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A new approach is proposed for modelling and monitoring bioprocesses dynamics characterized by different metabolic states. Bioprocesses cannot be described by a single model. For this reason, three phases characterised by the bioprocess are defined – periodic, exponential, and stationary. During each phase, the process passes through one or more physiological states. Each physiological state is described by a sub-model with a different structure and parameter values. The transition of the process from one physiological state to another is carried out by switching the sub-models based on a predefined key parameter. Monitoring is performed by a cascade of software sensors using the sub-models and real-time measurement of the concentrations of the main process variables. The proposed approach was tested by modelling and monitoring the Escherichia coli phytase production process.

This paper investigates the performance of various Electromagnetic Field Optimization (EFO) algorithms. Chaos maps are proposed to improve the performance of EFO algorithms. Ten chaotic maps are incorporated in EFO – Chebyshev, Circle, Gauss, Iterative, Logistic, Piecewise, Sine, Singer, Sinusoidal and Tent. To compare the performance of the constructed EFO algorithms, a case study of the identification of the model parameters of a cultivation process model is studied. An experimental data set from E. coli BL21(DE3)pPhyt109 fed-batch cultivation process is used. Based on the results of 30 runs of each EFO, some statistical and InterCriteria analyzes are performed. As a result, the best performing EFO algorithms are iterative EFO and tent chaotic map EFO. These algorithms gave the best objective value (best and mean value) and had a good distribution of results.

This paper presents an effective hybrid metaheuristic algorithm combining the genetic algorithm (GA) and a simple algorithm based on evolutionary computation. The evolutionary approach (EA) is applied to form the initial population of the GA, thus improving the algorithm’s performance, especially its convergence speed. To assess its effectiveness, the proposed hybrid algorithm, the EAGA, is evaluated on selected benchmark functions, as well as on a real optimisation process. The EAGA is used to identify parameters in a nonlinear system of differential equations modelling an E. coli fed-batch fermentation process. The obtained results are compared against published results from hybrid metaheuristic algorithms applied to the selected optimisation problems. The EAGA hybrid outperforms the competing algorithms due to its effective initial population generation strategy. The risk of premature convergence is reduced. Better numerical outcomes are achieved. The investigations validate the potential of the proposed hybrid metaheuristic EAGA for solving real complex nonlinear optimisation tasks.

This article summarizes the authors’ experiences in the development and application of the General Dynamical Model Approach related to adaptive linearizing control of biotechnological processes. Special attention has been given to some original, innovative solutions in model-based process control theory: new formalization of biotechnological process kinetics, derivation and tuning of the general software sensor of the full kinetics of biotechnological processes, and a general algorithm for fully adaptive linearizing control with software sensors. These theoretical solutions are the basis of three control strategies—fully adaptive control of the main substrate, partially adaptive control of intermediate metabolite, and recognition and stabilization of the desired physiological state based on the proposed theoretical solutions. Each strategy is illustrated in different case studies. The advantages and limitations of each of them are identified and discussed. The derived algorithms for monitoring and controlling the considered biotechnological processes are realized and included in a software platform named Interactive System for Education in Modelling and Control of Bioprocesses (InSEMCoBio). The InSEMCoBio modules and their main functions are discussed. The effectiveness of the proposed control strategies (achieving maximum productivity) has been proven through a series of simulation investigations of the considered case studies.

