonstrate it on a serial, batch chemical reactor network. In future research, we will extend this framework to consider the presence of uncertain unit parameters robustly.

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... [more]

With increasing emphasis on energy efficiency, more researchers are focusing on energy-efficient flexible job shop scheduling problems. Mathematical programming is a commonly used optimization method for such scheduling challenges, offering the advantages of achieving global optima and serving as a foundation for other approaches. However, current mathematical programming formulations face several challenges, including insufficient consideration of various forms of energy consumption and low efficiency, particularly in handling large-scale instances, which struggle to converge. In this study, we propose a novel global sequence-based approach with high computational efficiency. In this model, immediate precedence relationships are identified using constraints, enabling the precise determination of idle durations within any idle slots. The proposed formulation achieves a significant reduction in energy consumption by up to 20% relative to other formulations. Furthermore, it successfully... [more]

As demand for long and accurate molecular simulations increases so too does the computation demand. Beyond using new, enterprise scale processor developments - such as the ARM neoverse chips – or performing simulations leveraging Graphics Processing Unit compute, there exists a potentially faster and more power efficient option in the form of custom hardware. Using hardware description languages it is possible to transform existing algorithms into custom, high performance hardware layouts. This can lead to faster and more efficient simulations but compromises on the required development time and flexibility. In order to take the greatest advantage of the potential performance gains, the focus should be on transforming the most computationally expensive parts of the algorithms. When performing molecular dynamics simulations in a polar solvent like water, non-bonded electrostatic calculations dominate each simulation step, as the interactions between the solvent and the molecular structu... [more]

Real-time carbon accounting is crucial for advancing policies that effectively meet sustainability objectives. This work introduces a carbon tracking tool specifically designed for the European electricity grid. The tool collects hourly data on electricity consumption and generation, cross-border power exchanges, and weather information to assess the real-time environmental effects of electricity use, employing locally-specific emission factors for the generation sources. It utilizes weather data from various stations across Europe to produce week-ahead forecasts of carbon intensity in the grid. Predictions are created using a random forest regressor, integrated within the optimal controller of an operational industrial batch process. This prediction-based optimizer seeks to reduce total emissions tied to the process schedule's electricity consumption by implementing a rolling horizon strategy. By leveraging enhanced energy flexibility, the controller provides significant opportunities... [more]

In this work, we present recent algorithmic and implementation advances of the nonconvex two-stage robust optimization solver PyROS. Our advances include extensions of the scope of PyROS to models with uncertain variable bounds, improvements to the formulations and/or initializations of the various subproblems used by the underlying cutting set algorithm, and extensions to the pre-implemented uncertainty set interfaces. The effectiveness of PyROS is demonstrated through the results of an original benchmarking study on a library of over 8,500 small-scale instances, with variations in the nonlinearities, degree-of-freedom partitioning, uncertainty sets, and polynomial decision rule approximations. To demonstrate the utility of PyROS for large-scale process models, we present the results of a carbon capture case study. Overall, our results highlight the effectiveness of PyROS for obtaining robust solutions to optimization problems with uncertain equality constraints.

We present new modifications to superstructure optimization paradigms to i) enable their robust solution and ii) extend their applicability. Superstructure optimization of chemical process flowsheets on the basis of rigorous and detailed models of the various unit operations, such as in the state operator network (SON) paradigm, is prone to non-convergence. A key challenge in this optimization-based approach is that when process units are deselected from a superstructure flowsheet, the constraints that represent the deselected process unit can be numerically singular (e.g., divide by zero, logarithm of zero and rank-deficient Jacobian). In this paper, we build upon the recently-proposed modified state operator network (MSON) that systematically eliminates singularities due to unit deselection and is equally applicable to the context of both simulation-based and equation-oriented optimization. A key drawback of the MSON is that it is only applicable to the design of isobaric flowsheets... [more]

Process simulation problems often involve systems of nonlinear and nonconvex equations and may run into convergence issues due to the existence of recycle loops within such models. To that end, surrogate models have gained significant attention as an alternative to high-fidelity models as they significantly reduce the computational burden. However, these models do not always provide a guarantee on the prediction accuracy over the domain of interest. To address this issue, we strike a balance between computational complexity by developing a data-driven branch and prune-based framework that progressively leads to a guaranteed solution to the original system of equations. Specifically, we utilize interval arithmetic techniques to exploit Hessian information about the model of interest. Along with checking whether a solution can exist in the domain under consideration, we generate error-bounded convex hull surrogates using the sampled data and Hessian information. When integrated in a bran... [more]

