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In this paper, a Joint set-up procedure for tuning metaheuristic algorithms’ parameters is proposed. The approach is applied to a genetic algorithm (GA) and tested further on the artificial bee colony (ABC) algorithm. The joint influence of parameters (the crossover and mutation probabilities for GA and the number of population and limit for ABC) on the performance of the algorithms is investigated. As a case study, a model parameter identification of an E. coli fed-batch cultivation process is considered. E. coli is one of the most commonly used bacteria for producing medical substances in the pharmaceutical industry. The development of an effective model of a fed-batch cultivation process is very important. The processes in a bioreactor are usually described by a system of parametric nonlinear differential equations. The model parameter identification is a difficult optimization problem, which cannot be solved by applying traditional numerical methods. Feasibilities of GA and ABC for a model parameter identification of a nonlinear fed-batch cultivation process based on real experimental data are presented. The application of the proposed Joint set-up approach leads to a significant improvement in the performance of GA and ABC. As a result, a reasonable enhancement of the E. coli cultivation model accuracy is achieved. The main advantage of the tuning procedure, which searches an optimal set of values of GA and ABC control parameters, focusing on promising intervals of variation of the parameter values and refining their ranges, is that the computational efforts are reduced by more than 60% for the ABC algorithm and more than 90% for GA.

In this paper, the artificial bee colony (ABC) algorithm is hybridized with the genetic algorithm (GA) for a model parameter identification problem. When dealing with real-world and large-scale problems, it becomes evident that concentrating on a sole metaheuristic algorithm is somewhat restrictive. A skilled combination between metaheuristics or other optimization techniques, a so-called hybrid metaheuristic, can provide more efficient behavior and greater flexibility. Hybrid metaheuristics combine the advantages of one algorithm with the strengths of another. ABC, based on the foraging behavior of honey bees, and GA, based on the mechanics of nature selection, are among the most efficient biologically inspired population-based algorithms. The performance of the proposed ABC-GA hybrid algorithm is examined, including classic benchmark test functions. To demonstrate the effectiveness of ABC-GA for a real-world problem, parameter identification of an Escherichia coli MC4110 fed-batch cultivation process model is considered. The computational results of the designed algorithm are compared to the results of different hybridized biologically inspired techniques (ant colony optimization (ACO) and firefly algorithm (FA))—hybrid algorithms as ACO-GA, GA-ACO and ACO-FA. The algorithms are applied to the same problems—a set of benchmark test functions and the real nonlinear optimization problem. Taking into account the overall searchability and computational efficiency, the results clearly show that the proposed ABC–GA algorithm outperforms the considered hybrid algorithms.

The water cycle algorithm (WCA), which is a metaheuristic method inspired by the movements of rivers and streams towards the sea in nature, has been adapted and applied here for the first time for solving such a challenging problem as the parameter identification of fermentation process (FP) models. Bacteria and yeast are chosen as representatives of FP models that are subjected to parameter identification due to their impact in different industrial fields. In addition, WCA is considered in comparison with the genetic algorithm (GA), which is another population-based technique that has been proved to be a promising alternative of conventional optimisation methods. The obtained results have been thoroughly analysed in order to outline the advantages and disadvantages of each algorithm when solving such a complicated real-world task. A discussion and a comparative analysis of both metaheuristic algorithms reveal the impact of WCA on model identification problems and show that the newly applied WCA outperforms GA with regard to the model accuracy.

In combinatorial optimization, the goal is to find the optimal object from a finite set. Since such problems are hard to be solved, usually some metaheuristics is applied. One of the most successful techniques for a number of classes of problems is Ant Colony Optimization (ACO). Some start strategies can be applied, to the ACO algorithms, to improve their performance. Here, the InterCriteria Analysis (ICrA) is applied to the ACO algorithm. On the basis of the ICrA, we examine and analyse the ACO performance according to the different start strategies.

The workforce planning helps organizations to optimize the production process with the aim to minimize the assigning costs. The problem is to select a set of employees from a set of available workers and to assign this staff to the jobs to be performed. A workforce planning problem is very complex and requires special algorithms to be solved. The complexity of this problem does not allow the application of exact methods for instances of realistic size. Therefore, we will apply Ant Colony Optimization (ACO) algorithm, which is a stochastic method for solving combinatorial optimization problems. The ACO algorithm is tested on a set of 20 workforce planning problem instances. The obtained solutions are compared with other methods, as scatter search and genetic algorithm. The results show that ACO algorithm performs better than other the two algorithms. Further, we focus on the influence of the number of ants and the number of iterations on ACO algorithm performance. The tests are done on 16 different problem instances – ten structured and six unstructured problems. The results from ACO optimization procedures are discussed. In order to evaluate the influence of considered ACO parameters additional investigation is done. InterCriteria Analysis is performed on the ACO results for the regarded 16 problems. The results show that for the considered here workforce planning problem the best performance is achieved by the ACO algorithm with five ants in population.