Corn steep liquor is a waste product from the process of treating corn grain for starch extraction. It is used as a substrate in anaerobic digestion with simultaneous hydrogen and methane production in a cascade of two anaerobic bioreactors. For process research and optimisation, adequate mathematical models are required. So, the authors aim to present a high-quality model of the corn steep liquor process for the sequential production of H2 and CH4. This paper proposes a technique for identifying the best mathematical model of the process using the metaheuristics crow search algorithm (CSA). The CSA was applied for the first time to mathematical modelling of the considered two-stage anaerobic digestion process, using real experimental data. Based on the analysis of the numerical data from the model parameter identification procedures, the influence of the main CSA parameters—the flight length, fl, and the awareness probability, AP—was investigated. Applying classical statistical tests and an innovative approach, InterCriteria Analysis, recommendations about the optimal CSA parameter tuning were proposed. The best CSA algorithm performance was achieved for the AP = 0.05, fl = 3.0, followed by AP = 0.10, fl = 2.5, and AP = 0.15, fl = 3.0. The optimal tuning of the CSA parameters resulted in a 29% improvement in solution accuracy. As a result, a mathematical model of the considered two-stage anaerobic digestion process with a high degree of accuracy was developed.

In the presented paper, the functioning of the coyote optimization algorithm (COA) is described using the apparatus of generalized nets (GNs). The COA is a population-based metaheuristic for optimization inspired by the Canis latrans species. Based on a Universal GN-model of population-based metaheuristics, а GN-model of COA is constructed by setting different characteristic functions of the GN-tokens. The presented GN-model successfully describes the considered metaheuristic algorithm, conducting basic steps and performing an optimal search.,,,,,,,,,,,,,

Cultivation process (CP) modeling and optimization are ambitious tasks due to the nonlinear nature of the models and interdependent parameters. The identification procedures for such models are challenging. Metaheuristic algorithms exhibit promising performance for such complex problems since a near-optimal solution can be found in an acceptable time. The present research explores a new hybrid metaheuristic algorithm built upon the good exploration of the genetic algorithm (GA) and the exploitation of the crow search algorithm (CSA). The efficiency of the proposed GA-CSA hybrid is studied with the model parameter identification procedure of the E. coli BL21(DE3)pPhyt109 fed-batch cultivation process. The results are compared with those of the pure GA and pure CSA applied to the same problem. A comparison with two deterministic algorithms, i.e., sequential quadratic programming (SQP) and the Quasi-Newton (Q-N) method, is also provided. A more accurate model is obtained by the GA-CSA hybrid with fewer computational resources. Although SQP and Q-N find a solution for a smaller number of function evaluations, the resulting models are not as accurate as the models generated by the three metaheuristic algorithms. The InterCriteria analysis, a mathematical approach to revealing certain relations between given criteria, and a series of statistical tests are employed to prove that there is a statistically significant difference between the results of the three stochastic algorithms. The obtained mathematical models are then successfully verified with a different set of experimental data, in which, again, the closest one is the GA-CSA model. The GA-CSA hybrid proposed in this paper is proven to be successful in the collaborative hybridization of GA and CSA with outstanding performance.

The penalty corner (PC) is one of the most important game situations in hockey (both outdoors and indoors), which results in 30 – 40% of all goals. The aim of this paper is to study the influence of the quasi-experimental methodology on the dynamics in the development of indicators characterizing the accuracy of shooting when performing PC in the potentially effective goal zones. Through the application of InterCriteria Analysis (ICrA), the research team sought to establish relationships and directions of dependencies between indicators reflecting the accuracy of zone shooting. Four elite female indoor hockey players from the team of the National Sports Academy in Bulgaria, participants in the European Indoor Hockey Clubs Challenge, were involved in the examination sessions. According to the requirements of the quasi-experimental “Push & Flick” methodology, the duration of the specialized training was set to 16 weeks. Each player performed 4,800 shootings, or approximately 300 shootings each week. Tests were carried out at the beginning (the first week) and at the end (the sixteenth week) of the experiment in order to determine the accuracy of the shooting – push/flick from a penalty corner spot (9 meters, central from the goal line). We used InterCriteria Analysis and Variance Analysis to analyze the results. The results of the study provide valuable information related to the training and specialization of elite hockey players profiled in the execution of a penalty corner

