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Mathematics
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Mathematical Modelling and Multi-Criteria Optimisation in Engineering
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Mathematical Modelling and Multi-Criteria Optimisation in Engineering

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Fuzzy Sets, Systems and Decision Making".

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 12441

Special Issue Editors

Prof. Dr. Sambor Guze

E-Mail Website
Guest Editor
Gdynia Maritime University, Morska, 81-225 Gdynia, Poland
Interests: mathematical modelling; algorithms analysis; one and multi-criteria optimisation; transportation network analyze, planning and optimization; the safety and reliability of technical systems modelling and optimization
Prof. Dr. Enrico Zio

E-Mail Website
Guest Editor
1. Centre de Recherce sur les Risques et les Crises (CRC), MINES Paris-PSL Université, 06904 Paris, France
2. Energy Department, Politecnico di Milano, Via La Masa 34, 20156 Milano, Italy
Interests: risk assessment; reliability analysis; simulation; artificial intelligence; nuclear systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Scientists, engineers, and economists try to understand, develop, and optimise physical objects, systems, and processes. To make this possible, they must model them as complex systems composed of multiple and diverse elements. Thus, well-built mathematical models are at the heart of many modern engineering, scientific, and financial solutions. They allow you to conduct complex calculations and computer simulations for improving design and operation and obtains optimal solutions within a multi-criteria approach.

The aim of the Special Issue is bringing together the latest research achievements of scholars studying and developing mathematical models and multi-criteria optimisation methods and tools in science, engineering, and economics.

Primarily, this issue focuses on the latest and innovative solutions in the fields of:

  • Safety and reliability modelling and optimisation of systems and processes;
  • Transportation, computer and social network modelling and optimisation;
  • Transportation systems modelling and optimisation;
  • Applications of computational mathematics, including methods of artificial intelligence in science, engineering and economics;
  • Business processes modelling and optimisation;
  • Financial processes and systems modelling and optimisation;
  • Mathematical modelling and optimisation of economic processes;
  • Models, methods and algorithms of multi-criteria optimisation for scientific, engineering and economics applications.

Prof. Dr. Sambor Guze
Prof. Dr. Enrico Zio
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • Stochastic algorithms 
  • Constrained optimisation 
  • Unconstrained optimisation 
  • Global optimisation 
  • Safety, reliability and risk modelling 
  • Multi-criteria decision analysis 
  • Evolutionary algorithms 
  • Fuzzy optimisation 
  • Discrete optimisation 
  • Business and finacial process modelling 
  • Economic process modelling 
  • Multiple criteria decision making 
  • Pareto optimality 
  • Computational mathematics

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Published Papers (5 papers)