Ant Colony Optimization (ACO) has been used successfully to solve hard combinatorial optimization problems. This metaheuristics method is inspired by the foraging behavior of ant colonies, which manage to establish the shortest routes between their colonies to feeding sources and back. In this paper, ACO algorithms are developed to provide near-optimal solutions for Global Positioning System surveying problem (GSP). In designing Global Positioning System (GPS) surveying network, a given set of earth points must be observed consecutively (schedule). The cost of the schedule is the sum of the time needed to go from one point to another. The problem is to search for the best order in which this observation is executed, minimizing the cost of the schedule. We apply InterCriteria Analysis (ICrA) on the achieved results. Based on ICrA we examine some relations between considered GSPs and ACO algorithm performance.

The workforce planning helps organizations to optimize the production process with aim to minimize the assigning costs. A workforce planning problem is very complex and needs special algorithms to be solved. The problem is to select set of employers from a set of available workers and to assign this staff to the jobs to be performed. Each job requires a time to be completed. For efficiency, a worker must performs a minimum number of hours of any assigned job. There is a maximum number of jobs that can be assigned and a maximum number of workers that can be assigned. There is a set of jobs that shows the jobs on which the worker is qualified. The objective is to minimize the costs associated to the human resources needed to fulfill the work requirements. On this work we propose a variant of Ant Colony Optimization (ACO) algorithm to solve workforce optimization problem. The algorithm is tested on a set of 20 test problems. Achieved solutions are compared with other methods, as scatter search and genetic algorithm. Obtained results show that ACO algorithm performs better than other two algorithms.

In the present paper, the apparatus of generalized nets is used to describe the metaheuristic technique Bat algorithm. Generalized nets are considered an effective and appropriate tool for description of the logics of different optimization techniques. As a result, the developed generalized net model executes the Bat algorithm procedures, conducting basic steps and performing optimal search. The paper elaborates on the already proposed Universal generalized net model for description of the population-based metaheuristic algorithms, which was used so far to model the Cuckoo search, Firefly algorithm and Artificial bee colony optimization, and is used here for modelling of Bat algorithm. It is shown that the Bat algorithm can be described in terms of Universal generalized net model by only varying the characteristic functions of the tokens. Thus, verification of the Universal generalized net model is performed.

In the combinatorial optimization, the goal is to find the optimal object from a finite set of objects. From computational point of view the combinatorial optimization problems are hard to be solved. Therefore on this kind of problems usually is applied some metaheuristics. One of the most successful techniques for a lot of problem classes is metaheuristic algorithm Ant Colony Optimization (ACO). Some start strategies can be applied on ACO algorithms to improve the algorithm performance. We propose several start strategies when an ant chose first node, from which to start to create a solution. Some of the strategies are base on forbidding some of the possible starting nodes, for one or more iterations, because we suppose that no good solution starting from these nodes. The aim of other strategies are to increase the probability to start from nodes with expectations that there are good solutions starting from these nodes. We can apply any of the proposed strategy separately or to combine them. In this investigation InterCriteria Analysis (ICrA) is applied on ACO algorithms with the suggested different start strategies. On the basis of ICrA the ACO performance is examined and analysed.

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, a hybrid scheme using Bat Algorithm (BA) and Sequential Quadratic Programming (SQP) method is introduced. In the hybrid BA—SQP, the role of BA is to generate feasible solutions to a problem. The role of SQP is to exploit the information gathered by BA. This process obtains a solution which is at least as good as—but usually better than—the best solution devised by BA. To demonstrate the usefulness of the presented approach, the hybrid scheme was applied to parameter identification of an E. coli MC4110 fed-batch cultivation process model. A comparison with both the conventional BA and SQP method is presented. The results showed that the hybrid BA-SQP has the advantages of both BA's global search ability and SQP's local search ability, thus enhancing the overall search ability and computational efficiency. For comparison, the results obtained by applying Ant colony optimization algorithm in conditions similar to those of BA are further shown.

In this paper the apparatus of generalized nets is applied to describe the Cuckoo search (CS). The CS is a metaheuristic population-based algorithm inspired by the brood parasitism of some cuckoo species laying their eggs in the nests of other bird species. In addition, CS is enhanced by the so-called Levy flights rather than by simple isotropic random walks. Preliminary studies show that CS is very promising and could outperform existing algorithms such as Particle Swarm Optimization, Genetic Algorithms, and other algorithms. The proposed herewith model provides the opportunity to describe the logic of CS in the terms of the mathematical modeling paradigm of generalized nets.

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.

This paper presents an optimal tuning of a universal digital PID controller using metaheuristics as Genetic Algorithms (GA), Simulated Annealing (SA) and Tabu Search (TS). The controllers were used...

