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In this work, we address the optimal water management strategies and fair cost distribution among various shale gas companies placed in the same play. A mixed integer non-linear programming (MINLP) formulation with the objective of maximizing the Nash product is presented including the analysis of different policies to determine the most appropriate transportation cost distribution. As a result of Nash product maximization and transfer cost designation formulation, the problem includes non-linearities in the objective function which hinders its resolution. Therefore, to solve the model effectively, we apply logarithmic operation and separable programming approach to reformulate the Nash product and Glover's linearization to reformulate the bilinear terms appearing in the transfer cost designation. Finally, the applicability of the proposed approach is illustrated in a case study comprising 4 companies. Then, an example comprising 10 shale gas companies is performed to analyse the behaviour of the proposed formulation considering a larger problem.

Under the ever-increasing capital intensive environment that contemporary process industries face, oligopolies begin to form in mature markets where a small number of companies regulate and serve the customer base. Strategic and operational decisions are highly dependent on the firms’ customer portfolio and conventional modelling approaches neglect the rational behaviour of the decision makers, with regards to the problem of customer allocation, by assuming either static competition or a leader-follower structure. In this article, we address the fair customer allocation within oligopolies by employing the Nash bargaining approach. The overall problem is formulated as mixed integer program with linear constraints and a nonlinear objective function which is further linearised following a separable programming approach. Case studies from the industrial liquid market highlight the importance and benefits of the proposed game theoretic approach.

A large power generation facility is a complex multi-criteria system associated with multivariate couplings, high dependency, and non-linearity among the operating variables which present a major challenge to ensure efficient power production. In this research, an integrated artificial intelligence (AI) and response surface methodology (AI-RSM) framework to achieve the efficient power production operation of a 660 MW coal power plant is presented. Two AI algorithms, i.e., extreme learning machine (ELM) and support vector machine (SVM) are trained comprehensively on the power plant's operational data and are validated as well. Full factorial design of experiments on the three levels of the operating parameters are constructed and simulated from the better performing AI model which is an effective non-linear representation of the complex power plant operation. RSM analysis is carried out under three power generation scenarios to simulate the effective values of the operating variables which are tested on the power plant's operation and a reasonable agreement is found with the experimental observations. The notable improvement in fuel consumption rate, thermal efficiency, and heat rate of the power plant under Half Load, Mid Load, and Full Load capacity of the power plant is achieved by the AI-RSM framework enabled analyses. It is estimated that annual reduction in CO2, CH4 and Hg emissions measuring 210 kg tons per year (kt/y), 23.8 t/y and 2.7 kg/y, respectively can be obtained corresponding to Mid Load operating state of the power plant. The research presents the reliable and robust utilization of AI-RSM framework for simulating the effective operating conditions for the fossil-based power plants’ operation with an eventual goal to improve the techno-environmental performance which is expected to contribute to net-zero emissions goal from the energy sector.

In this article, we introduce a novel framework for the design of multi set-point nonlinear explicit controllers for process systems engineering problems where the set-points are treated as uncertain parameters simultaneously with the initial state of the dynamical system at each sampling instance. To this end, an algorithm for a special class of multi-parametric nonlinear programming problems with uncertain parameters on the right-hand side of the constraints and the cost coefficients of the objective function is presented. The algorithm is based on computed algebra methods for symbolic manipulation that enable an analytical solution of the optimality conditions of the underlying multi-parametric nonlinear program. A notable property of the presented algorithm is the computation of exact, in general nonconvex, critical regions that results in potentially great computational savings through a reduction in the number of convex approximate critical regions.

This work addresses the optimal management of a system through a two-stage stochastic Non-Linear Programming (NLP) formulation. This approach uses a scenario-based mathematical formulation to tackle uncertain information. Accurate representation of uncertainty usually involves increased number of scenarios, which may result in large-scale optimisation models. Thus, the proposed formulation aims to reduce the number of scenarios through a sensitivity analysis approach. The proposed model investigates the use of scenario reduction techniques to reduce computational requirements while maintaining good quality of the final optimal solution.

