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Symmetry
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Symmetry in Engineering Sciences
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Symmetry in Engineering Sciences

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".

Deadline for manuscript submissions: closed (15 April 2019) | Viewed by 84634

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Dr. Raúl Baños Navarro

E-Mail Website
Guest Editor
Department of Engineering, Electrical Engineering section, University of Almería, E-04120 Almería, Spain
Interests: energy economics; renewable energy; power meters; network analysis; engineering optimization
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Francisco G. Montoya

E-Mail Website
Guest Editor
Department of Engineering, Electrical Engineering Section, University of Almeria, 04120 Almeria, Spain
Interests: geometric algebra; power quality; power theory; power engineering; optimization techniques
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Symmetry is a frequent pattern widely studied in different research fields. In particular, complex systems with symmetry arise in engineering science (e.g., in mechanical engineering symmetric and synchronized systems are often used to satisfy stability criteria for rotating structures; in electrical engineering the study of symmetrical and asymmetrical faults in power systems is a critical issue; in telecommunications engineering many systems are symmetrical since data speed or quantity is the same in both directions; in civil engineering the strength of the objects depend on the symmetry; in computer engineering symmetric network structures and symmetric algorithms are often studied, etc.).

This Special Issue invites researchers to submit original research papers and review articles related to any engineering discipline in which theoretical or practical issues of symmetry are considered. The topics of interest include, but are not limited to:

  • Symmetry in electrical and electronic engineering
  • Symmetry in mechanical engineering
  • Symmetry in automation and robotic engineering
  • Symmetry in computer engineering
  • Symmetry in telecommunications engineering
  • Symmetry in civil engineering (transportation, hydraulics, etc.)
  • Symmetry in chemical engineering
  • Symmetry and topology of complex networks in engineering
  • Symmetry and optimization in engineering applications

Dr. Raúl Baños Navarro
Dr. Francisco G. Montoya
Guest Editor

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. Symmetry 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 2400 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

  • Symmetry and asymmetry  
  • Symmetry and synchronization
  • Symmetry and topology
  • Electrical and electronic circuits and devices
  • Mechanical structures and smart materials
  • Automata and robots
  • Engineering graphic modelling
  • Complex networks and graphs
  • Optimization in engineering
  • Computing applications in symmetry

Published Papers (14 papers)

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Editorial

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4 pages, 185 KiB  
Editorial
Symmetry in Engineering Sciences
by Francisco G. Montoya, Raúl Baños, Alfredo Alcayde and Francisco Manzano-Agugliaro
Symmetry 2019, 11(6), 797; https://doi.org/10.3390/sym11060797 - 15 Jun 2019
Cited by 3 | Viewed by 1957
Abstract
The symmetry concept is mainly used in two senses. The first from the aesthetic point of view of proportionality or harmony, since human beings seek symmetry in nature. Or the second, from an engineering point of view to attend to geometric regularities or [...] Read more.
The symmetry concept is mainly used in two senses. The first from the aesthetic point of view of proportionality or harmony, since human beings seek symmetry in nature. Or the second, from an engineering point of view to attend to geometric regularities or to explain a repetition process or pattern in a given phenomenon. This special issue dedicated to geometry in engineering deals with this last concept, which aims to collect both the aspects of geometric solutions in engineering, which may even have a certain aesthetic character, and the aspect of the use of patterns that explain observed phenomena. Full article
(This article belongs to the Special Issue Symmetry in Engineering Sciences)

