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Wu G.,National University of Defense Technology | Qiu D.,National University of Defense Technology | Yu Y.,Jiangxi Agricultural University | Pedrycz W.,University of Alberta | And 3 more authors.
Expert Systems with Applications | Year: 2014

Particle swarm optimization (PSO) is an evolutionary algorithm known for its simplicity and effectiveness in solving various optimization problems. PSO should have strong yet balanced exploration and exploitation capabilities to enhance its performance. A superior solution guided PSO (SSG-PSO) framework integrated with an individual level based mutation operator and different local search techniques is proposed in this study. In SSG-PSO, a collection of superior solutions is maintained and updated with the evolutionary process, such that each particle can comprehensively learn from the recorded superior solutions. In addition, to maintain the diversity of the particle swarm, SSG-PSO is combined with an individual level based mutation operator, which will be invoked when a particle is trapped in a local optimum (determined by the fitness and position states of the particle), thereby improving the adaptation and flexibility of each individual particle. Moreover, two gradient-based local search techniques, namely, the Broyden-Fletcher-Goldfarb-Shanno (BFGS) and Davidon-Fletcher-Powell (DFP) Quasi-Newton methods, and two derivative-free local search techniques, namely, pattern search and Nelder-Mead simplex search, are incorporated into SSG-PSO. The performances of SSG-PSO and that of its local search enhanced variants are extensively and comparatively studied on a suit of benchmark optimization functions. © 2014 Elsevier Ltd. All rights reserved.


Pedrycz W.,University of Alberta | Pedrycz W.,Warsaw School of Information Technology
Evolving Systems | Year: 2010

The emerging category of evolvable fuzzy systems has opened a new uncharted territory of system modeling by enhancing the capabilities of existing fuzzy models and formulating new methodological and algorithmic challenges and opportunities. In this study, we revisit the underlying concept and identify a number of essential optimization problems arising therein. It is shown that the behavior and characteristics of evolvable systems can be classified under the rubric of perception-based evolvability (being inherently associated with the humancentric systems and the development of efficient mechanisms of relevance feedback) and a distribution of knowledge representation resources of evolvable systems. We elaborate on the essence of these problems and define the corresponding optimization criteria. A selected detailed design scenario is presented as well in which the dynamics of information granules is exploited as a vehicle to cope with the evolving modeling environment. © Springer-Verlag 2010.


Krawczak M.,Warsaw School of Information Technology | Krawczak M.,Polish Academy of Sciences | Szkatula G.,Polish Academy of Sciences
Information Sciences | Year: 2015

A comparison of two objects may be viewed as an attempt to determine the degree to which they are similar or different in a given sense. Defining a good measure of proximity, or else similarity or dissimilarity between objects is very important in practical tasks as well as theoretical achievements. Each object is usually represented as a point in Cartesian coordinates, and therefore the distance between points reflects similarities between respective objects. In general, the space is assumed to be Euclidean, and a distance between points assigns a nonnegative number. From another point of view the concept of symmetry underlies essentially all theoretical treatments of similarity. Tversky (1977) provided empirical evidence of asymmetric similarities and argued that similarity should not be treated as a symmetric relation. According to Tversky's consideration, an object is described by sets of features instead of geometric points in a metric space. In this paper we propose a new measure of remoteness between sets of nominal values. Instead of considering distance between two sets, we introduce the measures of perturbation type 1 of one set by another. The consideration is based on set-theoretic operations and the proposed measure describes changes of the second set after adding the first set to it, or vice versa. The measure of sets' perturbation returns a value from [0, 1], and it must be emphasized that this measure is not symmetric in general. The difference between 1 and the sum of these two measures of perturbation of a pair of sets can be understood as Jaccard's extended similarity measure. In this paper several mathematical properties of the measure of sets' perturbation are studied, and interpretation of proximity is explained by the comparison of selected measures. © 2015 Elsevier Inc. All rights reserved.


Krawczak M.,Polish Academy of Sciences | Krawczak M.,Warsaw School of Information Technology | Szkatula G.,Polish Academy of Sciences
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2012

In this paper we developed a new methodology for grouping objects described by nominal attributes. We introduced a definition of condition's domination within each pair of cluster, and next the measure of ω-distinguishability of clusters for creating a junction of clusters. The developed method is hierarchical and agglomerative one and can be characterized both by high speed of computation as well as extremely good accuracy of clustering. © 2012 Springer-Verlag Berlin Heidelberg.