This work presents a study that aims to compare two discretization methods for solving parameter estimation using multiparametric programming. In our earlier work, parameter estimation using multiparametric programming was presented where model parameters were obtained as an explicit function of measurements. In this method, the nonlinear ordinary equations (ODEs) model was discretized by using explicit Euler’s method to obtain algebraic equations. Then, a square system of parametric nonlinear algebraic equations was obtained by formulating optimality condition. These equations were then solved symbolically to obtain model parameters as an explicit function of measurements. Thus, the online computation burden of solving optimization problems for parameter estimation is replaced by simple function evaluations. In this work, we use implicit Euler’s method for discretization of nonlinear ODEs model and compare with the explicit Euler’s method for parameter estimation using multiparametric programming. Complexity of explicit parametric functions, accuracy of parameter estimates and effect of step size are discussed.

Bi-level programming has been used widely to model interactions between hierarchical decision-making problems, and their solution is challenging, especially when the lower-level problem contains discrete decisions. The solution of such mixed-integer linear bi-level problems typically need decomposition, approximation or heuristic-based strategies which either require high computational effort or cannot guarantee a global optimal solution. To overcome these issues, this paper proposes a two-step reformulation strategy in which the first part consists of reformulating the inner mixed-integer problem into a nonlinear one, while in the second step the well-known Karush-Kuhn-Tucker conditions for the nonlinear problem are formulated. This results in a mixed-integer nonlinear problem that can be solved with a global optimiser. The computational and numerical benefits of the proposed reformulation strategy are demonstrated by solving five examples from the literature.

Advanced decision making in the process industries requires efficient use of information available at different decision levels. Traditionally, planning, scheduling, and optimal control problems are solved in a decoupled way, neglecting their strong interdependence. Integrated planning, scheduling and optimal control (iPSC) aims to address this issue. Formulating the iPSC, results in a large scale nonconvex mixed integer nonlinear programming problem. In the present work, we propose a new approach for the iPSC of continuous processes aiming to reduce model and computational complexity. For the planning and scheduling, a Traveling Salesman Problem-based formulation is employed, where the planning periods are modeled in discrete time while the scheduling within each week is in continuous time. Another feature of the proposed iPSC framework is that backlog, idle production time, and multiple customers are introduced. The resulting problem is a mixed integer programming problem and different solution strategi...

Fault detection has become increasingly important for improving the reliability and safety of process systems. This paper presents a model-based fault detection methodology for nonlinear process systems. The objective of this work is to detect faults by estimating the model parameters using multiparametric programming. The parameter estimates are obtained as an explicit function of the measurements by using multiparametric programming. The diagnosis of fault is carried out by monitoring the changes in the residual of model parameters. Case studies of fault detection for a single stage evaporator system and quadruple tank system are presented. A number of faulty and fault-free scenarios are considered to show the effectiveness of the presented approach. The proposed approach successfully estimates the model parameters and detects the faults through a simple function evaluation of explicit functions.

Multi-parametric programming has proven to be an invaluable tool for optimisation under uncertainty. Despite the theoretical developments in this area, the ability to handle uncertain parameters on the left-hand side remains limited and as a result, hybrid, or approximate solution strategies have been proposed in the literature. In this work, a new algorithm is introduced for the exact solution of multi-parametric linear programming problems with simultaneous variations in the objective function's coefficients, the right-hand side and the left-hand side of the constraints. The proposed methodology is based on the analytical solution of the system of equations derived from the first order Karush–Kuhn–Tucker conditions for general linear programming problems using symbolic manipulation. Emphasis is given on the ability of the proposed methodology to handle efficiently the LHS uncertainty by computing exactly the corresponding nonconvex critical regions while numerical studies underline further the advantages of the proposed methodology, when compared to existing algorithms.

In the present work, two new, (multi-)parametric programming (mp-P)-inspired algorithms for the solution of mixed-integer nonlinear programming (MINLP) problems are developed, with their main focus being on process synthesis problems. The algorithms are developed for the special case in which the nonlinearities arise because of logarithmic terms, with the first one being developed for the deterministic case, and the second for the parametric case (p-MINLP). The key idea is to formulate and solve the square system of the first-order Karush-Kuhn-Tucker (KKT) conditions in an analytical way, by treating the binary variables and/or uncertain parameters as symbolic parameters. To this effect, symbolic manipulation and solution techniques are employed. In order to demonstrate the applicability and validity of the proposed algorithms, two process synthesis case studies are examined. The corresponding solutions are then validated using state-of-the-art numerical MINLP solvers. For p-MINLP, the solution is given by an optimal solution as an explicit function of the uncertain parameters.