The immense application of mathematical modeling for the improvement of bioprocesses determines model development as a topical field. Metaheuristic techniques, especially hybrid algorithms, have become a preferred tool in model parameter identification. In this study, two efficient algorithms, the ant lion optimizer (ALO), inspired by the interaction between antlions and ants in a trap, and the genetic algorithm (GA), influenced by evolution and the process of natural selection, have been hybridized for the first time. The novel ALO-GA hybrid aims to balance exploration and exploitation and significantly improve its global optimization ability. Firstly, to verify the effectiveness and superiority of the proposed work, the ALO-GA is compared with several state-of-the-art hybrid algorithms on a set of classical benchmark functions. Further, the efficiency of the ALO-GA is proved in the parameter identification of a model of an Escherichia coli MC4110 fed-batch cultivation process. The obtained results have been studied in contrast to the results of various metaheuristics employed for the same problem. Hybrids between the GA, the artificial bee colony (ABC) algorithm, the ant colony optimization (ACO) algorithm, and the firefly algorithm (FA) are considered. A series of statistical tests, parametric and nonparametric, are performed. Both numerical and statistical results clearly show that ALO-GA outperforms the other competing algorithms. The ALO-GA hybrid algorithm proposed here has achieved an improvement of 6.5% compared to the GA-ACO model, 7% compared to the ACO-FA model, and 7.8% compared to the ABC-GA model.

Anaerobic Digestion (AD) of wastewater for hydrogen production is a promising technology resulting in the generation of value-added products and the reduction of the organic load of wastewater. The Two-Stage Anaerobic Digestion (TSAD) has several advantages over the conventional single-stage process due to the ability to control the acidification phase in the first bioreactor, preventing the overloading and/or the inhibition of the methanogenic population in the second bioreactor. To carry out any process research and process optimization, adequate mathematical models are required. To the best of our knowledge, no mathematical models of TSAD have been published in the literature so far. Therefore, the authors’ motivation is to present a high-quality model of the TSAD corn steeping process for the sequential production of H2 and CH4 considered in this paper. Four metaheuristics, namely Genetic Algorithm (GA), Firefly Algorithm (FA), Cuckoo Search Algorithm (CS), and Coyote Optimization Algorithm (COA), have been adapted and implemented for the first time for parameter identification of a new nonlinear mathematical model of TSAD of corn steep liquor proposed here. The superiority of some of the algorithms has been confirmed by a comparison of the observed numerical results, graphical results, and statistical analysis. The simulation results show that the four metaheuristics have achieved similar results in modelling the process dynamics in the first bioreactor. In the case of modelling the second bioreactor, a better description of the process dynamics trend has been obtained by FA, although GA has acquired the lowest value of the objective function.

Human health is reflected in all spheres of life and the economy. One of the main causes of morbidity and early mortality is polluted air. Ambient air pollution is a serious source of disease and mortality across the world. Cities are notorious for their high levels of air pollution and sickness. However, the precise degree of the health impacts of air pollution at the municipal level are still largely unclear. One of the main reasons for increased morbidity is the presence of particulate matter. The aim of our study is to show the relationship between elevated levels of particulate matter in the air and certain diseases. In this paper, we apply InterCriteria Analysis (ICrA) to find the correlation between the level of air pollution and the number of people seeking medical help. This is a new approach for the problem. The results show the affect of air pollution on certain diseases with a short exposure on polluted air and when the exposure is prolonged. We observed that some diseases are exacerbated by brief exposure to polluted air, while in others, exacerbation occurs after prolonged exposure.

In a series of papers, the initiation and development of forest fires are described in terms of the cellular automata-based Game Method for Modelling (GMM), modelling a particular area as an orthogonal grid of square cells whose values are changing with respect to predefined rules. In the present leg of this research, the simulation of the wildfire that occurred in the Kresna Gorge in Bulgaria in August 2017 is presented, rendering an account of the wind, characterized by its direction and intensity, and evaluating the impact of the fire iteratively in terms of temporal intuitionistic fuzzy sets that maintain the information about the degrees of burnt and unaffected areas. The results from the software product FireGrid, implementing the GMM-model developed by the authors, are also compared to the results from the software application FlamMap. Additionally, the paper presents for the first time the basic properties of the defined operations and operators over temporal intuitionistic fuzzy pairs.

