Institute of Fundamental Technological Research

This paper presents a novel approach to representing the Limit Order Book data at a given timestamp using the Ordered Fuzzy Numbers concept. The limit order book contains all buy and sell orders placed by investors, updated in real-time, for the most liquid securities, even several hundred times a minute. Due to its irregular nature (different and dynamic changes in the number of buy and sell orders), direct calculations on the order book data are not feasible without transforming it into feature vectors. Currently, most studies use a price level-based data representation scheme when applying deep learning models on limit order book data. However, this scheme has limitations, particularly its sensitivity to subtle perturbations that can negatively impact model performance. On the other hand, the ordered fuzzy number is a mathematical object (a pair of two functions) used to process imprecise and uncertain data. Ordered Fuzzy Numbers possess well-defined arithmetic properties. Converting the limit order book data to ordered fuzzy numbers allows the creation of a time series of ordered fuzzy numbers (order books) and use them for further calculations, e.g., to represent input data for deep learning models or employing the concept of fuzzy time series in various domains, such as defining liquidity measures based on limit order book data. In this paper, the proposed approach is tested using one-year market data from the Polish Stock Exchange for the five biggest companies. The DeepLOB model is employed to predict mid-price movement using different input data representations. The proposed representation of Limit Order Book data demonstrated remarkably stable out-of-sample prediction accuracy, even when subjected to data perturbation.

Limit order book, Ordered fuzzy number, High-frequency forecasting, Mid-price, Data perturbation

Various technological challenges are essentially material problems in our times. New functional and functional graded nanomaterials are constructed of components with predefined properties. The design of nanostructures with predefined mechanical properties was considered in this paper. This study applies the evolutionary algorithm (EA) to the optimization problem in the design of nanomaterials. The optimal design combined EA with molecular dynamics to identify the size of the void for the prescribed elastic properties in monolayer 2D MoS2 nanostructures. The numerical results show that the proposed EA and the use of optimization method allowed accurately obtaining nanostructures with predefined mechanical material properties by introducing elliptical voids in the 2D MoS2 nanosheet

optimization, MoS2 , nanostructure, mechanical properties

Artificial intelligence (AI) is changing many areas of technology in the public and private spheres, including the economy. This report reviews issues related to machine modelling and simulations concerning further development of mechanical devices and their control systems as part of novel projects under the Industry 4.0 paradigm. The challenges faced by the industry have generated novel technologies used in the construction of dynamic, intelligent, flexible and open applications, capable of working in real time envi-ronments. Thus, in an Industry 4.0 environment, the data generated by sensor networks requires AI/CI to apply close-to-real-time data analysis techniques. In this way industry can face both fresh opportunities and challenges, including predictive analysis using computer tools capable of detecting patterns in the data based on the same rules that can be used to formulate the prediction.

industry 4.0, Internet of Things, artificial intelligence, models, simulation

This paper presents a novel approach to forecast hourly day-ahead electricity prices. In recent years, many predictive models based on statistical methods and machine learning (deep learning) techniques have been proposed. However, the approach presented in this paper focuses on the problem of constructing a fair and unbiased model. In this considered case, unbiased means that the model can increase prediction accuracy and decrease categorical bias across different data clusters. For this purpose, a model combining techniques such as long short-term memory (LSTM) recurrent neural network, attention mechanism, and clustering is created. The proposed model’s main feature is that the attention weights for LSTM hidden states are calculated considering a context vector given for each sample individually as the cluster center to which the sample belongs. In training mode, the samples are iteratively (one time per epoch) clustered based on representation vectors given by the attention mechanism. In the empirical study, the proposed model was applied and evaluated on the Nord Pool market data. To confirm that the model decreases categorical bias, the obtained results were compared with results of similar LSTM models but without the proposed attention mechanism.

deep learning, electricity prices forecasting, time series forecasting, attention mechanism, debiasing, Nord Pool data