Process and energy models provide an invaluable tool for design, analysis and optimisation. These models are usually based upon a number of assumptions, simplifications and approximations, thereby introducing uncertainty in the model predictions. Making model based optimal decisions under uncertainty is therefore a challenging task. This issue is further exacerbated when more than one objective is to be optimised simultaneously, resulting in a Multi-Objective Optimisation (MO2MO2) problem. Even though, some methods have been proposed for MO2MO2 problems under uncertainty, two separate optimisation techniques are employed; one to address the multi-objective aspect and another to take into account uncertainty. In the present work, we propose a unified optimisation framework for linear MO2MO2 problems, in which the uncertainty and the multiple objectives are modelled as varying parameters. The MO2MO2 under uncertainty problem (MO2U2)(MO2U2) is thus reformulated and solved as a multi-parametric programming problem. The solution of the multi-parametric programming problem provides the optimal solution as a set of parametric profiles.

Development of fast, robust and reliable computational tools capable of addressing the process management under uncertain conditions, is an active topic in the current process systems engineering literature. In fact, scenario reduction strategies (for example SCENRED and OSCAR) have acquired a lot of attention to overcome the traditional issues associated to large-scale scenario-based problems. Thus, this work proposes a novel scenario-reduction alternative (henceforth known as SCANCODE approach) by combining Graph Theory to construct a network and community detection methods to identify the clusters within the network. The capabilities and limitations of the proposed approach were tested through the two-stage MILP optimisation of a bio-based energy network under raw material availability and energy demand uncertainties. For comparison purposes, the same problem was solved using the sets of scenarios obtained with SCENRED and OSCAR. This comparison demonstrates the quality of SCANCODE approach while states the potential benefits of the proposed approach over the current alternatives.

Haemodialysis is a blood treatment technique used for patients whose kidneys are not working normally. A number of Linear Model Predictive Control (LMPC) formulations for controlling haemodialysis have been proposed in the literature. In this paper, a Nonlinear Model Predictive Control (NMPC) formulation is proposed that instead of using an approximated linear model takes into account the nonlinear model for haemodialysis. One of the key advantages of the NMPC formulation is that it gives more comprehensive control of the haemodialysis process. Four manipulated variables are considered: the blood flow out of the body, the blood flow returned from the dialysis machine to the body, the dialysate rate and the sodium concentration of the inlet blood flow. By manipulating these variables, the fluid volumes and the toxin clearance are monitored and controlled. The results show that a better control performance for the blood volumes and toxin clearance is obtained while the blood and dialysate flow rates are held at a relatively low level, which is expected to reduce the risk of adverse reactions for the patients.

The work presented in this paper aims at developing a novel meshless parameter estimation framework for a system of partial differential equations (PDEs) using artificial neural network (ANN) approximations. The PDE models to be treated consist of linear and nonlinear PDEs, with Dirichlet and Neumann boundary conditions, considering both regular and irregular boundaries. This paper focuses on testing the applicability of neural networks for estimating the process model parameters while simultaneously computing the model predictions of the state variables in the system of PDEs representing the process. The capability of the proposed methodology is demonstrated with five numerical problems, showing that the ANN-based approach is very efficient by providing accurate solutions in reasonable computing times.

The development of fast, robust and reliable computational tools capable of addressing process management under uncertain conditions is an active topic in the current literature, and more precisely for the process systems engineering one. Particularly, scenario reduction strategies have emerged as an alternative to overcome the traditional issues associated with large-scale scenario-based problems. This work proposes a novel and flexible scenario-reduction alternative that integrates data mining, graph theory and community detection concepts to represent the uncertain information as a network and identify the most efficient communities/clusters. The capabilities of the proposed approach were tested by solving a set of two-stage mixed-integer linear programming problems under uncertainty. For comparison and validation purposes, these problems were also solved using two available methods (SCENRED and OSCAR). This comparison demonstrates that the results obtained by using the proposed approach are at least as good or better, in terms of quality and accuracy, than the results obtained bu using SCENRED and OSCAR. Additionally, the practical advantage of the proposed parameter definition rule is demonstrated as a way to overcome the limitations of the current alternatives (i.e. arbitrary user-defined parameters).

The quantitative description of the dynamic behaviour of reacting systems requires the identification of an appropriate set of kinetic model equations. The selection of the correct model may pose substantial challenges as there may be a large number of candidate kinetic model structures. In this work, a model selection approach is presented where an Artificial Neural Network classifier is trained for recognising appropriate kinetic model structures given the available experimental evidence. The method does not require the fitting of kinetic parameters and it is well suited when there is a high number of candidate kinetic mechanisms. The approach is demonstrated on a simulated case study on the selection of a kinetic model for describing the dynamics of a three-component reacting system in a batch reactor. The sensitivity of the approach to a change in the experimental design and to a change in the system noise is assessed.