In this paper, we consider the InterCriteria Analysis (ICrA), which is based on the index matrices and intuitionistic fuzzy sets. We demonstrate the application of ICrA using the software ICrAData. ICrAData implements five different algorithms for InterCriteria relations calculation, namely: μ-biased, Unbiased, ν-biased, Balanced and Weighted. The software ICrAData displays results in two panels – matrix and graphical view, and the results can also be exported in various formats: matrices, vectors, and graphics. In the matrix view, the column data can be sorted in ascending or descending order. The graphic view has options for resizing the intuitionistic fuzzy triangle, showing a grid and assigning different colours to the points. Moreover, a selected point in the graphic is outlined in the matrix view, and vice-versa. In the present paper some of the ICrAData software functionalities are illustrated by an example.

The paper presents a generalized net (GN) model of the process of terrain observation with the help of unmanned aerial vehicles (UAVs) for the prevention and rapid detection of wildfires. Using a GN, the process of monitoring a zone (through a UAV, which is further called a reconnaissance drone) and the localization of forest fires is described. For a more indepth study of the terrain, the reconnaissance drone needs to coordinate with a second UAV, called a specialized drone, so that video and sensory information is provided to the supervising fire command operational center. The proposed GN model was developed to assist in the decision-making process related to the coordination of the operation of both UAVs under dynamically changing terrain circumstances, such as those related to preventing or quickly containing wildfires. It describes the stages (transitions), logical determinants (transition predicate matrices), and directions of information flow (token characteristics) within the process of localization of fires using the pair of reconnaissance and specialized drones.

The index matrix (IM) is an extension of the ordinary matrix with indexed rows and columns. Over IMs’ standard matrix operations are defined and a lot of other ones that do not exist in the standard case. Intuitionistic fuzzy IMs (IFIMs) are modification of the IMs, when their elements are intuitionistic fuzzy pairs (IFPs). Extended IFIMs are IFIMs whose indices of the rows and columns are evaluated by IFPs. Different operations, relations and operators over IFIMs, and some specific ones, are defined for EIFIMs. In the paper, twelve new level operators are defined for EIFIMs and in the partial case, over IFIMs. The proposed level operators fall into two groups: operators that change the values of the EIFIM elements and operators that change the IFPs associated to the indices of the rows and columns. The basic properties of the operators are studied.

In this paper, the metaheuristics algorithm Cuckoo Search (CS), is adapted and applied for a model parameter identification of an E. coli fed-batch cultivation process. The dynamics of bacteria growth and substrate (glucose) utilization is described by a system of ordinary nonlinear differential equations. Using real experimental data set from an E. coli MC4110 fed-batch cultivation process a parameter optimization is performed. The simulation results indicate that the applied algorithm is effective and efficient. As a result, a model with high degree of accuracy is obtained applying the CS. The simulation results and comparison with genetic algorithm and ant colony optimization algorithm confirm the effectiveness of the applied CS algorithm in solving a cultivation model parameter identification problem.

In this paper, a novel meta-heuristics algorithm, namely the Firefly Algorithm (FA), is adapted and applied for a model parameter identification of an E. coli fed-batch cultivation process. A system of ordinary nonlinear differential equations is used to model the biomass growth and substrate utilization. Parameter optimization is performed using real experimental data set from an E. coli MC4110 fed-batch cultivation process. The FA adjustments are done based on several pre-tests according to the optimization problem considered here. The simulation results indicate that the applied algorithm is effective and efficient. As a result, a model with high degree of accuracy is obtained applying the FA.

