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Algorithms
Special Issues
Mathematical Models and Their Applications
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Mathematical Models and Their Applications

A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (15 March 2020) | Viewed by 22804

Special Issue Editors

Prof. Dr. Eugene Semenkin

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Guest Editor
Department of System Analysis and Operations Research, Siberian Institute of Applied System Analysis, Reshetnev Siberian State University of Science and Technology, 41031 Krasnoyarsk, Russia
Interests: modeling and optimization of complicated systems; computational intelligence; evolutionary algorithms; artificial intelligence; data mining
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Friedhelm Schwenker

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Guest Editor
Insitute of Neural Information Processing, Ulm University, James Frank Ring, 89081 Ulm, Germany
Interests: artificial neural networks; pattern recognition; cluster analysis; statistical learning theory; data mining; multiple classifier systems; sensor fusion; affective computing
Special Issues, Collections and Topics in MDPI journals
Dr. Andrej Škraba

E-Mail Website
Guest Editor
Cybernetics & Decision Support Systems Laboratory at the University of Maribor, Faculty of Organizational Sciences, Kranj, Slovenia
Interests: modeling and simulation, optimization, system dynamics modeling; Internet of things; systems theory; decision processes; cyber-physical systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The current Special Issue, “Mathematical Models and Their Applications”, is intended as an international forum for the presentation of original mathematical modeling results for software and hardware applications in various fields. It aims to stimulate lively discussion among researchers as well as industrialists.

Papers may discuss theories, applications, evaluation, limitations, general tools, and techniques. Discussion papers that critically evaluate approaches or processing strategies and prototype demonstration are especially welcome.

The Special Issue will cover a broad range of research topics including, but not limited to:

  • Mathematical models and their applications
  • Mathematical modeling techniques
  • Optimization techniques, including multi-criterion optimization and decision-making support
  • Data mining and knowledge discovery
  • Machine learning
  • Pattern recognition
  • Learning in evolutionary algorithms
  • Genetic programming
  • Artificial neural networks
  • Computational intelligence and its applications
  • Bio-inspired and swarm intelligence
  • Text/web/data mining
  • Human–computer interaction
  • Natural language processing
  • Applications in engineering, natural sciences, social sciences, computer science

Dr. Eugene Semenkin
Dr. Friedhelm Schwenker
Dr. Andrej Škraba
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical modeling
  • optimization
  • machine learning
  • data mining
  • computational intelligence
  • applications

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Related Special Issue

Published Papers (5 papers)