Research

Jump to: Editorial

17 pages, 1053 KiB  
Article
Feature Selection with Conditional Mutual Information Considering Feature Interaction
by Jun Liang, Liang Hou, Zhenhua Luan and Weiping Huang
Symmetry 2019, 11(7), 858; https://doi.org/10.3390/sym11070858 - 02 Jul 2019
Cited by 26 | Viewed by 5359
Abstract
Feature interaction is a newly proposed feature relevance relationship, but the unintentional removal of interactive features can result in poor classification performance for this relationship. However, traditional feature selection algorithms mainly focus on detecting relevant and redundant features while interactive features are usually [...] Read more.
Feature interaction is a newly proposed feature relevance relationship, but the unintentional removal of interactive features can result in poor classification performance for this relationship. However, traditional feature selection algorithms mainly focus on detecting relevant and redundant features while interactive features are usually ignored. To deal with this problem, feature relevance, feature redundancy and feature interaction are redefined based on information theory. Then a new feature selection algorithm named CMIFSI (Conditional Mutual Information based Feature Selection considering Interaction) is proposed in this paper, which makes use of conditional mutual information to estimate feature redundancy and interaction, respectively. To verify the effectiveness of our algorithm, empirical experiments are conducted to compare it with other several representative feature selection algorithms. The results on both synthetic and benchmark datasets indicate that our algorithm achieves better results than other methods in most cases. Further, it highlights the necessity of dealing with feature interaction. Full article
(This article belongs to the Special Issue Symmetry in Engineering Sciences)
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21 pages, 3493 KiB  
Article
A Time-Space Network Model Based on a Train Diagram for Predicting and Controlling the Traffic Congestion in a Station Caused by an Emergency
by Zihan Qu and Shiwei He
Symmetry 2019, 11(6), 780; https://doi.org/10.3390/sym11060780 - 12 Jun 2019
Cited by 5 | Viewed by 3855
Abstract
Timely predicting and controlling the traffic congestion in a station caused by an emergency is an important task in railway emergency management. However, traffic forecasting in an emergency is subject to a dynamic service network, with uncertainty surrounding elements such as the capacity [...] Read more.
Timely predicting and controlling the traffic congestion in a station caused by an emergency is an important task in railway emergency management. However, traffic forecasting in an emergency is subject to a dynamic service network, with uncertainty surrounding elements such as the capacity of the transport network, schedules, and plans. Accurate traffic forecasting is difficult. This paper proposes a practical time-space network model based on a train diagram for predicting and controlling the traffic congestion in a station caused by an emergency. Based on the train diagram, we constructed a symmetric time-space network for the first time by considering the transition of the railcar state. On this basis, an improved A* algorithm based on the railcar flow route was proposed to generate feasible path sets and a dynamic railcar flow distribution model was built to simulate the railcar flow distribution process in an emergency. In our numerical studies, these output results of our proposed model can be used to control traffic congestion. Full article
(This article belongs to the Special Issue Symmetry in Engineering Sciences)
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19 pages, 3990 KiB  
Article
Study on a Novel Fault Diagnosis Method Based on VMD and BLM
by Jianjie Zheng, Yu Yuan, Li Zou, Wu Deng, Chen Guo and Huimin Zhao
Symmetry 2019, 11(6), 747; https://doi.org/10.3390/sym11060747 - 02 Jun 2019
Cited by 29 | Viewed by 3210
Abstract
The bearing system of an alternating current (AC) motor is a nonlinear dynamics system. The working state of rolling bearings directly determines whether the machine is in reliable operation. Therefore, it is very meaningful to study the fault diagnosis and prediction of rolling [...] Read more.
The bearing system of an alternating current (AC) motor is a nonlinear dynamics system. The working state of rolling bearings directly determines whether the machine is in reliable operation. Therefore, it is very meaningful to study the fault diagnosis and prediction of rolling bearings. In this paper, a new fault diagnosis method based on variational mode decomposition (VMD), Hilbert transform (HT), and broad learning model (BLM), called VHBLFD is proposed for rolling bearings. In the VHBLFD method, the VMD is used to decompose the vibration signals to obtain intrinsic mode functions (IMFs). The HT is used to process the IMFs to obtain Hilbert envelope spectra, which are transformed into the mapped features and the enhancement nodes of BLM according to the complexity of the modeling tasks, and the nonlinear transformation mean according to the characteristics of input data. The BLM is used to classify faults of the rolling bearings of the AC motor. Next, the pseudo-inverse operation is used to obtain the fault diagnosis results. Finally, the VHBLFD is validated by actual vibration data. The experiment results show that the BLM can quickly and accurately be trained. The VHBLFD method can achieve higher identification accuracy for multi-states of rolling bearings and takes on fast operation speed and strong generalization ability. Full article