This paper focuses on design of a glucose concentration control system based on nonlinear model plant of E. coli MC4110 fed-batch cultivation process. Due to significant time delay in real time glucose concentration measurement, a correction is proposed in glucose concentration measurement and a Smith predictor (SP) control structure based on universal PID controller is designed. To reduce the influence of model error in SP structure the estimate of measured glucose concentration is used. For the aim an extended Kalman filter (EKF) is designed. To achieve good closed-loop system performance genetic algorithm (GA) based optimal controller tuning procedure is applied. A standard binary encoding GA is applied. The GA parameters and operators are specified for the considered here problem. As a result the optimal PID controller settings are obtained. The simulation experiments of the control systems based on SP with EKF and without EKF are performed. The results show that the control system based on SP with EKF has a better performance than the one without EKF. For a short time the controller sets the control variable and maintains it at the desired set point during the cultivation process. As a result, a high biomass concentration of 48.3 g·l-1 is obtained at the end of the process.

In this paper optimal control algorithms for two E. coli fed-batch fermentations are developed. Fed-batch fermentation processes of E. coli strain MC4110 and E. coli strain BL21(DE3)pPhyt109 are considered. Simple material balance models are used to describe the E. coli fermentation processes. The optimal feed rate control of a primary metabolite process is studied and a biomass production is used as an example. The optimization of the considered fed-batch fermentation processes is done using the calculus of variations to determine the optimal feed rate profiles. The problem is formulated as a free final time problem where the control objective is to maximize biomass at the end of the process. The obtained optimal feed rate profiles consist of sequences of maximum and minimum feed rates. The resulting profiles are used for optimization of the E. coli fed-batch fermentations. Presented simulations show a good efficiency of the developed optimal feed rate profiles.

In this work a genetic algorithm is proposed with the purpose of the feeding trajectory optimization during a fed-batch fermentation of E. coli. The feed rate profiles are evaluated based on a number of objective functions. Optimization results obtained for different feeding trajectories demonstrate that the genetic algorithm works well and shows good computational performance. Developed optimal feed profiles meet the defined criteria. The ration of the substrate concentration and the difference between actual cell concentration and theoretical maximum cell concentration is defined as the most appropriate objective function. In this case the final cell concentration of 43 g·l-1 and final product concentration of 125 g·l-1 are achieved and there is not significant excess of substrate.

This paper presents an overview of a biochemical correspondence to defined functional states based on specific metabolic mechanisms. For Escherichia coli fed-batch cultivation processes a set of four functional states is considered. It is shown that the process can be divided into several functional states by considering the cell metabolism in more detail. As a result through the proposed functional states the changes in metabolic pathways can be described accurately. For each functional state a respective local model is proposed. Simulations of the E. coli cultivation process with functional state modelling are presented. Furthermore different functional states in a real E. coli MC4110 fed-batch cultivation process are identified and local models are developed. By simulations and comparing results to experimental data is shown that the concept of functional state modelling works in practice and leads to more precise and adequate mathematical description.

This paper presents an overview of a biochemical correspondence to defined functional state based on specific metabolic mechanisms. For E. coli fed-batch cultivation processes a set of functional states is considered. As a result through proposed functional states the changes in metabolic pathways can be described accurately.

A new functional state, namely dissolved oxygen limitation state for both bacteria Escherichia coli and yeast Saccharomyces cerevisiae fed-batch cultivation processes is presented in this study. Functional state modelling approach is applied to cultivation processes in order to overcome the main disadvantages of using global process model, namely complex model structure and a big number of model parameters. Alongwith the newly introduced dissolved oxygen limitation state, second acetate production state and first acetate production state are recognized during the fed-batch cultivation of E. coli, while mixed oxidative state and first ethanol production state are recognized during the fed-batch cultivation of S. cerevisiae. For all mentioned above functional states both structural and parameter identification is here performed based on experimental data of E. coli and S. cerevisiae fed-batch cultivations.

