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In this paper eight differently tuned Artificial Bee Colony (ABC) algorithms are considered. The influence of the population size, the maximum number of iterations and the probability for choosing a food source \(({p_i})\) on the algorithm performance is investigated. Parameter identification of an E. coli fed-batch fermentation process model is used as a case study. The ABC algorithms with the best performance are defined based on the obtained numerical results. The considered ABC algorithms are compared applying InterCriteria Analysis. An additional knowledge about the ABC algorithms correlations is obtained as a result.

In this paper InterCriteria analysis (ICrA), based on the apparatus of the Index Matrices and the Intuitionistic Fuzzy Sets, is performed for a model parameters identification using different pure and hybrid metaheuristic techniques. As a case study a non-linear E. coli MC4110 fed-batch cultivation process model is considered. Series of cultivation model identification procedures using metaheuristics as genetic algorithms (GA), ant colony optimization (ACO), firefly algorithm (FA) and simulated annealing (SA) are done. The results are compared with the once obtained by applied hybrid algorithms ACO–GA, ACO–FA and GA–ACO. Further, the ICrA is used to explore the existing relations and dependences of defined cultivation model parameters, namely μ m a x , k S and Y X ∕ S , and considered metaheuristic algorithms outcomes, e.g. computation time T and objective function value J . Applying ICrA on the obtained average results of model parameters estimates, T and J , some relations between the defined criteria are established. The presented results show some dependences relating to the physical meaning of the considered model parameters and to stochastic nature of the applied in this paper metaheuristic techniques.

In this paper, the definitions of four operations over 3-dimensional index matrices are discussed. Some of their properties are discussed and an examples for their use are given.

In this paper, InterCriteria analysis (ICrA) approach for finding existing or unknown correlations between multiple objects against multiple criteria is considered. Five different algorithms for InterCriteria relations calculation, namely \(\mu \)-biased, Balanced, \(\nu \)-biased, Unbiased and Weighted, are compared using a new cross-platform software for ICrA approach – ICrAData. The comparison have been done based on numerical data from series of model parameter identification procedures. Real experimental data from an E. coli fed-batch fermentation process are used. In order to estimate the model parameters (\(\mu _{max}, k_{S}\) and \(Y_{S/X}\)) fourteen differently tuned Genetic algorithms are applied. ICrA is executed to evaluate the relation between the model parameters, objective function value and computation time. Some useful conclusions with respect to the selection of the appropriate ICrA algorithm for a given data are established. The considered example illustrates the applicability of the ICrA algorithms and demonstrates the correctness of the ICrA approach.

Contemporary InterCriteria analysis (ICrA) approach for searching of existing or unknown correlations between multiple objects against multiple criteria is applied here. Altogether five different algorithms for InterCriteria relations calculation have been examined to render the influence of the genetic algorithm parameters on the algorithm performance. Two cases, i.e. the model parameter identification of E. coli and S. cerevisiae fed-batch fermentation processes, are considered. In this investigation \(\mu \)-biased, Balanced, \(\nu \)-biased, Unbiased, as well as the newly elaborated and proposed here Weighted algorithm have been consequently applied and thoroughly examined. The obtained results for considered here two Case studies have been compared showing that the most reliable algorithm is the \(\mu \)-biased one.

In this paper two metaheuristics: Ant Colony Optimization (ACO) and Genetic Algorithms (GA), were compared for parameter identification of an E. coli fed-batch cultivation process model. A system of ordinary differential equations was used to model the biomass growth and substrate utilization. Parameter optimization was performed using a real experimental data set from an E. coli MC4110 fed-batch cultivation process. The GA and ACO adjustments were done based on several pre-tests on the optimization problem considered here. Two techniques were compared based on the obtained “best”, “worst” and “average” values for estimates and the objective function J. The results showed that the “best” value of the objective function J is achieved by ACO. At the same time, GA achieved better results for “worst” and “average” values. Analyzing the results, it could be concluded that both algorithms: ACO and GA, perform satisfactorily for the problem of parameter optimization of an E. coli fed-batch cultivation pr...

In this paper we propose a new method for dynamic parameter adaptation in the bat algorithm (BA). BA is a metaheuristic algorithm inspired by the behavior of micro bats, which has been applied to different optimization problems obtaining good results. In this paper we propose dynamic parameter adaptation of the BA using Interval Type-2 fuzzy logic. Simulation results show that the proposed method using Type-2 fuzzy logic is better in comparison with Type-1 fuzzy logic.

In this investigation the InterCriteria Analysis (ICrA) approach is applied. The apparatuses of index matrices and intuitionistic fuzzy sets are at the core of ICrA. They are used to examine the influences of two main genetic algorithms (GA) parameters—the rates of crossover (xovr) and mutation (mutr). A series of parameter identification procedures for S. cerevisiae and E. coli fermentation process models is fulfilled. Twenty GA with different xovr and mutr values are applied. Relations between ICrA criteria—GA parameters and outcomes, on the one hand, and fermentation process model parameters, on the other hand, are investigated. The ICrA approach is applied by pairs, as well as by triples. The obtained results are thoroughly analysed towards computation time and model accuracy and some conclusions about the derived criteria interactions are reported.

