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]

This paper focuses on the control and dynamics of an oil refinery process on an intermediate level - the flows, masses and compositions of and between units within the refining operation. It aims to elucidate optimal strategies for the routing of streams during upset events imposed on the process. A general flowsheet simulation technique including tunable controllers for flows, compositions, levels and reaction extents is incorporated in a Linear Programming model. A standard node represents a mixed receiving tank, with exit streams which can be split, converted and separated. These nodes can be inter-connected arbitrarily in the flowsheet. The method is demonstrated for the case of a planned 3-day shutdown of the catalytic cracker.

In the last decades, the growing awareness of climate change and the high political sensitivity of critical resources such as energy have emphasized a need for local, renewable and optimized energy mixes at various scales. Several studies have therefore aimed to optimize renewable energy technologies and plant locations to develop more renewable and efficient Energy Mixes. Following this trend, this paper applies and compares Goal Programming, Branch-and-Cut and NSGA-II to a multi-objective combinatorial optimization problem focused on the energy mix of Oise, France. Results show more optimality for Goal Programming and Branch-and-Cut, accompanied by a high sensitivity to constraints, while NSGA-II provides more technological diversity in the computed solutions.

The battle against climate change and the search for innovative solutions to mitigate its effects have become the focus of the researchers’ attention. One potential approach to reduce the impacts of the global warming could be the design of a Carbon Capture and Storage Supply Chain (CCS SC). However, the high complexity of the model requires exploring alternative ways to optimise it. In this work, a CCS multi-period supply chain for Europe is designed. Data on CO2 emissions have been sourced from the EDGAR database, which includes information spanning the last 50 years. Since this problem involves optimising the cost and operation decisions over a 10-year time horizon, it would be advisable to forecast carbon dioxide emissions to enhance the reliability of the data used. For this purpose, a neural network-based model is implemented for forecasting N-Beats. Furthermore, a temporal decomposition scheme is used to address the intractability issues of the model. The selected method is Lag... [more]

The urgent need to mitigate climate change and reduce reliance on fossil fuels highlights green hydrogen as a key component of the global energy transition. This study assesses the feasibility of producing hydrogen offshore using wind energy, focusing on economic and environmental aspects. Offshore wind energy offers several advantages: access to water for electrolysis, potentially lower hydrogen export costs compared to electricity, and storage systems that stabilize wind energy output. However, significant challenges remain, including the high costs of storage solutions, capital expenditures (CAPEX), and operational costs (OPEX). A Mixed-Integer Linear Programming (MILP) model optimizes the production units, storage, and distribution processes. A case study in southern France examines hydrogen production from a 150 MW floating wind farm. While hydrogen produced from offshore wind ranks among the most environmentally friendly, its costs remain high, and production volumes fall short o... [more]

Superstructure based approaches have long been employed for optimal process synthesis problems. Due to the difficulties of using rigorous process models and simultaneous solutions, shortcut calculations have been the preferred means of modeling unit operations within larger process network problems. However, even with the use of shortcut equations to model the behaviour of unit operations, the resulting mixed-integer programs can be challenging to solve. Furthermore, generating the problem superstructure has often been done manually, presenting issues for scaling to larger problems. We demonstrate the use of an algorithmic approach to generate network superstructures for synthesis problems coupled with equation reformulations to yield an MIQCP (Mixed-Integer Quadratically Constrained Program) for networks of thermally coupled distillation columns. The combination of rapid problem generation with the ability to leverage recent advances in the performance of QCP (Quadratically Constraine... [more]

A dual-stack fuel cell model was developed to simulate the hydrogen consumption a fuel cell-powered vehicle for a specific drive cycle. Two fuel cell stacks, each consisting of 65 parallel cells at different aging status and thus with different efficiency profiles (i.e., low and high) were considered. A constrained optimization for power distribution between individual stacks was performed where the objective function was to minimize the hydrogen consumption while meeting the total demand. For proper power management each stack has its own power controller which manipulates the stack current to control the stack power at its desired-set point. Computed optimal power values constitute the desired set-points for the local power PID controllers of the individual stacks. Closed-loop simulations were performed by simulating the developed mechanistic model together with optimization and PID controllers in SIMULINK platform. The closed loop simulations demonstrate how well the power demand of... [more]

Traditional steel processes are energy-intensive and rely heavily on fossil fuels, contributing to significant greenhouse gas emissions. By adopting electrification technologies, such as electric boilers and compressors, particularly when powered by renewable energy, steel plants can reduce their carbon footprint, enhance process flexibility, and lower long-term operational costs. This transition also aligns with increasing regulatory pressures and market demand for greener practices, positioning companies for a more competitive and sustainable future. This work investigates the potential of replacing conventional steam crackers in a steel plant that relies on the use of fossil fuels, with electrically driven heating systems powered by renewable energy sources. The overall aim was to significantly lower greenhouse gas emissions by integrating electric furnaces and heat pumps into the steel production process. This study evaluates the potential carbon savings from the integration of sol... [more]

This study presents the application of a Q-learning algorithm to optimize the selection of chemical reactions for methane reforming processes. Starting with a set of 11 candidate reactions, the algorithm identified three key reactions. These reactions effectively represent the experimental data while aligning with the underlying physics of the process and previously reported findings. The algorithm employed an epsilon-greedy policy to balance exploration and exploitation during the training process. Furthermore, simulations based on the identified reactions revealed trends consistent with experimental data. This work highlights the efficiency and adaptability of Q-learning in modeling complex catalytic systems and provides a framework for further exploration and optimization of methane reforming processes.