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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 the presented paper, the functioning and the results of the work of two metaheuristic algorithms, namely cuckoo search algorithm (CS) and firefly algorithm (FA), are described using the apparatus of generalized nets (GNs), which is an appropriate and efficient tool for describing the essence of various optimization methods. The two developed GN-models mimic the optimization processes based on the nature of cuckoos and fireflies, respectively. The proposed GN-models execute the two considered metaheuristic algorithms conducting basic steps and performing optimal search. Building upon these two GN-models, a universal GN-model is constructed that can be used for describing and simulating both the CS and the FA by setting different characteristic functions of the GN-tokens. Moreover, the universal GN-model itself can be transformed to each of the herewith presented GN-models by applying appropriate hierarchical operators. In order to validate the proposed universal GN-model, numerical experiments are performed for the operating of the universal GN-model (CS and FA) on benchmark mathematical functions. The obtained results are compared with the results of the GN-model of CS, GN-model of FA, as well as the results of the standard CS and FA.

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.

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 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.

One of the key objectives during wireless sensor networks deployment is full coverage of the monitoring region with a minimal number of sensors and minimized energy consumption of the network. In this paper we apply multi-objective Ant Colony Optimization (ACO) to solve this hard, from the computational point of view telecommunication problem. The number of ants is one of the key algorithm parameters in the ACO and it is important to find the optimal number of ants needed to achieve good solutions with minimal computational resources. The InterCriteria Analisys is applied in order to study the influence of ants number on the algorithm performance.

Optimization of the production process is important for every factory or organization. The better organization can be done by optimization of the workforce planing. The main goal is decreasing the assignment cost of the workers with the help of which, the work will be done. The problem is NP-hard, therefore it can be solved with algorithms coming from artificial intelligence. The problem is to select employers and to assign them to the jobs to be performed. The constraints of this problem are very strong and for the algorithms is difficult to find feasible solutions. We apply Ant Colony Optimization Algorithm to solve the problem.We investigate the algorithm performance according evaporation parameter. The aim is to find the best parameter setting.

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.

Wireless sensor networks are formed by spatially distributed sensors, which communicate in a wireless way. This network can monitor various kinds of environment and physical conditions like movement, noise, light, humidity, images, chemical substances etc. A given area needs to be fully covered with minimal number of sensors and the energy consumption of the network needs to be minimal too. We propose several algorithms, based on Ant Colony Optimization, to solve the problem. We study the algorithms behaviour when the number of ants varies from 1 to 10. We apply InterCriteria analysis to study relations between proposed algorithms and number of ants and analyse correlation between them.

The workforce planning is a difficult optimization problem. It is important real life problem which helps organizations to determine workforce which they need. A workforce planning problem is very complex and needs special algorithms to be solved using reasonable computational resources. The problem consists to select set of employers from a set of available workers and to assign this staff to the tasks to be performed. The objective is to minimize the costs associated to the human resources needed to fulfil the work requirements. A good workforce planing is important for an organization to accomplish its objectives. 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) method which is a stochastic method for solving combinatorial optimization problems. On this paper we focus on influence of the parameters on ACO algorithm performance.

Every organization and factory optimize their production process with a help of workforce planing. The aim is minimization of the assignment costs of the workers, who will do the jobs. The problem is very complex and needs exponential number of calculations, therefore special algorithms are developed to be solved. The problem is to select employers and to assign them to the jobs to be performed. This problem has very strong constraints and it is difficult to find feasible solutions. The objective is to fulfil the requirements and to minimize the assignment cost. We propose a hybrid Ant Colony Optimization (ACO) algorithm to solve the workforce problem, which is a combination between ACO and an appropriate local search procedure.

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.

In this paper an Ant Colony Optimization (ACO) algorithm for parameter identification of cultivation process models is proposed. In computational point of view it is a hard problem. To be solved problem with a high accuracy in reasonable time, metaheuristic techniques are used. The influence of ACO algorithm parameters, namely number of agents (ants) and number of iterations, to the quality of achieved solution is investigated. As a case study an E. coli fed-batch cultivation process is explored. Based on the parameter identification of E. coli MC4110 cultivation process model some conclusions for the optimal ACO parameter settings are done.