(This article belongs to the Special Issue Symmetry in Engineering Sciences)
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15 pages, 5079 KiB  
Article
Rampant Arch and Its Optimum Geometrical Generation
by Cristina Velilla, Alfredo Alcayde, Carlos San-Antonio-Gómez, Francisco G. Montoya, Ignacio Zavala and Francisco Manzano-Agugliaro
Symmetry 2019, 11(5), 627; https://doi.org/10.3390/sym11050627 - 03 May 2019
Cited by 7 | Viewed by 10986
Abstract
Gothic art was developed in western Europe from the second half of the 12th century to the end of the 15th century. The most characteristic Gothic building is the cathedral. Gothic architecture uses well-carved stone ashlars, and its essential elements include the arch. [...] Read more.
Gothic art was developed in western Europe from the second half of the 12th century to the end of the 15th century. The most characteristic Gothic building is the cathedral. Gothic architecture uses well-carved stone ashlars, and its essential elements include the arch. The thrust is transferred by means of external arches (flying buttresses) to external buttresses that end in pinnacles, which accentuates the verticality. The evolution of the flying buttresses should not only be considered as an aesthetic consideration, but also from a constructive point of view as an element of transmission of forces or loads. Thus, one evolves from a beam-type buttress to a simple arch, and finally to a rampant arch. In this work, we study the geometry of the rampant arch to determine which is the optimum from the constructive point of view. The optimum rampant arch obtained is the one with the common tangent to the two arches parallel to the slope line. A computer program was created to determine this optimal rampant arch by means of a numerical or graphical input. It was applied to several well-known and representative cases of Gothic art in France (church of Saint Urbain de Troyes) and Spain (Cathedral of Palma de Mallorca), establishing if they were designs of optimal rampant arches or not. Full article
(This article belongs to the Special Issue Symmetry in Engineering Sciences)
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16 pages, 4383 KiB  
Article
The Hay Inclined Plane in Coalbrookdale (Shropshire, England): Geometric Modeling and Virtual Reconstruction
by José Ignacio Rojas-Sola and Eduardo De la Morena-De la Fuente
Symmetry 2019, 11(4), 589; https://doi.org/10.3390/sym11040589 - 24 Apr 2019
Cited by 15 | Viewed by 3396
Abstract
This article shows the geometric modeling and virtual reconstruction of the inclined plane of Coalbrookdale (Shropshire, England) that was in operation from 1792 to 1894. This historical invention, work of the Englishman William Reynolds, allowed the transportation of boats through channels located at [...] Read more.
This article shows the geometric modeling and virtual reconstruction of the inclined plane of Coalbrookdale (Shropshire, England) that was in operation from 1792 to 1894. This historical invention, work of the Englishman William Reynolds, allowed the transportation of boats through channels located at different levels. Autodesk Inventor Professional software has been used to obtain the 3D CAD model of this historical invention and its geometric documentation. The material for the research is available on the website of the Betancourt Project of the Canary Orotava Foundation for the History of Science. Also, because the single sheet does not have a scale, it has been necessary to adopt a graphic scale so that the dimensions of the different elements are coherent. Furthermore, it has been necessary to establish some dimensional, geometric, and movement restrictions (degrees of freedom) so that the set will work properly. One of the main conclusions is that William Reynolds designed a mechanism seeking a longitudinal symmetry so that, from a single continuous movement, the mechanism allows two vessels to ascend and descend simultaneously. This engineering solution facilitated a doubling of the working capacity of the device, as well as a reduction of the energy needs of the system. Full article
(This article belongs to the Special Issue Symmetry in Engineering Sciences)
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20 pages, 10751 KiB  
Article
Anomaly Detection Based on Mining Six Local Data Features and BP Neural Network
by Yu Zhang, Yuanpeng Zhu, Xuqiao Li, Xiaole Wang and Xutong Guo