The concept of fuzzy random variable combines two sources of uncertainty: randomness and fuzziness, whereas the model of ordered fuzzy numbers provides a representation of inaccurate quantitative data, and is an alternative to the standard fuzzy numbers model proposed by Zadeh. This paper develops the model of ordered fuzzy numbers by defining the concept of fuzzy random variables for these numbers, called further ordered fuzzy random variables. Thanks to the well-defined arithmetic of ordered fuzzy numbers (existence of neutral and opposite elements) and the introduced ordered fuzzy random variables; it becomes possible to construct fully fuzzy stochastic time series models such as e.g., the autoregressive model or the GARCH model in the form of classical equations, which can be estimated using the least-squares or the maximum likelihood method. Furthermore, the concept of normality of ordered fuzzy random variables and the method to generate pseudo-random ordered fuzzy variables with normal distribution are introduced.

ordered fuzzy numbers, fuzzy random variables, ordered fuzzy random variables, normal ordered fuzzy random variable

The variation of elastic constants stiffness coefficients with respect to different percentage ratios of defects in monolayer molybdenum disulfide (MLMoS2) is reported for a particular set of atomistic nanostructural characteristics. The common method suggested is to use conventional defects such as single vacancy or di vacancy, and the recent studies use stone-walled multiple defects for highlighting the differences in the mechanical and electronic properties of 2D materials. Modeling the size influence of monolayer MoS2 by generating defects which are randomly distributed for a different percentage from 0% to 25% is considered in the paper. In this work, the geometry of the monolayer MoS2 defects modeled as randomized over the domain are taken into account. For simulation, the molecular static method is adopted and study the effect of elastic stiffness parameters of the 2D MoS2 material. Our findings reveals that the expansion of defects concentration leads to a decrease in the elastic properties, the sheer decrease in the elastic properties is found at 25%. We also study the diffusion of Molybdenum (Mo) in Sulphur (S) layers of atoms within MoS2 with Mo antisite defects. The elastic constants dwindle in the case of antisite defects too, but when compared to pure defects, the reduction was to a smaller extent in monolayer MoS2. Nevertheless, the Mo diffusion in sulfur gets to be more and more isotropic with the increase in the defect concentrations and elastic stiffness decreases with antisite defects concentration up to 25%. The distribution of antisite defects plays a vital role in modulating Mo diffusion in sulfur. These results will be helpful and give insights in the design of 2D materials.

mono-layer MoS2, mechanical properties, molecular statics/dynamics, defects, random distributed defects

A potentially new, single-atom thick semiconducting 2D-graphene-like material, called Anisotropic-cyclicgraphene, has been generated by the two stage searching strategy linking molecular and ab initio approach. The candidate was derived from the evolutionary-based algorithm and molecular simulations was then profoundly analysed using first-principles density functional theory from the structural, mechanical, phonon, and electronic properties point of view. The proposed polymorph of graphene (rP16-P1m1) is mechanically, dynamically, and thermally stable and can achieve semiconducting with a direct band gap of 0.829 eV.

carbon, graphene, graphyne, ab initio calculations, Semiconductors

Two potentially new, 2D-graphene-like materials have been generated by the two stage searching strategy combining molecular and ab initio approach. The two candidates obtained from the evolutionary based algorithm and molecular calculations were then in depth analysed using first-principles Density Functional Theory from the mechanical, structural, phonon and electronic properties point of view. Both proposed polymorphs of graphene (oP8-P2mm) are mechanically and dynamically stable and can be metallic-like.

Carbon, Graphene, Ab initio calculations, Mechanical properties, Elastic properties

The following article presents the description and application of an algorithm for optimal searching for the new stable atomic arrangements of two-dimensional graphenelike carbon lattices with predefined mechanical properties. The proposed method combines the evolutionary algorithm and the conjugate-gradient optimization. The main goal of the optimization is to find stable arrangements of carbon atoms placed in the unit cell with imposed periodic boundary conditions, which reveal desired mechanical properties. Examples of the newly obtained models of the flat, carbon materials are presented. Their mechanical properties are additionally validated during the simulation of the tensile tests using molecular dynamics.

