Swarm and Evolutionary Computation

This paper presents a work inspired by the

Pachycondyla apicalis

ants behavior for the clustering problem. These ants have a simple but efficient prey search strategy: when they capture their prey, they return straight to their nest, drop off the prey and systematically return back to their original position. This behavior has already been applied to optimization, as the API meta-heuristic. API is a shortage of

api-calis

. Here, we combine API with the ability of ants to sort and cluster. We provide a comparison against Ant clustering Algorithm and K-Means using Machine Learning repository datasets. API introduces new concepts to ant-based models and gives us promising results.

This paper presents an efficient PARAllelization of Differential Evolution on GPU hardware written as an EASEA (EAsy Specification of Evolutionary Algorithms) template for easy reproducibility and re-use. We provide results of experiments to illustrate the relationship between population size and efficiency of the parallel version based on GPU related to the sequential version on the CPU. We also discuss how the population size influences the number of generations to obtain a certain level of result quality.

In this paper we present a new 3D simulation environment, combining features of both discrete swarm agents and continuous environment defined implicitly as a locally updatable zero-level set surface. The advantage of the proposed framework is the natural support for swarm coordination, as well as for adding other continuum based processes, such as the Eulerian numerical simulation of fluid dynamics equations. In most biomedical applications the influence of gaseous/liquid flows and concentrations becomes a key aspect in any viable model. The level set equations are solved using the finite element method (FEM), which is routinely used for analysing physical properties such as aseous/liquid flows, heat transfer, diffusion and reaction etc.

In the present paper, we introduce two different algorithms for the two dimensional gathering problem for synchronous, fat (disk-like) robots with no global navigation or communication, and with limited visibility. One of the algorithms is a slightly modified version of the local smallest enclosing circle (local SEC) algorithm. The other algorithm uses a new method of the gathering: the robots moves towards the furthest visible robot, and the robots on the perimeter of the visibility graph applies a bigger extent of move than the others. With the help of computer simulations, the two proposed algorithms are shown to be applicable for the gathering problem above and they perform better than the earlier simple SEC algorithm developed for point like robots.

The influence of migration on the performance of differential evolution algorithm is studied. Six adaptive variants of differential evolution are applied to a parallel migration model with a star topology. The parallel algorithm with several different settings of parameters controlling the migration was experimentally compared with the adaptive serial algorithms in six benchmark problems of dimension

D

 = 30. The parallel algorithm was more efficient than the best serial adaptive DE variant in a half of the problems.

Music fingering is a cognitive process whose goal is to map each note of a music score to a

fingering

on some instrument. A

fingering

specifies the fingers of the hands that the player should use to play the notes. This problem arises for many instruments and it can be quite different from instrument to instrument; guitar fingering, for example, is different from piano fingering. Previous work focuses on specific instruments, in particular the guitar, and evolutionary algorithms have been used.

In this paper, we propose a differential evolution (DE) algorithm designed for general music fingering (any kind of music instruments). The algorithm uses an Adaptive Neuro-Fuzzy Inference System (ANFIS) engine that learns the fingering from music already fingered.

The algorithm follows the basic DE strategy but exploits also some customizations specific to the fingering problem. We have implemented the DE algorithm in Java and we have used the ANFIS network in Matlab. The two systems communicate by using the MatlabControl library. Several tests have been performed to evaluate its efficacy.

PSO-2S is a multi-swarm PSO algorithm using charged particles in a partitioned search space for continuous optimization problems. This algorithm uses two kinds of swarms, a main one that gathers the best particles of auxiliary ones. In this paper, we present a new variant of PSO-2S, called DEPSO-2S, which is a hybridization of DE and PSO. DE was used, in this variant, to construct the main swarm. We analyze the performance of the proposed approach on seven real problems. The obtained results show the efficiency of the proposed algorithm.

The Artificial Bee Colony (ABC) is the name of an optimization algorithm that was inspired by the intelligent behavior of a honey bee swarm. It is widely recognized as a quick, reliable, and efficient methods for solving optimization problems. This paper proposes a hybrid ABC (HABC) algorithm for graph 3-coloring, which is a well-known discrete optimization problem. The results of HABC are compared with results of the well-known graph coloring algorithms of today, i.e., the Tabucol and Hybrid Evolutionary algorithm (HEA), and results of the traditional evolutionary algorithm with SAW method (EA-SAW). Extensive experimentations has shown that the HABC matched the competitive results of the best graph coloring algorithms, and did better than the traditional heuristics EA-SAW when solving equi-partite, flat, and random generated medium-sized graphs.