This paper presents an algorithm for developing sparse surrogate models that satisfy mass/energy conservation even when the training data are noisy and violate the conservation laws. In the first step, we employ the Bayesian Identification of Dynamic Sparse Algebraic Model (BIDSAM) algorithm proposed in our previous work to obtain a set of hierarchically ranked sparse models which approximate system behaviors with linear combinations of a set of well-defined basis functions. Although the model building algorithm was shown to be robust to noisy data, conservation laws may not be satisfied by the surrogate models. In this work we propose an algorithm that augments a data reconciliation step with the BIDSAM model for satisfaction of conservation laws. This method relies only on known boundary conditions and hence is generic for any chemical system. Two case studies are considered-one focused on mass conservation and another on energy conservation. Results show that models with minimum bia... [more]

The demand for a reliable, cheap and environmentally friendly source of energy makes the integration of renewable energy into power networks a global challenge. Furthermore, reliability, as one of the core elements of efficient and cost-effective energy management options, is still among the dominant factors/techniques that receive more attention for realistic penetrations of renewable energy into the electricity grid. This paper proposes an efficient way of energy management for a grid-connected microgrid. The grid-connected microgrid used in the analysis consists of solar photovoltaic (P.V.) and battery. In this microgrid configuration, oftentimes, the output power might not be equal to the system demand; in this regard, it is expected that the mismatch between these output powers is not zero. However, to reduce the mismatch between demand and supply to be close to zero, this paper proposes strategies of increasing the rated power of solar, battery and grid separately and combining t... [more]

This article presents a machine learning (ML) application to examine artificial lift (AL) selection, using only field production datasets from a Sudanese oil field. Five ML algorithms were used to develop a selection model, and the results demonstrated the ML capabilities in the optimum selection, with accuracy reaching 93%. Moreover, the predicted AL has a better production performance than the actual ones in the field. The research shows the significant production parameters to consider in AL type and size selection. The top six critical factors affecting AL selection are gas, cumulatively produced fluid, wellhead pressure, GOR, produced water, and the implemented EOR. This article contributes significantly to the literature and proposes a new and efficient approach to selecting the optimum AL to maximize oil production and profitability, reducing the analysis time and production losses associated with inconsistency in selection and frequent AL replacement. This study offers a univer... [more]

The analyzed research issue provides a model for Carbon Footprint estimation at an early design stage. In the context of climate neutrality, it is important to introduce regenerative design practices in the architect’s design process, especially in early design phases when the possibility of modifying the design is usually high. The research method was based on separate consecutive research works−partial tasks: Developing regenerative design guidelines for simulation purposes and for parametric modeling; generating a training set and a testing set of building designs with calculated total Carbon Footprint; using the pre-generated set to train a Machine Learning Model; applying the Machine Learning Model to predict optimal building features; prototyping an application for a quick estimation of the Total Carbon Footprint in the case of other projects in early design phases; updating the prototyped application with additional features; urban layout analysis; preparing a new approach based... [more]

This paper presents a novel complete design procedure to convert a maximum power point tracking (MPPT) algorithm into a control system. The MPPT algorithm can be tuned by employing any control system design. In this paper, we adopted Bode diagrams using the criteria of module and phase as the power electronics specialists are habituated with such concepts. The MPPT control transfer functions were derived using the average state equations and small-signal analysis. The control loops were derived for power and voltage control loops. The design procedure was applied to the well-known perturb and observe (P&O) and incremental conductance (IC) algorithms, returning the P&O based on PI and IC based on PI algorithms. Such algorithms were evaluated through simulation and experimental results. Additionally, we showed that the proposed design methodology can optimize energy harvesting, allowing algorithms to have outstanding tracking factors (above 99%) and adaptability characteristics.

The 2D P colonies is a version of the P colonies with a two-dimensional environment designed for observing the behavior of the community of very simple agents living in the shared environment. Each agent is equipped with a set of programs consisting of a small number of simple rules. These programs allow the agent to act and move in the environment. The 2D P colonies have been shown to be suitable for the simulations of various (not only) multi-agent systems, and natural phenomena, like flash floods. The Grey wolf algorithm is the optimization-based algorithm inspired by social dynamics found in packs of grey wolves and by their ability to create hierarchies, in which every member has a clearly defined role, dynamically. In our previous papers, we extended the 2D P colony by the universal communication device, the blackboard. The blackboard allows for the agents to share various information, e.g., their position or the information about their surroundings. In this paper, we follow our... [more]