2D atomic structures, graphenelike materials, hybrid algorithm, evolutionary algorithm, mechanical properties

Instytuty Polskiej Akademii Nauk mają wśród polskich instytucji naukowych czołowy potencjał merytoryczny. W instytutach PAN w latach 2013-2016 powstało 19,7% prac afiliowanych w polskich instytucjach i umieszczonych w najbardziej prestiżowych pismach naukowych danych dziedzin (górne 10% z list pism danej dziedziny nauki uszeregowanych według rosnącego współczynnika wpływu, IF). Jest to najlepszy wynik wśród polskich instytucji akademickich. Kadra instytutów PAN zajmuje się nie tylko badaniami, ale też dydaktyką; 1607 osób (stan na 31 grudnia 2016) było na stacjonarnych studiach doktoranckich w Instytutach PAN. Stopień umiędzynarodowienia studiów w PAN (8%) jest największy wśród polskich uczelni. W związku z tym uzasadnione wydaje się powołanie Uniwersytetu PAN (UPAN), który mógłby stać się pierwszą w Polsce uczelnią badawczą. Planuje się, że docelowo kształciłoby się na nim 2,5 tys. osób, w przeważającej części studentek i studentów III stopnia. Taka liczba pozwoli na zagwarantowanie indywidualnej merytorycznej opieki każdemu studentowi, a także na wprowadzenie i przetestowanie nowatorskich programów dydaktycznych, właściwych erze Internetu i e-learningu, prowadzenia studiów online poprzez courser, studiów inter- i crossdyscyplinarnych. UPAN ma realne szanse stać się wizytówką polskiej nauki i szkolnictwa wyższego, gdyż otwarte, międzynarodowe wieloletnie programy konkursowe na pozycje: wizytujących profesorów, stażystów podoktorskich i doktorantów mogą podnieść umiędzynarodowienie zarówno kadry, jak i studentów UPAN do poziomu właściwego najlepszym uczelniom świata. Z uwagi na wielkość naszego budżetu nauki i szkolnictwa wyższego osiągnięcie takiego umiędzynarodowienia jest finansowo realne w najbliższym czasie tylko dla uczelni tak małej jak UPAN. Opisane działania będą projakościowe także dla samych instytutów PAN i istotnie podniosą ich poziom merytoryczny. Po kilku latach UPAN ma realne szanse na uplasowanie się w międzynarodowych rankingach na bardzo dobrych pozycjach, w pierwszej dwusetce, a nawet w pierwszej setce najlepszych światowych uczelni. Należy podkreślić, że warunkiem tego jest zapewnienie finansowania badań w instytutach PAN na co najmniej takim jak obecnie poziomie, uelastycznienie ich sieci, wytworzenie mechanizmów synergii pomiędzy instytutami (wspólny cel – UPAN) oraz wsparcie tego projektu długoletnim programem umiędzynarodowienia kadry i studentów.

research university, University of the Polish Academy of Sciences, excellence in science

The pap er describes an application of the hybrid intelligent algorithm to optimal searching for new, stable atomic arrangements of 2D graphene -like carbon lattices. The proposed approach combines the parallel evolutionary algorithm and the conjugated -gradient optimization technique. The main goal is to find stable arrangements of carbon atoms under certain imposed condi tions such as density, shape and size of the unit cell and also predefined mechanical properties. The nanostructure is considered a discrete atomic model and interactions between atoms are modeled using the AIREBO potential, especially developed for carbon. The parallel approach is used in computations. Validation of the obtaine d results and examples of new models of the new grapheme -like materials are presented

Hybrid intelligent algorithm, 2D nanostructures, new grapheme-like materials

The paper is devoted to the optimization of energy of carbon based atomic structure with use of the memetic algorithm. The graphene like atoms structure is coded into floating point genes and underwent evolutionary changes. The global optimization algorithm is supported by local gradient based improvement of chromosomes. The optimization problem is solved with the use of Intel PHI (Intel Many Integrated Core Architecture – Intel MIC). The example of optimization and speedup measurement for parallel optimization are given in the paper.