Finding optimal controllers of stochastic systems is a particularly challenging problem tackled by the optimal control and reinforcement learning communities. A classic paradigm for handling such problems is provided by Markov Decision Processes. However, the resulting underlying optimization problem is difficult to solve. In this paper, we explore the possible use of Particle Swarm Optimization to learn optimal controllers and show through some non-trivial experiments that it is a particularly promising lead.

Compact algorithms are Estimation of Distribution Algorithms which mimic the behavior of population-based algorithms by means of a probabilistic representation of the population of candidate solutions. Compared to an actual population, a probabilistic model requires a much smaller memory, which allows algorithms with limited memory footprint. This feature is extremely important in some engineering applications, e.g. robotics and real-time control systems. This paper proposes a compact implementation of Bacterial Foraging Optimization (cBFO). cBFO employs the same chemotaxis scheme of population-based BFO, but without storing a swarm of bacteria. Numerical results, carried out on a broad set of test problems with different dimensionalities, show that cBFO, despite its minimal hardware requirements, is competitive with other memory saving algorithms and clearly outperforms its population-based counterpart.

This paper introduces CoMiniMax, a coevolutionary Minimax algorithm, based on Differential Evolution, for the detection of Nash Equilibrium in games. We discuss the robust theoretical principles of the proposed algorithm. The algorithm is illustrated on examples in economics, transportation and deregulated electricity markets. Numerical experience demonstrates that the algorithm is a useful tool for the study of Nash Equilibrium problems.

In this paper we present a particle swarm optimization (PSO) based approach for marker-less full body motion tracking. The objective function is smoothed in an annealing scheme and then quantized. This allows us to extract a pool of candidate best particles. The algorithm selects a global best from such a pool to force the PSO jump out of stagnation. Experiments on 4-camera datasets demonstrate the robustness and accuracy of our method. The tracking is conducted on 2 PC nodes with multi-core CPUs, connected by 1 GigE. This makes our system capable of accurately recovering full body movements with 14 fps.

Metaoptimization is a way of tuning parameters of an optimization algorithm with use of a higher-level optimizer. In this paper it is applied to the problem of choosing among possible mutation range adaptation schemes in Differential Evolution (DE). We consider a new version of DE, called DE/rand/∞. In this algorithm, differential mutation is replaced by a Gaussian one, where the covariance matrix is determined from the contents of the current population. We exploit this property to separate the adaption of search directions from the adaptation of mutation range. The former is characterized by a norm of the covariance matrix while the latter can be expressed as a normed covariance matrix multiplied by the scaling factor. Such separation allows us to introduce a few schemes of direct, explicit control of the mutation range and to compare them with the basic, implicit scheme present in DE/rand/∞. To ensure fair comparisons all versions of DE/rand/∞ are first metaoptimized and then assessed on the CEC’05 benchmark.

Interpolated Ant Colony Optimization (IACO) for a continuous domain was proposed in the paper. The IACO uses the same mechanisms as the classical ACO applied to discrete optimization. The continuous search space is sampled by individuals on the basis of the linear interpolated trace of the pheromone. It allows to obtain a simple and efficient optimization algorithm. The proposed algorithm is then used to identify delays in linear dynamic systems. The examination results show that it is an effective tool for global optimization problems.

In this paper, we present a variable iterated greedy algorithm where its parameters (basically destruction size and probability of whether or not to apply the iterated greedy algorithm to an individual) are optimized by the differential evolution algorithm. A unique multi-chromosome solution representation is presented in such a way that the first chromosome represents the destruction size and the probability whereas the second chromosome is simply a job permutation assigned to each individual in the population randomly. The proposed algorithm is applied to the no-idle permutation flowshop scheduling problem with the makespan criterion. The performance of the proposed algorithm is tested on the Ruben Ruiz’s benchmark suite and compared to their best known solutions available in

http://soa.iti.es/rruiz

as well as to a very recent discrete differential evolution algorithm from the literature. The computational results show its highly competitive performance and ultimately, 183 out of 250 instances are further improved. In comparison to the very recent hybrid discrete differential evolution algorithm, 114 out of 150 new best known solutions they provided are also further improved.