In this work, a methodology for fault detection in wastewater treatment systems, based on parameter estimation, using multiparametric programming is presented. The main idea is to detect faults by estimating model parameters, and monitoring the changes in residuals of model parameters. In the proposed methodology, a nonlinear dynamic model of wastewater treatment was discretized to algebraic equations using Euler’s method. A parameter estimation problem was then formulated and transformed into a square system of parametric nonlinear algebraic equations by writing the optimality conditions. The parametric nonlinear algebraic equations were then solved symbolically to obtain the concentration of substrate in the inflow, , inhibition coefficient, , and specific growth rate, , as an explicit function of state variables (concentration of biomass, concentration of organic matter, concentration of dissolved oxygen, and volume, ). The estimated model parameter values were compared with values from the normal operation. If the residual of model parameters exceeds a certain threshold value, a fault is detected. The application demonstrates the viability of the approach, and highlights its ability to detect faults in wastewater treatment systems by providing quick and accurate parameter estimates using the evaluation of explicit parametric functions.

In this work we investigate the integrated planning, scheduling and control (iPSC) of process systems under uncertain conditions throughout the three levels of decision making. The planning problem is explored in a rolling horizon fashion coupled with demand forecasts. Proactive and reactive approaches are employed to handle the effect of stochastic variations. Depending on the nature of the uncertain parameters robust optimisation and chance constrained programming are employed. For the closed-loop implementation of the control, novel multi-parametric controllers are designed. The proposed framework is tested on the iPSC of a polymerisation process. Finally, Monte Carlo simulations are conducted to highlight the benefits of the “uncertainty-aware” solutions when compared to the deterministic ones.

Fault detection is becoming an important issue in fermentation processes. Any improper formulation or contamination in the fermentation may change the kinetic model parameters and lead to a process fault. In this work, a square system of parametric nonlinear algebraic equations is formulated and solved symbolically to obtain the kinetic model parameters as an explicit function of measurements, so as to estimate the parameters to detect and diagnose the faults in fermentation processes. A number of scenarios are considered to show the effectiveness of the presented approach. The proposed approach successfully estimates the model parameters and detects the faults in the system.

Further quantitative understanding of the biological effects and mechanisms involved in cellular and intracellular delivery of nucleic acid materials is critical to produce clinical applications in the area of gene therapy. Several modeling approaches have been used in this field; however, a comprehensive approach that integrates all the key pharmacological issues into a holistic framework that is applicable for in vivo conditions is still lacking. This contribution presents a pharmacokinetic/pharmacodynamic model-based control study of non-viral siRNA delivery describing the dynamics of the delivery process and takes into account the main multi-objective optimization issues such as efficacy and toxicity, as well as the effect of uncertainty in cell doubling time. The methodology developed in this work is used to predict the optimal dosage injection rate and optimal intracellular exposure of siRNAs in order to improve pharmacological effects before cell division occurs. The present analysis successfully provides quantitative predictions of non-viral siRNA activity paving the path for further experimental work to probe more efficient delivery systems. This article is protected by copyright. All rights reserved.

This work presents a Mixed Integer Linear Programming (MILP) approach based on a combination of a rolling horizon and stochastic programming formulation. The objective of the proposed formulation is the optimal management of the supply and demand of energy and heat in microgrids under uncertainty, in order to minimise the operational cost. Delays in the starting time of energy demands are allowed within a predefined time windows to tackle flexible demand profiles. This approach uses a scenario-based stochastic programming formulation. These scenarios consider uncertainty in the wind speed forecast, the processing time of the energy tasks and the overall heat demand, to take into account all possible scenarios related to the generation and demand of energy and heat. Nevertheless, embracing all external scenarios associated with wind speed prediction makes their consideration computationally intractable. Thus, updating input information (e.g., wind speed forecast) is required to guarantee good quality and practical solutions. Hence, the two-stage stochastic MILP formulation is introduced into a rolling horizon approach that periodically updates input information.