Parallel computing, Intel PHI, Optimization, Graphene-like materials

As we delve deeper into the Digital Age, we are witnessing an explosive growth in the variety, velocity, and volume of data being transmitted over the Internet. The rapid migration of Big Data Information Systems (e.g., fraud detection in banking transaction, product sentiment analysis, smart cities, etc.) to datacentre computing environments is fueling an increasing concern about the growing demand for electricity and related carbon emissions. Big Data is emerging news around the world. For example, studies by CISCO [1] and IBM [2] found we now generate 2.5 quintillion bytes of data per day. According to IDC [3], the data universe is set to explode to 40 yottabytes by 2020 5200 gigabytes for every person on earth. Together with the rapidly increasing volume of data being generated, opportunities for analysing such data to distil knowledge that can help solve problems that benefit individuals, the industry and government, and our entire society presents a monumental technical challenge. Considering the large volume and velocity of Big Data, smart information systems, will exploit the elastic storage and computational power of datacentre computing servers for undertaking learning and other analytics tasks.

The article describes the application of a Hybrid Parallel Evolutionary Algorithm (HPEA) to optimal searching for new, stable atomic arrangements of two-dimensional graphene-like carbon lattices. The proposed approach combines the parallel evolutionary algorithm and the conjugated-gradient optimization technique. The main goal of the optimization is to find stable arrangements of carbon atoms under certain imposed conditions (e.g. density, shape and size of the unit cell). The fitness function is formulated as the total potential energy of an atomic system. The optimized structure is considered as a discrete atomic model and interactions between atoms are modeled using the AIREBO potential, especially developed for carbon and hydrocarbon materials. The parallel approach used in computations allows significant reduction of computation time. Validation of the obtained results and examples of the models of the new 2D materials obtained using the described algorithm are presented, along with their mechanical properties.

Graphene-like materials, Optimization at the nano level, AIREBO potential, Evolutionary algorithm, Parallel computing

Methods of creating digital material representations of polycrystalline structures based on molecular dynamics (MD) simulations are presented in this paper. All simulations are performed using the massively parallel MD solver and the canonical ensemble. The simple pair-wise model and the more sophisticated many-body atomic potential model are utilized. All of the unique features and parameters (e.g., size and crystallographic orientation grain) of each approach, along with the results of the simulations, are discussed in detail and illustrated with proper numerical examples. Additionally, a comparison of the mechanical properties between the ideal monocrystal structure and a series of obtained polycrystalline structures is included, along with a description of the algorithm used in the computation of the mechanical properties and the stress-strain relationships.

nanomechanics, mono- and polycrystals, molecular dynamics, digital material representation, mechanical properties

Development and application of the hybrid parallel evolutionary-conjugated gradient algorithm for searching for new, stable atomic arrangements of the two-dimensional graphene-like carbon lattices was described in this paper. The main goal of the optimization is to find stable arrangements of carbon atoms under imposed conditions (e.g. density, shape and size of the unit cell). Such configurations correspond to the minimal values of the total potential energy of the atomic system. Thus, the fitness function is formulated as the total potential energy of the atoms. Interactions between carbon atoms are modeled using Adaptive Intermolecular Reactive Bond Order potential. The parallel approach used in computations allows significant reduction of computation time. Validation of the achieved results and example of the model of new 2D material obtained using presented method were presented in this paper. The numerical scalability tests of the algorithm were performed on the IBM BlueGene/Q supercomputer.

nano-scale modeling, carbon materials, AIREBO potential, evolutionary algorithm, conjugate gradient minimization, parallel computing

The goal of the paper is to present an experimental evaluation of fuzzy time series models which are based on ordered fuzzy numbers to predict financial time series. Considering this approach the financial data is modeled using Ordered Fuzzy Numbers (OFNs) called further by Ordered Fuzzy Candlesticks (OFCs). The use of them allows modeling uncertainty associated with financial data and maintaining more information about price movement at assumed time interval than comparing to commonly used price charts (e.g. Japanese Candlestick chart). Thanks to well-defined arithmetic of OFN, one can construct models of fuzzy time series, such as an Ordered Fuzzy Autoregressive Process (OFAR), where all input values are OFC, while the coefficients and output values are arbitrary OFN; in the form of classical equations, without using rule-based systems. In an empirical study ordered fuzzy autoregressive models are applied to modeling and predict price movement of futures contracts on Warsaw Stock Exchange Top 20 Index.