A method for finding the optimal feeding profile for whey fermentation by strain Kluyveromyces lactic MC 5 in a fed-batch bioreactor was developed. The optimal profile maximizes the process effectiveness and minimizes the bioprocess duration. The method is based on Neuro-dynamic Programming (NDP), wherein the optimal control decision is parameterized in the form of a cost-to-go function. The suggested method employs simulations from a heuristic feeding strategy as an initial point to generate the cost-to-go to experimental data. A neural network is applied to obtain cost-to-go as a function of system state. Iterations of the Bellman equation are included to improve the cost function. Thus, the obtained approach guarantees optimal control of the bioreactor when disturbances are present. The developed approach was compared with other methods—the Pontryagin's Maximum Principle and Fuzzy Sets Theory. The NDP method provided better results than the other methods.

In this paper we apply an approach based on the apparatus of the Index Matrices and the Intuitionistic Fuzzy Sets - namely InterCriteria Analysis. The main idea is to use the InterCriteria Analysis to establish the existing relations and dependencies of defined parameters in non-linear model of an E. coli fed-batch cultivation process. Moreover, based on results of series of identification procedures we observe the mutual relations between model parameters and considered optimization techniques outcomes, such as execution time and objective function value. Based on InterCriteria Analysis we examine the obtained identification results and discuss the conclusions about existing relations and dependencies between defined, in terms of InterCriteria Analysis, criteria.

This paper presents the implementation of functional state approach to modelling of Escherichia coli fed-batch cultivation. Due to the complex metabolic pathways of microorganisms, the accurate modelling of bioprocesses is rather difficult. The functional state approach of a process is an alternative concept which helps in modelling and control of complex processes. The approach main idea is developing of models based on multiple submodels for each functional states (operating regime). In each functional state the process is described by a conventional type of model, called the local model, which is valid in this state. For parameter identification of the model the genetic algorithms are used. Genetic algorithms are directed random search techniques, applying the mechanics of natural selection and natural genetics, which can find the global optimal solution in complex multidimensional search spaces. Based on the available experimental data and simulations of E. coli fed-batch cultivation it is sho...

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, a hybrid scheme, to solve optimization problems, using a Genetic Algorithm (GA) and an Ant Colony Optimization (ACO) is introduced. In the hybrid GA-ACO approach, the GA is used to find a feasible solutions to the considered optimization problem. Next, the ACO exploits the information gathered by the GA. This process obtains a solution, which is at least as good as—but usually better than—the best solution devised by the GA. To demonstrate the usefulness of the presented approach, the hybrid scheme is applied to the parameter identification problem in the E. coli MC4110 fed-batch fermentation process model. Moreover, a comparison with both the conventional GA and the stand-alone ACO is presented. The results show that the hybrid GA-ACO takes the advantages of both the GA and the ACO, thus enhancing the overall search ability and computational efficiency of the solution method.

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 apparatus of Generalized Nets (GN) is applied here to describe different kinds of genetic algorithms (GA). Failure of conventional optimization methods to lead to a satisfied solution in parameter identification of non-linear and time-dependent parameters provokes an idea some stochastic algorithms to be applied. As such genetic algorithms (GA), as a promising metaheuristic technique, are widely used. Different modifications of simple genetic algorithms (SGA) have been investigated and successfully applied to parameter identification of fermentation processes aiming to improve the model accuracy and the algorithm convergence time. Altogether six modifications of SGA have been proposed with a different sequence of implementation of basic genetic operators selection, crossover and mutation. In the present GN model the user is allowed to choose the sequence of execution of main GA operators, thus resulting in one of the six considered here modifications of SGA. © 2012 IEEE.

In this paper a hybrid scheme using GA and SQP method is introduced. In the hybrid GA-SQP the role of the GA is to explore the search place in order to either isolate the most promising region of the search space. The role of the SQP is to exploit the information gathered by the GA. To demonstrate the usefulness of the presented approach, two cases for parameter identification of different complexity are considered. The hybrid scheme is applied for modeling of E. coli MC4110 fed-batch cultivation process. The results show that the GA-SQP takes the advantages of both GA's global search ability and SQP's local search ability, hence enhances the overall search ability and computational efficiency.

The apparatus of Generalized Nets is applied here to a description of a selection operator, which is one of the basic genetic algorithm operators. This genetic operator performs a probabilistic selection based upon the individual's fittness such that the better individuals have an increased chance of being selected for the next generation. The resulting GN model could be considered as a separate module, but can also be accumulated into a GN model to describe a whole genetic algorithm.

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.

A modified genetic algorithm is proposed for a parameter identification of an E. coli fed-batch fermentation model. In the simple genetic algorithm the best chromosome does not always keep on improving in each generation. Obtained good solutions could be destroyed by either crossover or mutation or both operations. The aim of the modified genetic algorithm is to prevent this disadvantage. In view of the fact that there is no general theory about tuning the genetic algorithm parameters, some adjustments of genetic parameters, according to the regarded problem, are done to improve the conventional genetic algorithm. The simulation results illustrate that the use of proposed modified genetic algorithm for a parameter identification of fermentation processes is highly efficient and effective. The functions and parameter adjustments, proposed here, enhance the algorithm performance. Still more, the implementation of the modified genetic algorithm leads to noticeable decreasing of the solution time.