A set of three competing, unstructured models has been proposed to model biomass growth, glucose utilization, acetate formation, dissolved oxygen consumption and carbon dioxide accumulation of a fed-batch cultivation process of Escherichia coli. The inhibiting effect of acetate on growth of E. coli cultures is included in the considered models. The model identification is carried out using experimental data from the cultivation process. Genetic algorithms are used for parameter estimation. The model discrimination is based on the four criteria, namely sum of square errors, Fisher criterion, Akaike information criterion and minimum description length criterion. The most suitable model is identified that reflects the state variables curves adequately by considering acetate inhibited growth according to the Jerusalimsky approach.

In this paper the problem of a parameter estimation using genetic algorithms is examined. A case study considering the estimation of 6 parameters of a nonlinear dynamic model of E. coli fermentation is presented as a test problem. The parameter estimation problem is stated as a nonlinear programming problem subject to nonlinear differential-algebraic constraints. This problem is known to be frequently ill-conditioned and multimodal. Thus, traditional (gradient-based) local optimization methods fail to arrive satisfied solutions. To overcome their limitations, the use of different genetic algorithms as stochastic global optimization methods is explored. These algorithms are proved to be very suitable for the optimization of highly non-linear problems with many variables. Genetic algorithms can guarantee global optimality and robustness. These facts make them advantageous in use for parameter identification of fermentation models. A comparison between simple, modified and multi-population genetic algorithms is presented. The best result is obtained using the modified genetic algorithm. The considered algorithms converged very closely to the cost value but the modified algorithm is in times faster than other two.

In this paper an optimal control algorithm for E. coli fed-batch fermentation has been developed. A simple material balance model is used to describe the E. coli fermentation process. The optimal feed rate control of a primary metabolite process is studied and a biomass production is used as an example. An optimization of a fed-batch fermentation process is usually done using the calculus of variations to determine an optimal feed rate profile. In the optimal control literature the problem is formulated as a free final time problem where the control objective is to maximise biomass at the end of the process. The obtained optimal feed rate profile consists of sequences of maximum and minimum feed rates. The obtained results are used for optimization of E. coli fed-batch fermentation and the presented simulations show a good efficiency of the developed optimal feed rate profile.

In order to render the specific peculiarities of the fermentation processes, as well as to avoid the complexity of mathematical description with systems of differential equations, the elaboration of some new methods and approaches for their modelling and control is predetermined. As a new, alternative approach for modelling of fermentation processes, an application of generalized nets is presented in this paper. The theory of generalized nets is applied to the fermentation process of Brevibacterium flavul 22LD for L-lysine production. A generalized net model of considered process is developed. For comparison and completeness, model with differential equations is also provided. The generalized nets model developed for the fed-batch cultivation of Brevibacterium flavul 22LD allows changing the concentration of the feeding solution and the aeration rate. In this way some inhibition effects are prevented and a possibility for optimal carrying out of the considered fermentation process is provided.

This paper presents the use of genetic algorithms for identification of Escherichia coli fed-batch fermentation process. Genetic algorithms are a directed random search technique, based on the mechanics of natural selection and natural genetics, which can find the global optimal solution in complex multidimensional search space. The dynamic behavior of considered process has known nonlinear structure, described with a system of deterministic nonlinear differential equations according to the mass balance. The parameters of the model are estimated using genetic algorithms. Simulation examples for demonstration of the effectiveness and robustness of the proposed identification scheme are included. As a result, the model accurately predicts the process of cultivation of E. coli.

In this paper the metaheuristic Simulated Annealing (SA) is applied for parameter identification of non-linear model of cultivation process. SA algorithm is a stochastic relaxation technique, using the Metropolis algorithm based on the Boltzmann distribution in statistical mechanics, for solving nonconvex optimization problems. A real E. coli MC4110 fed-batch cultivation process is considered. The mathematical model is presented by a system of five ordinary differential equations, describing the regarded cultivation process variables - biomass, substrate, acetate, dissolved oxygen and bioreactor volume increasing. The obtained criteria values show that the developed model is adequate and has a high degree of accuracy. The presented results are a confirmation of successful application of the SA algorithm and of the choice of SA algorithm parameters.