In this work, motivated by the need for closed loop implementation of the control objectives set within the integrated planning, scheduling and control (iPSC) problem we introduce: a new algorithm for the solution of multi-parametric nonlinear programming problems, a novel concept for the design of explicit multi-setpoint controllers. In addition, the planning and scheduling decisions are modelled using a TSP-based (Traveling Salesman Problem) formulation. Disturbance rejection is considered at the control level so as to secure the validity of the open-loop solution from the iPSC along with rescheduling considerations. Finally, a case study illustrates the benefits and necessity of the proposed closed loop framework.

This work addresses the optimal management of a microgrid through a two-stage Mixed Integer Linear Programming (MILP) approach. This approach uses a scenario-based mathematical formulation to deal with uncertain information. Sufficient representation of uncertainty usually requires increased number of scenarios, which result in large-scale optimisation models. This paper investigates the use of scenario reduction techniques to reduce computational requirements while maintaining good quality of the final optimal solution. The proposed approach is then applied to optimally manage the heat demand uncertainty within a microgrid so as to minimise the operational cost while considering electricity and heat generation, purchases, sales, storage and demand profiles.

Microreaction technology is an interdisciplinary field that has gained significant momentum in recent years due to the numerous advantages it offers compared to conventional systems in terms of enhanced heat and mass transfer and safer operation. The experimental efficiency achieved through the well-defined conditions offered by microchannel reactors has been utilised to elucidate intrinsic reaction kinetics, often in reaction spaces that were previously unexplored. In this review, we discuss prospects for advancing catalytic process development by combined application of microstructured flow reactors with techniques for in situ catalyst characterisation and mathematical optimisation.

Key points • Cystic fibrosis (CF) is a common genetic disease caused by loss-of-function mutations in the cystic fibrosis transmembrane conductance regulator gene, which encodes a channel protein, selective for anions. • In the lungs, the site of the most severe symptoms, CF causes abnormal electrolyte transport in epithelial cells which line the airways. • Airway epithelial ion transport can be assessed by measuring the trans-epithelial potential difference (Vt) which shows characteristic changes in CF individuals. We developed a biophysical model of ion transport in human nasal epithelia, in order to investigate quantitatively which transport parameters underlie these observed bioelectric changes. • We found that loss of apical Cl− permeability alone is insufficient to explain the bioelectric properties of CF epithelia. An increase of apical Na+ permeability must also occur. • This insight has important implications for our understanding of the physiology of CF disease, and hence for potential therapies aimed at correcting the CF ion transport defect. Abstract Cystic fibrosis (CF) is caused by mutations in the cystic fibrosis transmembrane conductance regulator (CFTR) gene, which encodes an anion channel. In the human lung CFTR loss causes abnormal ion transport across airway epithelial cells. As a result CF individuals produce thick mucus, suffer persistent bacterial infections and have a much reduced life expectancy. Trans-epithelial potential difference (Vt) measurements are routinely carried out on nasal epithelia of CF patients in the clinic. CF epithelia exhibit a hyperpolarised basal Vt and a larger Vt change in response to amiloride (a blocker of the epithelial Na+ channel, ENaC). Are these altered bioelectric properties solely a result of electrical coupling between the ENaC and CFTR currents, or are they due to an increased ENaC permeability associated with CFTR loss? To examine these issues we have developed a quantitative mathematical model of human nasal epithelial ion transport. We find that while the loss of CFTR permeability hyperpolarises Vt and also increases amiloride-sensitive Vt, these effects are too small to account for the magnitude of change observed in CF epithelia. Instead, a parallel increase in ENaC permeability is required to adequately fit observed experimental data. Our study provides quantitative predictions for the complex relationships between ionic permeabilities and nasal Vt, giving insights into the physiology of CF disease that have important implications for CF therapy.

Production optimization and planning is a key part of the modern process industry operations. It plays a major role in sustaining the profitability of the operations and providing decision making guidelines to attain business objectives through achieving best margins and minimum operating costs. Numerous industries have benefited from planning models to achieve optimal operations subject to technologies involved, resources requirements, production constraints and available markets for the products sales.

The aim of this research work is to take a step towards a patient individual optimal haemodialysis treatment by describing and optimising the treatment through a physiological model of the kidney. Therefore, a mathematical model consiting of a set of ordinary differential equations (ODE) that describes the distribution of fluids, ions, proteins and toxins in the human body is used in this work. The ODEs are transformed to algebraic equations using Artificial Neural Networks (ANN) which then are solved.