We consider the problem of optimal partitional clustering of real data sets by optimizing three basic criteria (trace of within scatter matrix, variance ratio criterion, and Marriottt’s criterion). Four variants of the algorithm based on differential evolution with competing strategies are compared on eight real-world data sets. The experimental results showed that hybrid variants with

k

-means algorithm for a local search are essentially more efficient than the others. However, the use of Marriottt’s criterion resulted in stopping hybrid variants at a local minimum.

This paper compares the binomial crossover used in the Differential Evolution with a variant named the contiguous binomial crossover. In the latter, a contiguous block of variables is used for selecting which variables are exchanged, in a fashion similar to that of the exponential crossover, allowing to using a single, normally-distributed random number to decide the number of exchanged variables. Experimental results show that this variant of the binomial crossover exhibits in general similar or better performance than the original one, and allows to increase significantly the execution speed of the Differential Evolution, especially in higher dimension problems.

This paper presents a novel differential evolution algorithm for optimization of state-of-the-art real world industry challenges. The algorithm includes the self-adaptive jDE algorithm with one of its strongest extensions, population reduction, and is now combined with multiple mutation strategies. The two mutation strategies used are run dependent on the population size, which is reduced with growing function evaluation number. The problems optimized reflect several of the challenges in current industry problems tackled by optimization algorithms nowadays. We present results on all of the 22 problems included in the Problem Definitions for a competition on Congress on Evolutionary Computation (CEC) 2011. Performance of the proposed algorithm is compared to two algorithms from the competition, where the average final best results obtained for each test problem on three different number of total function evaluations allowed are compared.

The aim of the contribution is to present Cognitive Analysis of fuzzy rule bases used in Genetic optimization of Multiagent system behaviour. This Cognitive analysis allows to analyze behaviour caused by rules and sort them to Social, Group or Individual sets of the rules. Rules, which have same behaviour, can be reduced. This allows to decrease of the rules and number of genes in chromosome and also GA Search Space. The Fuzzy Rule Based Evolution System is presented. This system consists of three main parts the FUZNET, the GA-MPI and the Webots. Simple example based on the Box Pushing problem is presented.

Memetic algorithms are popular approaches to improve pure evolutionary methods. But were and when in the system the local search should be applied and does it really speed up evolutionary search is a still an open question. In this paper we investigate the influence of the memetic extensions on globally induced regression and model trees. These evolutionary induced trees in contrast to the typical top-down approaches globally search for the best tree structure, tests at internal nodes and models at the leaves. Specialized genetic operators together with local greedy search extensions allow to the efficient tree evolution. Fitness function is based on the Bayesian information criterion and mitigate the over-fitting problem. The proposed method is experimentally validated on synthetical and real-life datasets and preliminary results show that to some extent memetic approach successfully improve evolutionary induction.

This paper presents a method of searching for the best decomposition strategy for logical functions. The strategy is represented by a decision tree, where each node corresponds to a single decomposition step. In that way the multistage decomposition of complex logical functions may be specified. The tree evolves using the developmental genetic programming. The goal of the evolution is to find a decomposition strategy for which the cost of FPGA implementation of a given function is minimal. Experimental results show that our approach gives significantly better outcomes than other existing methods.

A tournament searching method with new mutation operators for a problem of the feature subset selection is presented. The probability of the bit mutation in a classical approach is fixed. In the proposed methods this probability is dependent on the history of the searching process. Bit position whose mutation from 0 to 1 (from 1 to 0) improved the evaluation of the solution in early iterations, are mutated more frequently from 0 to 1 (from 1 to 0). The roulette wheel method and the tournament method are used to select the bits for the mutation according to the adaptive probability. The algorithms were tested on several tasks of the feature selection in the supervised learning. The experiments showed the faster convergence of the algorithm with directed mutations in relation to the classical mutation.

The paper presents a new Fully Controllable Ant Colony Algorithm (FCACA) for the clustering of the text documents in vector space. The proposed new FCACA is a modified version of the Lumer and Faieta Ant Colony Algorithm (LF-ACA). The algorithm introduced new version of the basic heuristic decision function significantly improves the convergence and greater control over the process of the grouping data. The proposed solution was shown in a text example proving efficiency of the proposed solution in comparison with other grouping algorithms.