Symmetry 2019, 11(4), 571; https://doi.org/10.3390/sym11040571 - 19 Apr 2019
Cited by 9 | Viewed by 3590
Abstract
Key performance indicators (KPIs) are time series with the format of (timestamp, value). The accuracy of KPIs anomaly detection is far beyond our initial expectations sometimes. The reasons include the unbalanced distribution between the normal data and the anomalies as well as the [...] Read more.
Key performance indicators (KPIs) are time series with the format of (timestamp, value). The accuracy of KPIs anomaly detection is far beyond our initial expectations sometimes. The reasons include the unbalanced distribution between the normal data and the anomalies as well as the existence of many different types of the KPIs data curves. In this paper, we propose a new anomaly detection model based on mining six local data features as the input of back-propagation (BP) neural network. By means of vectorization description on a normalized dataset innovatively, the local geometric characteristics of one time series curve could be well described in a precise mathematical way. Differing from some traditional statistics data characteristics describing the entire variation situation of one sequence, the six mined local data features give a subtle insight of local dynamics by describing the local monotonicity, the local convexity/concavity, the local inflection property and peaks distribution of one KPI time series. In order to demonstrate the validity of the proposed model, we applied our method on 14 classical KPIs time series datasets. Numerical results show that the new given scheme achieves an average F1-score over 90%. Comparison results show that the proposed model detects the anomaly more precisely. Full article
(This article belongs to the Special Issue Symmetry in Engineering Sciences)
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14 pages, 2925 KiB  
Article
Adaptive Edge Preserving Weighted Mean Filter for Removing Random-Valued Impulse Noise
by Nasar Iqbal, Sadiq Ali, Imran Khan and Byung Moo Lee
Symmetry 2019, 11(3), 395; https://doi.org/10.3390/sym11030395 - 18 Mar 2019
Cited by 22 | Viewed by 4063
Abstract
This paper proposes an adaptive noise detector and a new weighted mean filter to remove random-valued impulse noise from the images. Unlike other noise detectors, the proposed detector computes a new and adaptive threshold for each pixel. The detection accuracy is further improved [...] Read more.
This paper proposes an adaptive noise detector and a new weighted mean filter to remove random-valued impulse noise from the images. Unlike other noise detectors, the proposed detector computes a new and adaptive threshold for each pixel. The detection accuracy is further improved by employing edge identification stage to ensure that the edge pixels are not incorrectly detected as noisy pixels. Thus, preserving the edges avoids faulty detection of noise. In the filtering stage, a new weighted mean filter is designed to filter only those pixels which are identified as noisy in the first stage. Different from other filters, the proposed filter divides the pixels into clusters of noisy and clean pixels and thus takes into only clean pixels to find the replacement of the noisy pixel. Simulation results show that the proposed method outperforms state-of-the-art noise detection methods in suppressing random valued impulse noise. Full article
(This article belongs to the Special Issue Symmetry in Engineering Sciences)
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15 pages, 2483 KiB  
Article
Parametric Fault Diagnosis of Analog Circuits Based on a Semi-Supervised Algorithm
by Ling Wang, Dongfang Zhou, Hui Tian, Hao Zhang and Wei Zhang
Symmetry 2019, 11(2), 228; https://doi.org/10.3390/sym11020228 - 14 Feb 2019
Cited by 8 | Viewed by 2848
Abstract
The parametric fault diagnosis of analog circuits is very crucial for condition-based maintenance (CBM) in prognosis and health management. In order to improve the diagnostic rate of parametric faults in engineering applications, a semi-supervised machine learning algorithm was used to classify the parametric [...] Read more.
The parametric fault diagnosis of analog circuits is very crucial for condition-based maintenance (CBM) in prognosis and health management. In order to improve the diagnostic rate of parametric faults in engineering applications, a semi-supervised machine learning algorithm was used to classify the parametric fault. A lifting wavelet transform was used to extract fault features, a local preserving mapping algorithm was adopted to optimize the Fisher linear discriminant analysis, and a semi-supervised cooperative training algorithm was utilized for fault classification. In the proposed method, the fault values were randomly selected as training samples in a range of parametric fault intervals, for both optimizing the generalization of the model and improving the fault diagnosis rate. Furthermore, after semi-supervised dimensionality reduction and semi-supervised classification were applied, the diagnosis rate was slightly higher than the existing training model by fixing the value of the analyzed component. Full article