Krawczak M.,Polish Academy of Sciences | Krawczak M.,Warsaw School of Information Technology | Szkatula G.,Polish Academy of Sciences
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2013

In this paper we developed a new methodology for grouping objects described by nominal attributes. We introduced a measure of perturbation of one cluster by another cluster in order to create a junction of clusters. The developed method is hierarchical and agglomerative and can be characterized both by high speed of computation as well as surprising good accuracy of clustering. keywords cluster analysis, nominal attributes, sets theory. © 2013 Springer-Verlag.


Krawczak M.,Warsaw School of Information Technology | Szkatula G.,Polish Academy of Sciences
Information Sciences | Year: 2014

Many methods of dimensionality reduction of data series (time series) have been introduced over the past decades. Some of them rely on a symbolic representation of the original data, however in this case the obtained dimensionality reduction is not substantial. In this paper, we introduce a new approach referred to as Symbolic Essential Attributes Approximation (SEAA) to reduce the dimensionality of multidimensional time series. In such a way we form a new nominal representation of the original data series. The approach is based on the concept of data series envelopes and essential attributes generated by a multilayer neural network. The real-valued attributes are discretized, and in this way symbolic data series representation is formed. The SEAA generates a vector of nominal values of new attributes which form the compressed representation of original data series. The nominal attributes are synthetic, and while not being directly interpretable, they still retain important features of the original data series. A validation of usefulness of the proposed dimensionality reduction is carried out for classification and clustering tasks. The experiments have shown that even for a significant reduction of dimensionality, the new representation retains information about the data series sufficient for classification and clustering of the time series. © 2013 Elsevier Inc. All rights reserved.


Figielska E.,Warsaw School of Information Technology
Control and Cybernetics | Year: 2011

This paper deals with the problem of preemptive scheduling in a two-stage flowshop with parallel unrelated machines and additional renewable resources. The objective is the minimization of makespan. The problem is NP-hard. Heuristic algorithms are proposed which join the linear programming based procedures with metaheuristic algorithms: genetic, simulated annealing and tabu search algorithm. The performance of the proposed algorithms is experimentally evaluated by comparing the solutions with a lower bound on the optimal makespan. Results of a computational experiment show that these algorithms are able to produce good solutions in short computation time and that the metaheuristics significantly improve the results for the most difficult problems.


Krawczak M.,Warsaw School of Information Technology
Studies in Computational Intelligence | Year: 2013

In this book, the natural structure of multilayer neural networks was used in order to consider this class of neural networks from the systems point of view: the aggregated neurons lying within one layer constitute the stage of the system and the bordering stages exchange the information on their states. The outputs of the neurons, from the same layer, constitute the state vectors. Connection weights between the neurons of the same layer are arranged in vectors and are treated as controls. In this way, we developed the interpretation of the multilayer neural networks as the multistage control systems © Springer International Publishing Switzerland 2013.


Krawczak M.,Warsaw School of Information Technology | Szkatula G.,Warsaw School of Information Technology
Proceedings of the 2013 Joint IFSA World Congress and NAFIPS Annual Meeting, IFSA/NAFIPS 2013 | Year: 2013

Defining a proper measure of proximity (or remoteness) between two groups of objects is of crucial importance in applied research. Much attention has been paid to consideration of continuous-valued attributes while nominal-valued attributes seems to be more difficult to handle. In this paper we defined non empty groups of objects, and each group is described as K-tuple sets of attributes values. Next, we defined interactions between two groups and description of the groups interactions. Instead of considering dissimilarities between groups, we introduced a measure of perturbation of one group by another. The introduced measure is in general asymmetrical, and therefore cannot be considered as the distance between the groups. The measure of perturbation one group by another group can be applied to e.g. clustering problems. The proposed method is both hierarchical and agglomerative, and is characterized by high speed of computation as well as surprising good accuracy of grouping. © 2013 IEEE.


Szmidt E.,Warsaw School of Information Technology | Kacprzyk J.,Warsaw School of Information Technology
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2010

The correlation coefficient (Pearson's r) is one of the most frequently used tools in statistics. In this paper we propose a correlation coefficient of Atanassov's intuitionistic fuzzy sets (A-IFSs). It provides the strength of the relationship between A-IFSs and also shows if the considered sets are positively or negatively correlated. Next, the proposed correlation coefficient takes into account not only the amount of information related to the A-IFS data (expressed by the membership and non-membership values) but also the reliability of the data expressed by a so-called hesitation margin. © 2010 Springer-Verlag Berlin Heidelberg.

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