Ordered fuzzy number, Directional predictability, Fuzzy autoregressive, Financial time series, Stock return

The paper is devoted to the identification of microscale heat-transfer parameters. The numerical modeling of short-pulse laser interaction with thin metal films is considered. The hyperbolic two-temperature model describing the temporal and spatial evolution of the lattice and electrons temperatures in the irradiated metal is applied. This model consists of four equations: two equations concern the electron and lattice temperatures; the later ones determine the dependencies between heat fluxes and temperatures. The short-pulse laser interaction with the film is taken into account by introducing an internal volumetric heat source to the equation describing the electron temperature. The equations concerning the electrons and lattice temperatures are joined by coupling factor G, which characterizes the energy exchange between phonons and electrons. The relations between electron heat flux and electron temperature and between the lattice heat flux and lattice temperature contain the parameters ?e and ?l, respectively. The parameter ?e is the relaxation time of free electrons in metals; the parameter ?l is the relaxation time in phonon collisions. The one-dimensional problem is analyzed. (Heat transfer in the direction perpendicular to the thin film is taken into account.) The nonflux conditions can be accepted at the front surface irradiated by a laser pulse and the back surface. The initial conditions are also assumed. The direct problem is solved by the explicit scheme of the finite difference method. The results of the computations are partially compared with the experimental data available in literature. The inverse problem discussed here consists in the simultaneous identification of three parameters, namely, the coupling factor G and relaxation times ?e and ?l. To solve such a problem, the electron temperature history at the irradiated surface of the thin film is taken into account. The inverse problems can be formulated as optimization problems and solved by means of bioinspired algorithms. The objective function is formulated on the basis of the known measured and numerical simulated values of temperature. The minimization of the objective function allows one to find the design variables vector, which may contain the parameters of the coupling factor and time coefficients in the presented case. The inverse problems are ill-defined problems, and the identification may lead to different results with the same objective function value. The objective function can have many local minima, and therefore the bioinspired algorithm is used in the paper.

multiscale modeling, two-temperature model, identification, bioinspired algorithms

The paper deals with the two-scale approach to the identification of material constants in composite materials. Structures made of unidirectionally fibre-reinforced composites are examined. Composite constituents’ elastic constants in a micro scale are identified on the basis of measurements performed in a macro scale. Numerical homogenization methods using a representative volume element are employed. Static (displacements in sensor points) and dynamic (eigenfrequencies) data are considered as measurements. Ideal and disturbed measurements are taken into account. Computational intelligence methods in the form of evolutionary algorithms and artificial immune systems are used to perform the identification procedure. Finite element method is used to solve the boundary-value problem for composites in both scales. Numerical examples presenting the effectiveness of the proposed approach are attached. Statistical data are considered to compare the efficiency of the identification procedure for both algorithms and different measurement data.

Composite, Numerical homogenization, Identification, Evolutionary algorithm, Artificial immune system

The paper deals with an application of the evolutionary algorithm (EA) and the particle swarm optimizer (PSO), to the optimization of shape, topology and material properties of spatial structures. Structures considered in this work are analyzed by the finite element method (FEM). Optimization criteria that are taken into account concern minimize mass and/or compliance. Numerical examples demonstrate that the method based on soft computing is a very effective technique for solving computer aided optimal design.

Evolutionary algorithms, Particle swarm optimizer, Topology optimization, Finite element method, Level set method

The paper is devoted to new computational techniques in structural dynamics where one tries to study, model, analyse and optimise very complex phenomena, for which more precise scientific tools of the past were incapable of giving low cost and complete solution. Soft computing methods differ from conventional (hard) computing in that, unlike hard computing, they are tolerant of imprecision, uncertainty, partial truth and approximation. The paper deals with an application of the bio-inspired methods, like the evolutionary algorithms (EA), the artificial immune systems (AIS) and the particle swarm optimisers (PSO) to optimisation problems. Structures considered in this work are analysed by the finite element method (FEM) and the boundary element method (BEM). The bio-inspired methods are applied to optimise shape, topology and material properties of 3D structures modelled by the FEM and to optimise location of stiffeners in 2D reinforced plates modelled by the coupled BEM/FEM. The structures are optimised using the criteria dependent on frequency, displacements or stresses. Numerical examples demonstrate that the methods based on the soft computation are effective for solving computer aided optimal design problems.