(This article belongs to the Special Issue Symmetry in Engineering Sciences)
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16 pages, 9156 KiB  
Article
A Prediction Method for the Damping Effect of Ring Dampers Applied to Thin-Walled Gears Based on Energy Method
by Yanrong Wang, Hang Ye, Xianghua Jiang and Aimei Tian
Symmetry 2018, 10(12), 677; https://doi.org/10.3390/sym10120677 - 30 Nov 2018
Cited by 12 | Viewed by 3212
Abstract
In turbomachinery applications, thin-walled gears are cyclic symmetric structures and often subject to dynamic meshing loading which may result in high cycle fatigue (HCF) of the thin-walled gear. To avoid HCF failure, ring dampers are designed for gears to increase damping and reduce [...] Read more.
In turbomachinery applications, thin-walled gears are cyclic symmetric structures and often subject to dynamic meshing loading which may result in high cycle fatigue (HCF) of the thin-walled gear. To avoid HCF failure, ring dampers are designed for gears to increase damping and reduce resonance amplitude. Ring dampers are installed in the groove. They are held in contact with the groove by normal pressure generated by interference or centrifugal force. Vibration energy is attenuated (converted to heat) by frictional force on the contact interface when the relative motion between ring dampers and gears takes place. In this article, a numerical method for the prediction of friction damping in thin-walled gears with ring dampers is proposed. The nonlinear damping due to the friction is expressed as equivalent mechanical damping in the form of vibration stress dependence. This method avoids the forced response analysis of nonlinear structures, thereby significantly reducing the time required for calculation. The validity of this numerical method is examined by a comparison with literature data. The method is applied to a thin-walled gear with a ring damper and the effect of design parameters on friction damping is studied. It is shown that the rotating speed, geometric size of ring dampers and friction coefficient significantly influence the damping performance. Full article
(This article belongs to the Special Issue Symmetry in Engineering Sciences)
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9 pages, 1287 KiB  
Article
A Novel Tool for Supervised Segmentation Using 3D Slicer
by Daniel Chalupa and Jan Mikulka
Symmetry 2018, 10(11), 627; https://doi.org/10.3390/sym10110627 - 12 Nov 2018
Cited by 10 | Viewed by 4179
Abstract
The rather impressive extension library of medical image-processing platform 3D Slicer lacks a wide range of machine-learning toolboxes. The authors have developed such a toolbox that incorporates commonly used machine-learning libraries. The extension uses a simple graphical user interface that allows the user [...] Read more.
The rather impressive extension library of medical image-processing platform 3D Slicer lacks a wide range of machine-learning toolboxes. The authors have developed such a toolbox that incorporates commonly used machine-learning libraries. The extension uses a simple graphical user interface that allows the user to preprocess data, train a classifier, and use that classifier in common medical image-classification tasks, such as tumor staging or various anatomical segmentations without a deeper knowledge of the inner workings of the classifiers. A series of experiments were carried out to showcase the capabilities of the extension and quantify the symmetry between the physical characteristics of pathological tissues and the parameters of a classifying model. These experiments also include an analysis of the impact of training vector size and feature selection on the sensitivity and specificity of all included classifiers. The results indicate that training vector size can be minimized for all classifiers. Using the data from the Brain Tumor Segmentation Challenge, Random Forest appears to have the widest range of parameters that produce sufficiently accurate segmentations, while optimal Support Vector Machines’ training parameters are concentrated in a narrow feature space. Full article
(This article belongs to the Special Issue Symmetry in Engineering Sciences)
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10 pages, 2582 KiB  
Article
Accessibility Evaluation of High Order Urban Hospitals for the Elderly: A Case Study of First-Level Hospitals in Xi’an, China
by Ke Ruan and Qi Zhang
Symmetry 2018, 10(10), 489; https://doi.org/10.3390/sym10100489 - 12 Oct 2018
Cited by 5 | Viewed by 2422
Abstract
With reference to the hospitalizing trips made by the elderly, the impedance of these trips that require the use of public transportation, is introduced. An evaluation model that can accurately detect the accessibility of high order urban hospitals (HOUHs) for the elderly is [...] Read more.