© Springer International Publishing Switzerland 2016. Generalized nets (GN) are applied here to describe some basic operators of genetic algorithms, namely selection, crossover and mutation and different functions for selection (roulette wheel selection method and stochastic universal sampling), different crossover techniques (one-point crossover, two-point crossover, and “cut and splice” technique), as well as mutation operator (mutation operator of the Breeder genetic algorithm). The resulting GN models can be considered as separate modules, but they can also be accumulated into a single GN model to describe a whole genetic algorithm.

In this investigation InterCriteria Analysis (ICA) is applied to examine the influences of one of the genetic algorithms parameters—the generation gap (ggap). The investigation is carried out during the model parameter identification of E. coli MC4110 cultivation process. The apparatuses of index matrices and intuitionistic fuzzy sets, which are the core of ICA, are used to establish the relations between ggap and GAs outcomes (computational time and decision accuracy), on one hand, and cultivation process model parameters on the other hand. The obtained results after ICA application are analyzed in terms of convergence time and model accuracy and some conclusions about derived interactions are reported.

In this investigation recently developed InterCriteria Analysis (ICA) is applied aiming at examination of the influence of a genetic algorithm (GA) parameter in the procedure of a parameter identification of a fermentation process model. Proven as the most sensitive GA parameter, generation gap is in the focus of this investigation. The apparatuses of index matrices and intuitionistic fuzzy sets, laid in the ICA core, are implemented to establish the relations between investigated here generation gap, from one side, and model parameters of fed-batch fermentation process of Saccharomyces cerevisiae, from the other side. The obtained results after ICA application are analysed towards convergence time and model accuracy and some conclusions about observed interactions are derived.

The present paper proposes a developed generalized net model that compares different mathematical models of the process of E. coli fed-batch cultivation. A system of four ordinary differential equations describes the main variables of the considered cultivation process, namely, biomass, substrate and acetate. For the purposes of model simulation, we use the software package GN Lite. The GN model compares the simulated performance of the proposed set of mathematical models and selects the best performing one one the basis of a predefined criterion. During the simulation, GN Lite calls the Matlab software environment to solve the process model, presented as a system of nonlinear differential equations, and plots the dynamics of the main process variables’ of the model that has been computed to perform best.

In this paper, an investigation of the influence of the population size on the Genetic Algorithm (GA) and Ant Colony Optimization (ACO) performance for a model parameter identification problem, is considered. The mathematical model of an E. coli fed-batch cultivation process is studied. The three model parameters—maximum specific growth rate (\(\mu _{max}\)), saturation constant (\(k_{S}\)) and yield coefficient (\(Y_{S/X}\)) are estimated using different population sizes. Population sizes between 5 and 200 chromosomes and 5 and 100 ants in the population are tested with constant number of generations. In order to obtain meaningful information about the influence of the population size a considerable number of independent runs of the GA are performed. The observed results show that the optimal population size is 100 chromosomes for GA and 70 ants for ACO for 200 generations. In this case accurate model parameters values are obtained in reasonable computational time. Further increase of the population size, above 100 chromosomes for GA and 70 ants for ACO, does not improve the solution accuracy. Moreover, the computational time is increased significantly.

In this paper a hybrid scheme using Firefly Algorithm (FA) - Genetic Algorithm (GA) is introduced. The novel hybrid meta-heuristics algorithm is realized and applied to PID controller parameter tuning in Smith Predictor for a nonlinear control system. The controller is used to control feed rate and to maintain glucose concentration at the desired set point for an E. coli MC4110 fed-batch cultivation process. The hybrid FA-GA adjustments are done based on several pre-tests. Simulation results indicate that the applied hybrid algorithm is effective. Good closed-loop system performance is achieved on the basis of the considered PID controllers tuning procedures. Moreover, the observed results are compared to the ones obtained by applying the pure FA and pure GA. The comparison shows that the proposed hybrid algorithm is highly competitive with standard FA and GA for considered here optimization problem.

E. coli plays significant role in modern biological engineering and industrial microbiology. In this paper the Ant Colony Optimization algorithm is proposed for parameter identification of an E. coli fed-batch cultivation process model. A system of nonlinear ordinary differential equations is used to model the biomass growth and the substrate utilization. We use real experimental data set from an E. coli MC4110 fed-batch cultivation process for performing parameter optimization. The objective function was formulated as a distance between the model predicted and the experimental data. Two different distances were used and compared — the Least Square Regression and the Hausdorff Distance. The Hausdorff Distance was used for the first time to solve the considered parameter optimization problem. The results showed that better results concerning model accuracy are obtained using the objective function with a Hausdorff Distance between the modeled and the measured data. Although the Hausdorff Distance is more time consuming than the Least Square Distance, this metric is more realistic for the considered problem.

The present work offers a novel approach to parameter identification of an E. coli cultivation process model, using hybrids of three metaheuristics - ant colony optimisation ACO, firefly algorithm FA and genetic algorithm GA. The motivation behind this hybridisation is to combine the benefits of these approaches, aimed at achieving commensurate calculations precision with less computation resources, in terms of time and memory. The proposed hybrids are approbated with the estimation of the parameters of a real E. coli cultivation process model. In the considered non-linear mathematical model three parameters are estimated, namely, maximum specific growth rate, saturation constant and yield coefficient. Based on the numerical and simulation results, it is shown that the models obtained by the proposed hybrid algorithms are competitive with standard ACO, FA and GA. The hybrids show two advantages - have much less running time and require much less memory compared to standard ACO, FA and GA.