Soft computing, Evolutionary algorithm, Artificial immune system, Particle swarm optimiser, Optimisation, Finite element method, Boundary element method, Dynamics

The purpose of this chapter is to present an original concept of financial fuzzy time series models based on financial data in the form of Japanese Candlestick Charts. In this approach the Japanese Candlesticks are modeled using Ordered Fuzzy Numbers (OFN) called further Ordered Fuzzy Candlesticks (OFC). The use of ordered fuzzy numbers allows modeling uncertainty associated with financial data. Thanks to well-defined arithmetic of ordered fuzzy numbers, one can construct models of fuzzy time series, such as e.g. an autoregressive process, where all input values are OFC, while the coefficients and output values are arbitrary OFN, in the form of classical equations, without using rule-based systems. Finally, several applications of these models for modeling and forecasting selected financial time series are presented.

Fuzzy Number, Arithmetic Operation, Autoregressive Process

In present paper an improved multi-objective evolutionary algorithm is used for Pareto optimization of selected coupled problems. Coupling of mechanical, electrical and thermal fields is considered. Boundary-value problems of the thermo-elasticity, piezoelectricity and electro-thermo-elasticity are solved by means of finite element method (FEM). Ansys Multiphysics and MSC.Mentat/Marc software are used to solve considered coupled problems. Suitable interfaces between optimization tool and the FEM software are created. Different types of functionals are formulated on the basis of results obtained from the coupled field analysis. Functionals depending on the area or volume of the structure are also proposed. Parametric curves NURBS are used to model some optimized structures. Numerical examples for exemplary three-objective optimization are presented in the paper.

multiobjective optimization, evolutionary algorithms, multiphysics, coupled field problems, finite element method

The paper is devoted to the application of the swarm methods and the finite element method to optimization of the stiffeners location in the 2-D structures (plane stress, bending plate s and shells). The structures are optimized for the stress an d displacement criteria. The numerical examples demonstrate that the method based on the swarm computation is an effective technique for solving t he computer aided optimal design. The additional comparisons of the effectiveness of the particle swarm optimizer (PSO) and evolutionary algorithms (EA) are presented.

swarm algorithms, optimization, finite element method, bar s, plane stress, bending plates, shells

The paper is devoted to multiscale identification of material properties in microscale. The identification process allows one to identify properties (like material constants, geometry) in microscale on the basis of measurements performed for macroscale. The presented approach assumes stochastic material properties in microscale. The identification problem is formulated as minimization of a functional which represents a distance between measured and theoretical values of displacements and strains. The Monte Carlo method combined with the finite element method is used to obtain theoretical displacements and strains values. The identification problem is solved with use of an evolutionary algorithm.

identification, stochastic, multiscale, FEM

In order to make decisions in multi-criteria environments there is a need to find solutions with compromises. All solutions which are compromises for all criteria create the set of solutions named the Pareto frontier. Based on these possibilities the decision maker can choose the best solution looking at the current preferences. It is not trivial to solve such a multiobjective problem, however there are several methods which try to do it, with differing degrees of success. Methods based on behaviors of different biological phenomena belong to the most successful set. Genetic and evolutionary algorithms and artificial immune systems are included that group of methods. On the other hand, the game theory is a branch which mathematically analyzes conflict situations. This chapter is dedicated to methods of finding solutions in multi-criteria environments using bio-inspired methods and the game theory, as well as coupling both approaches to create a new intelligent hybrid system of decision making.

Game Theory, Multiobjective Optimization, Clonal Selection, Pareto Frontier

Artificial immune systems (AIS) have become popular among researchers and have been applied to a variety of tasks. Developing supervised learning algorithms based on metaphors from the immune system is still an area in which there is much to explore. In this paper a novel supervised immune algorithm based on clonal selection framework is proposed. It evolves a population of linear classifiers used to construct a set of classification rules. Aggregating strategies, such as bagging and boosting, are shown to work w ell with the proposed algorithm as the base classifier.

artificial immune systems, clonal selection, linear classifiers, bagging, boosting