With reference to the hospitalizing trips made by the elderly, the impedance of these trips that require the use of public transportation, is introduced. An evaluation model that can accurately detect the accessibility of high order urban hospitals (HOUHs) for the elderly is established with the help of Geographic Information System (GIS) technology. Furthermore, the established model is employed to detect the accessibility of first-level hospitals in Xi’an City. Results showed that the traffic connection between hospitals and their service objects is an important factor for the feasibility and effectiveness of an accessibility evaluation. It is suggested that special evaluations of the accessibility of hospitals for the elderly are needed to achieve the human-oriented goal of urban traffic planning. The well-served spatial pattern of hospitalizing accessibility for the elderly in Xi’an City has been established in recent years because of the strategies for public transit metropolis. The accessibility constraints can be divided into three types: The imprisonment, the antagonism and the running-in, for which the corresponding countermeasures to settle the low accessibility of hospitals will be taken by the planning administration. Attention is paid to specific population groups during their hospitalizing trips in the accessibility research, which is beneficial for enabling the improvement of the current traditional method which is mainly based on travel facilities. Full article
(This article belongs to the Special Issue Symmetry in Engineering Sciences)
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17 pages, 1918 KiB  
Article
Path Planning for the Mobile Robot: A Review
by Han-ye Zhang, Wei-ming Lin and Ai-xia Chen
Symmetry 2018, 10(10), 450; https://doi.org/10.3390/sym10100450 - 01 Oct 2018
Cited by 242 | Viewed by 28926
Abstract
Good path planning technology of mobile robot can not only save a lot of time, but also reduce the wear and capital investment of mobile robot. Several methodologies have been proposed and reported in the literature for the path planning of mobile robot. [...] Read more.
Good path planning technology of mobile robot can not only save a lot of time, but also reduce the wear and capital investment of mobile robot. Several methodologies have been proposed and reported in the literature for the path planning of mobile robot. Although these methodologies do not guarantee an optimal solution, they have been successfully applied in their works. The purpose of this paper is to review the modeling, optimization criteria and solution algorithms for the path planning of mobile robot. The survey shows GA (genetic algorithm), PSO (particle swarm optimization algorithm), APF (artificial potential field), and ACO (ant colony optimization algorithm) are the most used approaches to solve the path planning of mobile robot. Finally, future research is discussed which could provide reference for the path planning of mobile robot. Full article
(This article belongs to the Special Issue Symmetry in Engineering Sciences)
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15 pages, 1004 KiB  
Article
Modeling the Service Network Design Problem in Railway Express Shipment Delivery
by Siqi Liu, Boliang Lin, Jianping Wu and Yinan Zhao
Symmetry 2018, 10(9), 391; https://doi.org/10.3390/sym10090391 - 10 Sep 2018
Cited by 8 | Viewed by 3272
Abstract
As air pollution becomes increasingly severe, express trains play a more important role in shifting road freight and reducing carbon emissions. Thus, the design of railway express shipment service networks has become a key issue, which needs to be addressed urgently both in [...] Read more.
As air pollution becomes increasingly severe, express trains play a more important role in shifting road freight and reducing carbon emissions. Thus, the design of railway express shipment service networks has become a key issue, which needs to be addressed urgently both in theory and practice. The railway express shipment service network design problem (RESSNDP) not only involves the selection of train services and determination of service frequency, but it is also associated with shipment routing, which can be viewed as a service network design problem (SNDP) with railway characteristics. This paper proposes a non-linear integer programming model (INLP) which aims at finding a service network and shipment routing plan with minimum cost while satisfying the transportation time constraints of shipments, carrying capacity constraints of train services, flow conservation constraint and logical constraints among decision variables. In addition, a linearization technique was adopted to transform our model into a linear one to obtain a global optimal solution. To evaluate the effectiveness and efficiency of our approach, a small trial problem was solved by the state-of-the-art mathematical programming solver Gurobi 7.5.2. Full article
(This article belongs to the Special Issue Symmetry in Engineering Sciences)
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