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Mathematics
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Multivariable Optimization by Intelligent and Numerical Modelling and Simulation
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Multivariable Optimization by Intelligent and Numerical Modelling and Simulation

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (30 April 2021) | Viewed by 14303

Special Issue Editor

Prof. Dr. William Guo

E-Mail Website
Guest Editor
School of Engineering and Technology, Central Queensland University, North Rockhampton, QLD 4702, Australia
Interests: mathematics education; computational intelligence; data mining; modelling and simulation; geophysics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

With great assistance from computers and computing networks developed in recent decades, numerical computation has found new dimensions in solving various scientific and engineering problems with high complexity. Whenever a numerical approach is applied to a complicated problem, the problem would likely have either no exact solution or take an unacceptably long time to determine the exact solution. Therefore, in a broad sense, most numerical approaches can be regarded as an abstract problem of optimization which aims to find the best possible acceptable solution with respect to the preset constraints.

While traditional numerical approaches keep evolving to solve various problems alone, intelligent techniques have emerged in the last three decades as an untraditional means to enrich numerical computation for complicated problems that were regarded as ill-defined problems in traditional mathematical sciences. Though mathematically unsound, nevertheless, such problems widely exist in various disciplines for application, such as multivariable scheduling, sequencing, forecasting, alignment and so forth, or in other words, multivariable optimizations.

This Special Issue aims to solicit high-quality papers reporting latest applications of numerical and intelligent medaling and simulation for solving multivariable optimization problems in all disciplines, including but not limited to:

  • Biology, medical, health, and bioinformatics;
  • Mathematical, physical, chemical, information, and computing sciences;
  • Agricultural, environmental, and earth sciences;
  • Business, economy, finance, commence, trading, education, and other related areas;
  • Supply chain management, production-inventory control, and other related areas;
  • All engineering and technology disciplines.

Prof. Dr. William Guo
Guest Editor

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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. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

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Published Papers (5 papers)