The paper presents a methodology of the multiscale bone mode ling in which the task of identification of material parameters plays the crucial role. A two-scale analysis of the bone is considered and the problem of identification, formulated as an inverse problem, is examined as an important stage of the modelling process. The human femur bone, built form cancellous and cortical bone, is taken as an example of an n osseous tissue, and the computational multiscale approach is considered. The methodology presented in the paper allows one to analyze the two-scale model with the use of computational homogenization. The representative volume element (RVE) is created for the microstructure of the basis of micro-CT scans. The macro and micro model analyses are performed by using the finite element method. The identification of trabeculae material parameters on the micro-level is considered as the minimization problem which is solved using evolutionary computing.

multiscale modeling of bone, computational homogenization, identification of material parameters

During the last decade artificial immune systems have drawn much of the researchers’ attention. All the work that has been done allowed to develop many interesting algorithms which come in useful when solving engineering problems such as data mining and analysis, anomaly detection and many others. Being constantly developed and improved, the algorithms based on immune metaphors have some limitations, though. In this paper we elaborate on the concept of a novel artificial immune algorithm by considering the possibility of combining the clonal selection principle and the well known K-means algorithm. This novel approach and a new way of performing suppression (based on the usefulness of the evolving lymphocytes) in clonal selection result in a very effective and stable immune algorithm for both unsupervised and supervised learning. Further improvements to the cluster analysis by means of the proposed algorithm, immune K-means, are introduced. Different methods for clusters construction are compared, together with multi-point cluster validity index and a novel strategy based on minimal spanning tree (mst) and a analysis of the midpoints of the edges of the (mst). Interesting and useful improvements of the proposed approach by means of negative selection algorithms are proposed and discussed.

Artificial immune systems, Clonal selection, Negative selection, Clustering, Data analysis

The chapter is devoted to applications of selected methods of computational intelligence: evolutionary algorithms and artificial neural networks, in identification of physical systems being under the uncertain conditions. Uncertainties can occur in boundary conditions, in material coefficients or some geometrical parameters of systems and are modeled by three kinds of granularity: interval mathematics, fuzzy sets and theory of probability. In order to evaluate fitness functions the interval, fuzzy and stochastic finite element methods are applied to solve granular boundary-value problems for considered physical systems. Several numerical tests and examples of identification of uncertain parameters are presented.

Fuzzy Number, Granular Computing, Stochastic Case, Interval Case, Sensor Point

The paper presents a new algorithm for feature selection and classification. The algorithm is based on an immune metaphor, and combines both negative and clonal selection mechanisms characteristic for B- and T-lymphocytes. The main goal of the algorithm is to select the best subset of features for classification. Two level evolution is used in the proposed system for detectors creation and feature selection. Subpopulations of evolving detectors (T-lymphocytes) are able to discover subsets of features well suited for classification. The subpopulations cooperate during evolution by means of a novel suppression mechanism which is compared to the traditional suppression mechanism. The proposed suppression method proved to be superior to the traditional suppression in both recognition performance and its ability to select the proper number of subpopulations dynamically. Some results in the task of ECG signals classification are presented. The results for binary and real coded T-lymphocytes are compared and discussed.

Artificial immune system, Feature selection, ECG signals classification, Negative selection, Clonal selection, Evolutionary feature selection, Evolutionary algorithms, Immune metaphors, Hybrid immune algorithm

Shape optimization of heat conducting, elastic bodies subjected to thermal and standard loads is considered. Interaction of stress and temperature fields is modelled using the formulation of steady state thermoelasticity. The presence of heat radiation with mutual irradiation of the boundaries and the presence of shadow zones is taken into account. Evolutionary algorithm is used to evaluate the optimal shape. The boundary element method is applied to discretize the thermoelasticity, conduction and radiation problems.

Evolutionary algorithm, Shape optimization, Thermoelasticity, Radiation, Stress, BEM, Parallel computing

The flat, two dimensional materials play important role in the research and industrial applications in the last 15 years. The new materials with flat atomic structures are discovered almost every month. The focus of the paper is on the discrete modellingof the single layer molybdenum disulphide based material (SLMoS2). Two methods, based on the molecular statics and molecular dynamics of estimation of materials properties and numerical simulations at the nanolevel are described and discussed.