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Research

18 pages, 11016 KiB  
Article
Investigation of the iCC Framework Performance for Solving Constrained LSGO Problems
by Alexey Vakhnin and Evgenii Sopov
Algorithms 2020, 13(5), 108; https://doi.org/10.3390/a13050108 - 26 Apr 2020
Cited by 6 | Viewed by 4027
Abstract
Many modern real-valued optimization tasks use “black-box” (BB) models for evaluating objective functions and they are high-dimensional and constrained. Using common classifications, we can identify them as constrained large-scale global optimization (cLSGO) tasks. Today, the IEEE Congress of Evolutionary Computation provides a special [...] Read more.
Many modern real-valued optimization tasks use “black-box” (BB) models for evaluating objective functions and they are high-dimensional and constrained. Using common classifications, we can identify them as constrained large-scale global optimization (cLSGO) tasks. Today, the IEEE Congress of Evolutionary Computation provides a special session and several benchmarks for LSGO. At the same time, cLSGO problems are not well studied yet. The majority of modern optimization techniques demonstrate insufficient performance when confronted with cLSGO tasks. The effectiveness of evolution algorithms (EAs) in solving constrained low-dimensional optimization problems has been proven in many scientific papers and studies. Moreover, the cooperative coevolution (CC) framework has been successfully applied for EA used to solve LSGO problems. In this paper, a new approach for solving cLSGO has been proposed. This approach is based on CC and a method that increases the size of groups of variables at the decomposition stage (iCC) when solving cLSGO tasks. A new algorithm has been proposed, which combined the success-history based parameter adaptation for differential evolution (SHADE) optimizer, iCC, and the ε-constrained method (namely ε-iCC-SHADE). We investigated the performance of the ε-iCC-SHADE and compared it with the previously proposed ε-CC-SHADE algorithm on scalable problems from the IEEE CEC 2017 Competition on constrained real-parameter optimization. Full article
(This article belongs to the Special Issue Mathematical Models and Their Applications)
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19 pages, 11395 KiB  
Article
How to Identify Varying Lead–Lag Effects in Time Series Data: Implementation, Validation, and Application of the Generalized Causality Algorithm
by Johannes Stübinger and Katharina Adler
Algorithms 2020, 13(4), 95; https://doi.org/10.3390/a13040095 - 16 Apr 2020
Cited by 3 | Viewed by 6423
Abstract
This paper develops the generalized causality algorithm and applies it to a multitude of data from the fields of economics and finance. Specifically, our parameter-free algorithm efficiently determines the optimal non-linear mapping and identifies varying lead–lag effects between two given time series. This [...] Read more.
This paper develops the generalized causality algorithm and applies it to a multitude of data from the fields of economics and finance. Specifically, our parameter-free algorithm efficiently determines the optimal non-linear mapping and identifies varying lead–lag effects between two given time series. This procedure allows an elastic adjustment of the time axis to find similar but phase-shifted sequences—structural breaks in their relationship are also captured. A large-scale simulation study validates the outperformance in the vast majority of parameter constellations in terms of efficiency, robustness, and feasibility. Finally, the presented methodology is applied to real data from the areas of macroeconomics, finance, and metal. Highest similarity show the pairs of gross domestic product and consumer price index (macroeconomics), S&P 500 index and Deutscher Aktienindex (finance), as well as gold and silver (metal). In addition, the algorithm takes full use of its flexibility and identifies both various structural breaks and regime patterns over time, which are (partly) well documented in the literature. Full article
(This article belongs to the Special Issue Mathematical Models and Their Applications)
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29 pages, 2498 KiB  
Article
Success History-Based Position Adaptation in Fuzzy-Controlled Ensemble of Biology-Inspired Algorithms
by Shakhnaz Akhmedova, Vladimir Stanovov, Danil Erokhin and Olga Semenkina
Algorithms 2020, 13(4), 89; https://doi.org/10.3390/a13040089 - 9 Apr 2020
Viewed by 3071
Abstract
In this study, a new modification of the meta-heuristic approach called Co-Operation of Biology-Related Algorithms (COBRA) is proposed. Originally the COBRA approach was based on a fuzzy logic controller and used for solving real-parameter optimization problems. The basic idea consists of a cooperative [...] Read more.
In this study, a new modification of the meta-heuristic approach called Co-Operation of Biology-Related Algorithms (COBRA) is proposed. Originally the COBRA approach was based on a fuzzy logic controller and used for solving real-parameter optimization problems. The basic idea consists of a cooperative work of six well-known biology-inspired algorithms, referred to as components. However, it was established that the search efficiency of COBRA depends on its ability to keep the exploitation and exploration balance when solving optimization problems. The new modification of the COBRA approach is based on other method for generating potential solutions. This method keeps a historical memory of successful positions found by individuals to lead them in different directions and therefore to improve the exploitation and exploration capabilities. The proposed technique was applied to the COBRA components and to its basic steps. The newly proposed meta-heuristic as well as other modifications of the COBRA approach and components were evaluated on three sets of various benchmark problems. The experimental results obtained by all algorithms with the same computational effort are presented and compared. It was concluded that the proposed modification outperformed other algorithms used in comparison. Therefore, its usefulness and workability were demonstrated. Full article
(This article belongs to the Special Issue Mathematical Models and Their Applications)
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15 pages, 453 KiB  
Article
Confidence-Based Voting for the Design of Interpretable Ensembles with Fuzzy Systems
by Vladimir Stanovov, Shakhnaz Akhmedova and Yukihiro Kamiya
Algorithms 2020, 13(4), 86; https://doi.org/10.3390/a13040086 - 6 Apr 2020
Cited by 1 | Viewed by 3216
Abstract
In this study, a new voting procedure for combining the fuzzy logic based classifiers and other classifiers called confidence-based voting is proposed. This method combines two classifiers, namely the fuzzy classification system, and for the cases when the fuzzy system returns high confidence [...] Read more.
In this study, a new voting procedure for combining the fuzzy logic based classifiers and other classifiers called confidence-based voting is proposed. This method combines two classifiers, namely the fuzzy classification system, and for the cases when the fuzzy system returns high confidence levels, i.e., the returned membership value is large, the fuzzy system is used to perform classification, otherwise, the second classifier is applied. As a result, most of the sample is classified by the explainable and interpretable fuzzy system, and the second, more accurate, but less interpretable classifier is applied only for the most difficult cases. To show the efficiency of the proposed approach, a set of experiments is performed on test datasets, as well as two problems of estimating the person’s emotional state with the data collected by non-contact vital sensors, which use the Doppler effect. To validate the accuracies of the proposed approach, the statistical tests were used for comparison. The obtained results demonstrate the efficiency of the proposed technique, as it allows for both improving the classification accuracy and explaining the decision making process. Full article
(This article belongs to the Special Issue Mathematical Models and Their Applications)
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17 pages, 2252 KiB  
Article
Research and Study of the Hybrid Algorithms Based on the Collective Behavior of Fish Schools and Classical Optimization Methods
by Liliya A. Demidova and Artyom V. Gorchakov
Algorithms 2020, 13(4), 85; https://doi.org/10.3390/a13040085 - 3 Apr 2020
Cited by 14 | Viewed by 4711
Abstract
Inspired by biological systems, swarm intelligence algorithms are widely used to solve multimodal optimization problems. In this study, we consider the hybridization problem of an algorithm based on the collective behavior of fish schools. The algorithm is computationally inexpensive compared to other population-based [...] Read more.
Inspired by biological systems, swarm intelligence algorithms are widely used to solve multimodal optimization problems. In this study, we consider the hybridization problem of an algorithm based on the collective behavior of fish schools. The algorithm is computationally inexpensive compared to other population-based algorithms. Accuracy of fish school search increases with the increase of predefined iteration count, but this also affects computation time required to find a suboptimal solution. We propose two hybrid approaches, intending to improve the evolutionary-inspired algorithm accuracy by using classical optimization methods, such as gradient descent and Newton’s optimization method. The study shows the effectiveness of the proposed hybrid algorithms, and the strong advantage of the hybrid algorithm based on fish school search and gradient descent. We provide a solution for the linearly inseparable exclusive disjunction problem using the developed algorithm and a perceptron with one hidden layer. To demonstrate the effectiveness of the algorithms, we visualize high dimensional loss surfaces near global extreme points. In addition, we apply the distributed version of the most effective hybrid algorithm to the hyperparameter optimization problem of a neural network. Full article
(This article belongs to the Special Issue Mathematical Models and Their Applications)
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