The acquisition of the knowledge which is useful for developing of artificial intelligence systems is still a problem. We usually ask experts, apply historical data or reap the results of mensuration from a real simulation of the object. In the paper we propose a new algorithm to generate a representative training set. The algorithm is based on analytical or discrete model of the object with applied the

k

–nn and genetic algorithms. In this paper it is presented the control case of the issue illustrated by well known truck backer–upper problem. The obtained training set can be used for training many AI systems such as neural networks, fuzzy and neuro–fuzzy architectures and

k

–nn systems.

Following earlier results, the purpose of this paper is to show a new evolutionary algorithm whose parameters are moving in ranges defined by experiments. That is to say, no parameters must be fixed at the beginning of the course of generations. Comparing the performance of two methods, we arrive to the conclusion that the random often is a better way.

The paper presents a generalization of the Pittsburgh approach to learn fuzzy classification rules from data. The proposed approach allows us to obtain a fuzzy rule-based system with a predefined level of compromise between its accuracy and interpretability (transparency). The application of the proposed technique to design the fuzzy rule-based classifier for the well known benchmark data sets (

Dermatology

and

Wine

) available from the

http://archive.ics.uci.edu/ml

is presented. A comparative analysis with several alternative (fuzzy) rule-based classification techniques has also been carried out.

The paper presents a genetic fuzzy rule-based technique for the modelling of generalized time series (containing both, numerical and non-numerical, qualitative data) which are a comprehensive source of information concerning the behaviour of many complex systems and processes. The application of the proposed approach to the fuzzy rule-based modelling of an industrial gas furnace system using measurement data available from the repository at the

http://www.stat.wisc.edu/~reinsel/bjr-data

(the so-called Box-Jenkins’ benchmark) is also presented.

In this paper the parametric inverse heat conduction problem with the third kind boundary condition is solved by applying the Ant Colony Optimization algorithm introduced in recent years and belonging to the group of optimization algorithms inspired by the behavior of swarms of individuals living in real word. In this case the applied algorithm is based on the technique of searching for the shortest way connecting the ant-hill with the source of food and is used for minimizing the functional playing a crucial role in the proposed procedure prepared for reconstruction of the thermal conductivity coefficient.

In this paper we present the comparison of numerical methods applied for solving the inverse heat conduction problem in which two algorithms of swarm intelligence are used: Artificial Bee Colony algorithm (ABC) and Ant Colony Optimization algorithm (ACO). Both algorithms belong to the group of algorithms inspired by the behavior of swarms of insects and they are applied for minimizing the proper functional representing the crucial part of the method used for solving the inverse heat conduction problems. Methods applying the respective algorithms are compared with regard to their velocity and precision of the received results.

In this paper, an approach to automatic optimisation of the retrieval quality of search engines using a language model paradigm is presented. The topics of information retrieval (IR) and natural language processing (NLP) have already been investigated. However, most of the approaches were focused on learning retrieval functions from existing examples and pre-set feature lists. Others used surface statistics in the form of

n

-grams or efficient parse tree utilisations – either performs poorly with a language open to changes. Intuitively, an IR system should present relevant documents high in its ranking, with less relevant following below. To accomplish that, semantics/ontologies, usage of grammatical information and document structure analysis were researched. An evolutionary enrichment of language model for typed dependency analysis acquired from documents and queries can adapt the system to the texts encountered. Futhermore, the results in controlled experiments verify the possibility of outperforming existing approaches in terms of retrieval quality.

The Invasive Weed Optimization algorithm (IWO) is an optimization method inspired by dynamic growth of weeds colony. The authors of the present paper have modified the IWO algorithm introducing a hybrid strategy of the search space exploration. The goal of the project was to evaluate the modified version by testing its usefulness for numerical functions minimization. The optimized multidimensional functions: Griewank, Rastrigin, and Rosenbrock are frequently used as benchmarks which allows to compare the experimental results with outcomes reported in the literature. Both the results produced by the original version of the IWO algorithm and the Adaptive Particle Swarm Optimization (APSO) method served as the reference points.

This paper proposes a hybrid particle swarm optimization (PSO) algorithm for solving the job-shop scheduling problem with fuzzy processing times. The objective is to minimize the maximum fuzzy completion time, i.e., the fuzzy makespan. In the proposed PSO-based algorithm performs global explorative search, while the tabu search (TS) conducts the local exploitative search. One-point crossover operator is developed for the individual to learn information from the other individuals. Experimental results on three well-known benchmarks and a randomly generated case verify the effectiveness and efficiency of the proposed algorithm.