A volatility forecasting comparative study between the most popular original GARCH model and the same model defined based on concepts of Ordered Fuzzy Numbers and Ordered Fuzzy Candlsticks is presented. These approaches offer a suitable tool to handle both imprecision of measurements and uncertainty associated with financial data. Therefore, they are particularly useful for volatility forecasting, since the volatility is unobservable and a proxy for it is used (realised volatility). In presented study, based on intra-daily data of theWarsaw Stock Exchange Top 20 Index (WIG 20), one showed that based on the adjusted-R squared and several prediction measurements, the fuzzy approach does perform better than the original GARCH model and forecasts more precisely in both the in-sample and out-of-sample predictions

Volatility forecasting, Realized volatility, Ordered fuzzy number, Kosinski's fuzzy number, Ordered fuzzy candlestick, Ordered fuzzy GARCH model, Financial high-frequency data

In this paper, we consider a multi-objective portfolio diversification problem under real constraints in fuzzy environment, where the objective is to minimize the variance of portfolio and maximize expected return rate of portfolio. The return rates of assets are modeled using concept of Ordered Fuzzy Candlesticks, which are Ordered Fuzzy Numbers. The use of them allows modeling uncertainty associated with financial data based on high-frequency data. Thanks to well-defined arithmetic of Ordered Fuzzy Numbers, the estimators of fuzzy-valued expected value and covariance can be computed in the same way as for real random variables. In an empirical study, 20 assets included in the Warsaw Stock Exchange Top 20 Index are used to compare considered fuzzy model with crisp mean-variance model

Ordered fuzzy number, Kosinski's fuzzy number, Ordered fuzzy candlestick, Fuzzy portfolio diversification, Fuzzy returns, Multi-objective optimization, Financial high-frequency data

In the paper an application of the particle swarm optimizer (PSO) and artificial immune system (AIS) to optimization problems is presented. Reinfored structures considered in this work are dynamically loaded and analyzed by the coupled boundary and finite element method (BEM/FEM). The metod is applied to optimize location of stiffeners in plates using criteria depended on displacements. The main advantage of the particle swarm optimizer, contrary to gradient methods of optimization, is the fact that it does not need any information about the gradient of fitness function. A comparison of the PSO, artificial immune system and evolutionary algorithm (EA) is also shown and it proves the efficiency of the former over other artificial intelligence methods of optimization. The coupled BEM/FEM, which is used to analyse structures, is very accu-rate in analysis and attractive in optimization tasks. It is because of problem dimensionality reduction in comparison with more frequently used domain methods, like for instance the FEM. Numerical examples demonstrate that the combination of the PSO with the BEM/FEM is an effective technique for solving computer aided optimal design problems, both with respect to accuracy and computational resources.

Particle swarm optimization, Immune optimization, Boundary element method, Finite element method, Dynamics

The paper deals with an application of the artificial immune system (AIS) to the optimization of shape, topology and material properties of 2-D and 3-D structures. Structures considered in this work are analyzed by the finite element method (FEM). Optimization criteria that are taken into account concern minimize mass of the structure. Numerical examples demonstrate that the method based on soft computing is a very effective technique for solving computer aided optimal design.

Artificial immune system (AIS), Optimization Finite element method (FEM), Computational intelligence, Shape and topology optimization

The paper is devoted to an application of the swarm methods and the finite element method to optimization of the stiffeners location in the 2-D structures (plane stress, bending plates and shells). The structures are optimized for the stress and displacement criteria. The numerical examples demonstrate that the method based on swarm computation is an effective technique for solving computer aided optimal design.

swarm algorithms, optimization, finite element method (FEM), bars, plane stress, bending plates, shells

optimization, material properties, MoS2, molecular statics

The flat, two dimensional materials play important role in the research and industrial applications in the last 15 years. The new materials with flat atomic structures are discovered every month. The focus of the paper is on the modelling of the single layer molybdenum disulphide based material. The numerical simulations and mechanical material properties are described and discussed.

molybdenum, two dimensional materials, molecular modelling, MoS2

carbon nano-structures, atom structures, memetic algorithms

carbon nano-structures, conjugated gradient method, evolutionary algorithm