InterCriteria Analysis is a recently developed approach for the evaluation of the correlation between multiple objects against multiple criteria. As such, it is expected to prove any existing correlations between the criteria themselves or even to discover any new. In this investigation different algorithms for InterCriteria relations calculation are explored to render the influence of the genetic algorithm (GA) parameters on the algorithm performance. GA is chosen as an optimization technique as they are among the most widely used out of the biologically inspired approaches for global search. GA is here applied to parameter identification of a S. cerevisiae fed-batch fermentation process model.

In this chapter, the Artificial bee colony (ABC) algorithm, based on the foraging behaviour of honey bees, is introduced for a numerical optimization problem. The ABC algorithm is one of the efficient population-based biological-inspired algorithms. To demonstrate the usefulness of the presented approach, the ABC algorithm is applied to parameter identification of an E. coli MC4110 fed-batch cultivation process model. The mathematical model of E. coli MC4110 cultivation process is considered as a system of three ordinary differential equations, describing the two main process variables, namely biomass and substrate dynamics, as well as the volume variation. This case study has not been solved previously in the literature by application of ABC algorithm. To obtain a better performance of the ABC algorithm, i.e. high accuracy of the solution within reasonable time, the influence of the algorithm parameters has been investigated. Eight ABC algorithms are applied to parameter identification of the E. coli cultivation process model. The results are compared, based on obtained estimates of model parameters, objective function value, computation time and some statistical measures. As a result, two algorithms are chosen—ABC1 and ABC8, respectively, with 60 × 500 number and 20 × 400 (population×maximum cycle number), such as algorithms with the best performance. Further, the best ABC algorithms are compared with four population-based biological-inspired algorithms, namely Genetic algorithm, Ant colony optimization, Firefly algorithm and Cuckoo search algorithm. The results from literature of metaheuristics applied for the considered here parameter identification problem are used. The results clearly show that the ABC algorithm outperforms the biological-inspired algorithms under consideration, taking into account the overall search ability and computational efficiency.

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.

International audience; In this paper we apply InterCriteria Analysis (ICrA), which is based on the apparatus of Index Matrices and Intuitionistic Fuzzy Sets. We apply ICrA on the well-known Ant Colony Optimization (ACO) general framework including environment change. The environment is simulated by means of the Logistic map, that is used in ACO for perturbing the update of the pheromone trails. We compare different levels of perturbation of the one of the most important parameters in ACO – the pheromone. Based on ICrA we examine the obtained identification results and discuss the conclusions about existing relations and dependencies between defined criteria, defined in terms of ICrA.

Osteoporosis is a growing major public health problem with impact that crosses medical, social, and economic lines. It is now recognized that it is extremely important to diagnose osteoporosis before a fragility fracture occurs. The purpose of the present study is to give an example of application of Generalized Nets in orthopedics and traumatology and to propose a novel approach for diagnosing the asymptomatic osteoporosis in elderly patients.

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.

In this paper we apply InterCriteria Analysis (ICrA) approach based on the apparatus of Index Matrices and Intuitionistic Fuzzy Sets. The main idea is to use ICrA to establish the existing relations and dependencies of defined parameters in a non-linear model of an E. coli fed-batch cultivation process. We perform a series of model identification procedures applying Genetic Algorithms (GAs). We proposed a schema of ICrA of ICrA results to examine the obtained model identification results. The discussion about existing relations and dependencies is performed according to criteria defined in terms of ICrA. We consider as ICrA criteria model parameters and GAs outcomes on the one hand, and 14 differently tuned GAs on the other. Based on the results, we observe the mutual relations between model parameters and GAs outcomes, such as computation time and objective function value. Moreover, some conclusions about the preferred tuned GAs for the considered model parameter identification in terms of achieved accuracy for given computation time are presented.

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.