Gene therapy provides a new avenue for the treatment of life-threatening diseases such as cancer, HIV and a wide range of other illnesses. A successful approach depends on the effectiveness and safety of the delivery of therapeutic genetic materials. Thus, knowledge of the effects (pharmacodynamics) and kinetics (pharmacokinetics) of therapeutic agents in the body is critical. In this work, mathematical and computational modelling is used for analysis, optimisation and control of siRNA delivery. A pharmacokinetic (PK) model was developed using the experimental data reported in the literature to describe the transport of siRNA therapeutics by non-viral nano-carriers (NCs) between different compartments in the cell. The model development involves estimating the rate constants of siRNA translocation over the intracellular barriers. Following that, the developed PK models are used to obtain optimal gene infusion rates. The current work includes providing a balance between two main and conflicting objectives: high efficacy and low toxicity.

Despite the great industrial importance of benzaldehyde as a reaction intermediate, only a few attempts have been made in the literature to develop kinetic models able of characterising the catalytic oxidation of benzyl alcohol to benzaldehyde quantitatively both in batch and flow systems. The purpose of this paper is to merge the information obtained from a laboratory scale batch glass stirred reactor (GSR) with the information obtained from a continuous-flow micro-packed bed reactor (MPBR) for an accurate and quantitative description of the products distribution in these reaction systems. A two-stage procedure is applied for this purpose where experimental design techniques are used for evaluating the most promising regions of the experimental space for the identification of kinetic models.

In this paper, reduced nonlinear refinery models are developed by generating and using input–output data from a process simulator. In particular, rigorous process models of continuous catalytic reformer (CCR) and naphtha splitter units are used for generating the data. To deal with complexity associated with large amounts of data, that is usually available in the refineries, a disaggregation–aggregation based approach is presented. The data is split (disaggregation) into smaller subsets and reduced artificial neural network (ANN) models are obtained for each of the subset. These ANN models are then combined (aggregation) to obtain an ANN model which represents all the data originally generated. The disaggregation step can be carried out within a parallel computing platform. Refinery optimization studies are carried out to demonstrate the applicability and the usefulness of the proposed model reduction approach.

In this work a new approach for parameter estimation which is based upon decomposing the problem into two subproblems is proposed, the first subproblem generates an Artificial Neural Network (ANN) model from the given data and then the second subproblem uses the ANN model to obtain an estimate of the parameters. The analytical derivates from the ANN model obtained from the first subproblem are used for obtaining the differential terms in the formulation of the second subproblem. This greatly simplifies the parameter estimation problem. The key advantage of the proposed approach is that solution of a large optimization problem requiring high computational resources is avoided and instead two smaller problems are solved. This approach is particularly useful for large and noisy data sets and nonlinear models where ANN models are known to perform quite well and therefore plays an important role in the solution of the overall parameter estimation problem.

This article presents model predictive controllers (MPCs) and multi-parametric model-based controllers for delivery of anaesthetic agents. The MPC can take into account constraints on drug delivery rates and state of the patient but requires solving an optimization problem at regular time intervals. The multi-parametric controller has all the advantages of the MPC and does not require repetitive solution of optimization problem for its implementation. This is achieved by obtaining the optimal drug delivery rates as a set of explicit functions of the state of the patient. The derivation of the controllers relies on using detailed models of the system. A compartmental model for the delivery of three drugs for anaesthesia is developed. The key feature of this model is that mean arterial pressure, cardiac output and unconsciousness of the patient can be simultaneously regulated. This is achieved by using three drugs: dopamine (DP), sodium nitroprusside (SNP) and isoflurane. A number of dynamic simulation experiments are carried out for the validation of the model. The model is then used for the design of model predictive and multi-parametric controllers, and the performance of the controllers is analyzed.

A mathematical programming approach for automatic computation of the optimal configuration of artificial neural networks (ANNs) is presented. Training of the network is modelled as a mixed-integer program (MIP) where 0–1 binary variables are introduced to represent the existence (binary variable = 1) and non-existence (binary variable = 0) of the nodes and the interconnections between the nodes. The objective is to minimize the number of nodes and/or interconnections to meet a given error criteria. From modelling point of view, the key advantage of the proposed approach is that the user does not have to try different configurations of the network, a solution of the proposed MIP formulation automatically generates the optimal configuration of the network. From the implementation of ANN point of view, a simplified representation of the network is obtained, where redundant nodes and interconnections have been eliminated. A number of examples are presented to demonstrate the applicability of the proposed approach.