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Research

16 pages, 3760 KiB  
Article
Nonlinear Control of Hydrostatic Thrust Bearing Using Multivariable Optimization
by Waheed Ur Rehman, Wakeel Khan, Nasim Ullah, M. D. Shahariar Chowdhury, Kuaanan Techato and Muhammad Haneef
Mathematics 2021, 9(8), 903; https://doi.org/10.3390/math9080903 - 19 Apr 2021
Cited by 5 | Viewed by 2398
Abstract
This research work is focused on the nonlinear modeling and control of a hydrostatic thrust bearing. In the proposed work, a mathematical model is formulated for a hydrostatic thrust bearing system that includes the effects of uncertainties, unmodelled dynamics, and nonlinearities. Depending on [...] Read more.
This research work is focused on the nonlinear modeling and control of a hydrostatic thrust bearing. In the proposed work, a mathematical model is formulated for a hydrostatic thrust bearing system that includes the effects of uncertainties, unmodelled dynamics, and nonlinearities. Depending on the type of inputs, the mathematical model is divided into three subsystems. Each subsystem has the same output, i.e., fluid film thickness with different types of input, i.e., viscosity, supply pressure, and recess pressure. An extended state observer is proposed to estimate the unavailable states. A backstepping control technique is presented to achieve the desired tracking performance and stabilize the closed-loop dynamics. The proposed control technique is based on the Lyapunov stability theorem. Moreover, particle swarm optimization is used to search for the best tuning parameters for the backstepping controller and extended state observer. The effectiveness of the proposed method is verified using numerical simulations. Full article
(This article belongs to the Special Issue Multivariable Optimization by Intelligent and Numerical Modelling and Simulation)
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13 pages, 3155 KiB  
Article
Optimization and Simulation of Dynamic Performance of Production–Inventory Systems with Multivariable Controls
by Huthaifa AL-Khazraji, Colin Cole and William Guo
Mathematics 2021, 9(5), 568; https://doi.org/10.3390/math9050568 - 7 Mar 2021
Cited by 17 | Viewed by 2442
Abstract
The production–inventory system is a problem of multivariable input and multivariant output in mathematics. Selecting the best system control parameters is a crucial managerial decision to achieve and dynamically maintain an optimal performance in terms of balancing the order rate and stock level [...] Read more.
The production–inventory system is a problem of multivariable input and multivariant output in mathematics. Selecting the best system control parameters is a crucial managerial decision to achieve and dynamically maintain an optimal performance in terms of balancing the order rate and stock level under dynamic influence of many factors affecting the system operations. The dynamic performance of the popular APIOBPCS model and the newly modified 2APIOBPCS model for optimal control of production–inventory systems is examined in the study. This examination is based on the leveled ground with a new simulation scheme that incorporates a designated multi-objective particle swarm optimization (MOPSO) algorithm into the simulation, which enables the optimal set of system control parameters to be selected for achieving the situational best possible performance of the production–inventory system under study. The dynamic performance is measured by the variance ratio between the order rate and the sales rate related to the bullwhip effect, and the integral of absolute error related to the inventory responsiveness in response to a random customer demand. Our simulation indicates that the 2APIOBPCS model performed better than or at least no worse than, and more robust than the APIOBPCS model under different conditions. Full article
(This article belongs to the Special Issue Multivariable Optimization by Intelligent and Numerical Modelling and Simulation)
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15 pages, 2987 KiB  
Article
Model-Based Design Approach to Improve Performance Characteristics of Hydrostatic Bearing Using Multivariable Optimization
by Waheed Ur Rehman, Xinhua Wang, Yiqi Cheng, Yingchun Chen, Hasan Shahzad, Hui Chai, Kamil Abbas, Zia Ullah and Marya Kanwal
Mathematics 2021, 9(4), 388; https://doi.org/10.3390/math9040388 - 15 Feb 2021
Cited by 15 | Viewed by 2587
Abstract
Research in the field of tribo-mechatronics has been gaining popularity in recent decades. The objective of the current research is to improve static/dynamics characteristics of hydrostatic bearings. Hydrostatic bearings always work in harsh environmental conditions that effect their performance, and which may even [...] Read more.
Research in the field of tribo-mechatronics has been gaining popularity in recent decades. The objective of the current research is to improve static/dynamics characteristics of hydrostatic bearings. Hydrostatic bearings always work in harsh environmental conditions that effect their performance, and which may even result in their failure. The current research proposes a mathematical model-based system for hydrostatic bearings that helps to improve its static/dynamic characteristics under varying conditions of performance-influencing variables such as temperature, spindle speed, external load, and clearance gap. To achieve these objectives, the capillary restrictors are replaced with servo valves, and a mathematical model is developed along with robust control design systems. The control system consists of feedforward and feedback control techniques that have not been applied before for hydrostatic bearings in the published literature. The feedforward control tries to remove a disturbance before it enters the system while feedback control achieves the objective of disturbance rejection and improves steady-state characteristics. The feedforward control is a trajectory-based controller and the feedback controller is a sliding mode controller with a PID sliding surface. The particle swarm optimization algorithm is used to tune the 6-dimensional vector of the tuning parameters with multi-objective performance criteria. Numerical investigations have been carried out to check the performance of the proposed system under varying conditions of viscosity, clearance gap, external load and the spindle speed. The comparison of our results with the published literature shows the effectiveness of the proposed system. Full article
(This article belongs to the Special Issue Multivariable Optimization by Intelligent and Numerical Modelling and Simulation)
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31 pages, 12038 KiB  
Article
A Comparative Study of Swarm Intelligence Algorithms for UCAV Path-Planning Problems
by Haoran Zhu, Yunhe Wang, Zhiqiang Ma and Xiangtao Li
Mathematics 2021, 9(2), 171; https://doi.org/10.3390/math9020171 - 15 Jan 2021
Cited by 18 | Viewed by 3133
Abstract
Path-planning for uninhabited combat air vehicles (UCAV) is a typically complicated global optimization problem. It seeks a superior flight path in a complex battlefield environment, taking into various constraints. Many swarm intelligence (SI) algorithms have recently gained remarkable attention due to their capability [...] Read more.
Path-planning for uninhabited combat air vehicles (UCAV) is a typically complicated global optimization problem. It seeks a superior flight path in a complex battlefield environment, taking into various constraints. Many swarm intelligence (SI) algorithms have recently gained remarkable attention due to their capability to address complex optimization problems. However, different SI algorithms present various performances for UCAV path-planning since each algorithm has its own strengths and weaknesses. Therefore, this study provides an overview of different SI algorithms for UCAV path-planning research. In the experiment, twelve algorithms that published in major journals and conference proceedings are surveyed and then applied to UCAV path-planning. Moreover, to demonstrate the performance of different algorithms in further, we design different scales of problem cases for those comparative algorithms. The experimental results show that UCAV can find the safe path to avoid the threats efficiently based on most SI algorithms. In particular, the Spider Monkey Optimization is more effective and robust than other algorithms in handling the UCAV path-planning problem. The analysis from different perspectives contributes to highlight trends and open issues in the field of UCAVs. Full article
(This article belongs to the Special Issue Multivariable Optimization by Intelligent and Numerical Modelling and Simulation)
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19 pages, 3357 KiB  
Article
AIRC: Attentive Implicit Relation Recommendation Incorporating Content Information for Bipartite Graphs
by Xintao Ma, Liyan Dong, Yuequn Wang, Yongli Li and Minghui Sun
Mathematics 2020, 8(12), 2132; https://doi.org/10.3390/math8122132 - 30 Nov 2020
Cited by 7 | Viewed by 2888
Abstract
With users being exposed to the growing volume of online information, the recommendation system aiming at mining the important or interesting information is becoming a modern research topic. One approach of recommendation is to integrate the graph neural network with deep learning algorithms. [...] Read more.
With users being exposed to the growing volume of online information, the recommendation system aiming at mining the important or interesting information is becoming a modern research topic. One approach of recommendation is to integrate the graph neural network with deep learning algorithms. However, some of them are not tailored for bipartite graphs, which is a unique type of heterogeneous graph having two entity types. Others, though customized, neglect the importance of implicit relation and content information. In this paper, we propose the attentive implicit relation recommendation incorporating content information (AIRC) framework that is designed for bipartite graphs based on the GC–MC algorithm. First, through reconstructing the bipartite graphs, we obtain the implicit relation graphs. Then we analyze the content information of users and items with a CNN process, so that each user and item has its feature-tailored embeddings. Besides, we expand the GC–MC algorithms by adding a graph attention mechanism layer, which handles the implicit relation graph by highlighting important features and neighbors. Therefore, our framework takes into consideration both the implicit relation and content information. Finally, we test our framework on Movielens dataset and the results show that our framework performs better than other state-of-art recommendation algorithms. Full article
(This article belongs to the Special Issue Multivariable Optimization by Intelligent and Numerical Modelling and Simulation)
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