Genetic operators are used in genetic algorithms (GA) to generate individuals for the new population. Much research focuses on finding most suitable operators for applications or on solving large-scale problems. However, rarely research addresses the performance of different operators in small- or medium-scale problems. This paper studies the impact of genetic operators on solving the traveling salesman problem (TSP). Using permutation coding, a number of different GAs are designed and analyzed with respect to the impact on the global search capability and convergence rate for small- and medium-scale TSPs. In addition, the differences between small- and medium-scale TSPs on suitable GA design are studied. The experiments indicate that the inversion mutation produces better solutions if combined with insertion mutation. Dividing the population into small groups does generate better results in medium-scale TSP; on the contrary, it is better to apply operators to the whole population in case of small-scale TSP.

Differential Evolution (DE) is an efficient optimizer in current use. Although many new DE mutant vectors have been proposed by alter the differential operator, there are few works studying the differential operator’s effect in DE algorithm. This paper proposes a correlation between the DE performance and the mutant vector. That is, for a particular mutant vector, increase the number of differential operator would influence the performance of the algorithm linearly. These mutant vectors are evaluated by 23 benchmarks selected from Congress on Evolutionary Computation (CEC) competition. Additionally, this paper proposes an unrestrained method to generate mutant vector. Unlike the old method selects mutually exclusive individuals, the new method allows same individuals appear repeatedly to generate mutant vector. This new method could enhance the potential diversity of the population and improve the performance of DE in general.

abstract

environment.

Clustering analysis is the task of assigning a set of objects to groups such that objects in one group or cluster are more similar to each other than to those in other clusters. Clustering analysis is the major application area of data mining where Particle Swarm Optimisation (PSO) is being widely implemented due to its simplicity and efficiency. When compared with techniques like

K

-means, Fuzzy

C

-means,

K

-Harmonic means and other traditional clustering approaches, in general, the PSO algorithm produces better results with reference to inter-cluster and intra-cluster distances, while having quantization errors comparable to the other algorithms. In recent times, many hybrid algorithms with PSO as one of the techniques have been developed to harness the strong points of PSO and increase its efficiency and accuracy. This paper provides an extensive review of the variants and hybrids of PSO which are being widely used for the purpose of clustering analysis.

Modern optimization algorithms are often metaheuristic, and they are very effective and promising in solving NP-hard optimization problems. Many of them are based on nature, like the particle swarm optimization, which purely outperforms its predecessors. This paper provides an insight into improved metaheuristic of Particle Swarm Optimization extended with stronger social links.

Two adaptive approaches applied in competitive differential evolution and in differential evolution with an ensemble of mutation strategies and parameter values are compared. The approach used in each of these two algorithms can be divided into two parts: adaptive mechanism and pool of strategies. Four variants of adaptation in differential evolution mutually combining these two parts of the two algorithms are experimentally compared in six benchmark functions at two levels of dimension. It was found out that the algorithms with the pool of competitive differential evolution are more reliable, whereas the variants using the pool of the other algorithm need mostly a smaller number of function evaluations to reach the stopping condition.

The article presents the idea of the intelligent system for the multiobjective optimization. The system consists of the genetic algorithm (GA) and the fuzzy logic controller (FLC). In experiments we investigated the maintenance of genetic algorithms with the variable length of genes. The genes of individuals are encoded and represented by real numbers. The FLC controls the length of individuals’ genotypes in the genetic algorithm. The variable length of the genotype of individuals allows for the limitation of the computational effort, when the length of the genotype of an individual grows smaller. We chose the problem of the distribution of Access Points in a given area in a wireless network as the test-function for our experiments. In the article we presented the results obtained during the optimization of the test-function. The experiments show, that the proposed system is an efficient tool for solving the multiobjective optimization problems. The proposed system can be used to solve similar problems of multiobjective optimization.

Our aim is to propose a new approach to soft selection in evolutionary algorithms for optimization problems with constraints. It is based on the notion of a filter as introduced by Fletcher and his co-workers. The proposed approach occurred to be quite efficient.

Discrete Ant System (DAS) algorithm, a modification of classical Ant System algorithm formulated by M. Dorigo, is presented. Definition of optimization problem and a detailed description of component rules of DAS method are given. Then a probabilistic algebraic model of DAS heuristic describing its evolution in terms of Markov chains is presented. The final result in the form of a pointwise convergence of Discrete Ant System algorithm is established.

This paper deals with the optimization of control of Hénon Map, which is a discrete chaotic system. This paper introduces and compares evolutionary approach representing tuning of parameters for an existing control method, as well as meta-evolutionary approach representing synthesis of whole control law by means of Analytic Programming (AP). These two approaches are used for the purpose of stabilization of the stable state and higher periodic orbits, which stand for oscillations between several values of chaotic system. For experimentation, Self-Organizing Migrating Algorithm (SOMA) and Differential Evolution (DE) were used.

In this paper, we propose an intelligent system developed for personal computer (PC) hardware configuration. The PC hardware configuration is a hard decision problem, because nowadays in the computer market we have very large number of PC hardware components. Therefore, a choice process of personal computer having maximal efficiency and minimal price is a very hard task. Proposed in this paper, the PC hardware configuration system is based on multi-objective evolutionary algorithm. All detailed information about PC particular components are stored in database. Using proposed system, personal computer can be easily configured without any knowledge about PC hardware components. As a test of the proposed system, in this paper we have configured personal computers for game players and for office work.

An optimal trade-off between exploration and exploitation properties of genetic algorithm is very important in optimization process. Due value steering of these two factors we can prevent a premature convergence of the algorithm. Therefore, better results can be obtained during optimization process with the use of genetic algorithm. In this paper the type-2 fuzzy logic control of trade-off between exploration and exploitation properties of genetic algorithm is presented. Our novel selection method (with application of type-2 fuzzy logic to steering of key parameter in this selection method) is based on previously elaborated mix selection method. In proposed method two factors are taken into consideration: the first is a number of generations of genetic algorithm, and second is a population diversity. Due to these two factors, we can control the trade-off between global and local search of solution space; also due to the type-2 fuzzy control the proposed method is more ”immune” in falling into the trap of local extremum. The results obtained using proposed method (during optimization of test functions chosen from literature) are compared with the results obtained using other selection methods. Also, a statistically importance of obtained results is checked using statistical t-Student test. In almost all cases, the results obtained using proposed selection method are statistically important and better than the results obtained using other selection techniques.

We consider the problem of propensity modeling in consumer finance. These modeling problems are characterized by the two aspects: the model needs to optimize a business objective which may be nonstandard, and the rate of occurence of the event to be modeled may be very low. Traditional methods such as logistic regression are ill-equipped to deal with nonstandard objectives and low event rates. Methods which deal with the low event rate problem by learning on biased samples face the problem of overlearning. We propose a parallel genetic algorithm method that addresses these challenges. Each parallel process evolves propensity models based on a different biased sample, while a mechanism for validation and cross-pollination between the islands helps address the overlearning issue. We demonstrate the utility of the method on a real-life dataset.

The paper deals with an application of an hybrid particle swarm optimizer (HPSO) to identification problems. The HPSO is applied to identify complex impedances of room walls and it is based on the mechanism discovered in the nature during observations of the animals social behaviour and supplemented with some additional gradient information. The numerical example demonstrate that the method based on hybrid swarm optimization is an effective technique for computing in identification problems.

A coevolutionary algorithm called reCORE for rule extraction from databases was proposed in the paper. Knowledge is extracted in the form of simple implication rules IF-THEN-ELSE. There are two populations involved, one for rules and second for rule sets. Each population has a distinct evolution scheme. One individual from rule set population and a number of individuals from rule population contribute to final result. Populations are synchronized to keep the cross-references up to date. The concept of the algorithm and the results of comparative research are presented. A cross-validation is used for examination, and the final conclusions are drawn based upon statistically analyzed results. They state that, the effectiveness of the reCORE algorithm is comparable to other rule classifiers, such as Ridor or JRip.

This paper introduces a new modular algorithm MGPSO. It merges random probing, new particle swarm optimization and local search algorithms. The proposed algorithm was implemented according to a new proposal of modular architecture. It allows for flexible mixing different techniques of the optimization in a single optimization. The architecture allows to macro–manage the search process by modifiable set of rules. Thus, a selection of suitable tools for different phases of the optimization depending on current requirements is possible. As a consequence, the modular algorithm achieves good performance acknowledged in performed experiments. The proposed architecture can help in application of machine learning methods for the selection of efficient sequence of tools during the optimization.