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Research

26 pages, 1120 KiB  
Article
Optimal Parameters Selection in Advanced Multi-Metallic Co-Extrusion Based on Independent MCDM Analytical Approaches and Numerical Simulation
by Daniel Fernández, Álvaro Rodríguez-Prieto and Ana M. Camacho
Mathematics 2022, 10(23), 4489; https://doi.org/10.3390/math10234489 - 28 Nov 2022
Cited by 1 | Viewed by 1255
Abstract
Multi-material co-extrusion is a complex thermo-mechanical forming process used to obtain bimetallic billets. Its complexity is due to the combination of diffusion phenomena in the interface of both materials together with the high temperature and pressure generated and the different flow stress characteristics [...] Read more.
Multi-material co-extrusion is a complex thermo-mechanical forming process used to obtain bimetallic billets. Its complexity is due to the combination of diffusion phenomena in the interface of both materials together with the high temperature and pressure generated and the different flow stress characteristics created by the joining of dissimilar materials. Accordingly, the selection of optimal process parameters becomes key to ensure process feasibility. In this work, a comparison among different multi-criteria decision making (MCDM) methodologies, together with different weighting methods, were applied to the simulation results by using DEFORM3D© software to select the optimal combination of process parameters to fulfil the criteria of minimum damage, extrusion force, and tool wear, together with the maximum reduction in the average grain size. Full article
(This article belongs to the Special Issue Mathematical Modelling and Multi-Criteria Optimisation in Engineering)
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17 pages, 2381 KiB  
Article
Multicriteria Analytical Model for Mechanical Integrity Prognostics of Reactor Pressure Vessels Manufactured from Forged and Rolled Steels
by Alvaro Rodríguez-Prieto, Manuel Callejas, Ernesto Primera, Guglielmo Lomonaco and Ana María Camacho
Mathematics 2022, 10(10), 1779; https://doi.org/10.3390/math10101779 - 23 May 2022
Cited by 1 | Viewed by 2252
Abstract
The aim of this work is to present a new analytical model to evaluate jointly the mechanical integrity and the fitness-for-service of nuclear reactor pressure-vessels steels. This new methodology integrates a robust and regulated irradiation embrittlement prediction model such as the ASTM E-900 [...] Read more.
The aim of this work is to present a new analytical model to evaluate jointly the mechanical integrity and the fitness-for-service of nuclear reactor pressure-vessels steels. This new methodology integrates a robust and regulated irradiation embrittlement prediction model such as the ASTM E-900 with the ASME Fitness-for-Service code used widely in other demanding industries, such as oil and gas, to evaluate, among others, the risk of experiencing degradation mechanisms such as the brittle fracture (generated, in this case, due to the irradiation embrittlement). This multicriteria analytical model, which is based on a new formulation of the brittle fracture criterion, allows an adequate prediction of the irradiation effect on the fracture toughness of reactor pressure-vessel steels, letting us jointly evaluate the mechanical integrity and the fitness-for-service of the vessel by using standardized limit conditions. This allows making decisions during the design, manufacturing and in-service of reactor pressure vessels. The results obtained by the application of the methodology are coherent with several historical experimental works. Full article
(This article belongs to the Special Issue Mathematical Modelling and Multi-Criteria Optimisation in Engineering)
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29 pages, 924 KiB  
Article
A Modified Coronavirus Herd Immunity Optimizer for the Power Scheduling Problem
by Sharif Naser Makhadmeh, Mohammed Azmi Al-Betar, Mohammed A. Awadallah, Ammar Kamal Abasi, Zaid Abdi Alkareem Alyasseri, Iyad Abu Doush, Osama Ahmad Alomari, Robertas Damaševičius, Audrius Zajančkauskas and Mazin Abed Mohammed
Mathematics 2022, 10(3), 315; https://doi.org/10.3390/math10030315 - 20 Jan 2022
Cited by 20 | Viewed by 2810
Abstract
The Coronavirus herd immunity optimizer (CHIO) is a new human-based optimization algorithm that imitates the herd immunity strategy to eliminate of the COVID-19 disease. In this paper, the coronavirus herd immunity optimizer (CHIO) is modified to tackle a discrete power scheduling problem in [...] Read more.
The Coronavirus herd immunity optimizer (CHIO) is a new human-based optimization algorithm that imitates the herd immunity strategy to eliminate of the COVID-19 disease. In this paper, the coronavirus herd immunity optimizer (CHIO) is modified to tackle a discrete power scheduling problem in a smart home (PSPSH). PSPSH is a combinatorial optimization problem with NP-hard features. It is a highly constrained discrete scheduling problem concerned with assigning the operation time for smart home appliances based on a dynamic pricing scheme(s) and several other constraints. The primary objective when solving PSPSH is to maintain the stability of the power system by reducing the ratio between average and highest power demand (peak-to-average ratio (PAR)) and reducing electricity bill (EB) with considering the comfort level of users (UC). This paper modifies and adapts the CHIO algorithm to deal with such discrete optimization problems, particularly PSPSH. The adaptation and modification include embedding PSPSH problem-specific operators to CHIO operations to meet the discrete search space requirements. PSPSH is modeled as a multi-objective problem considering all objectives, including PAR, EB, and UC. The proposed method is examined using a dataset that contains 36 home appliances and seven consumption scenarios. The main CHIO parameters are tuned to find their best values. These best values are used to evaluate the proposed method by comparing its results with comparative five metaheuristic algorithms. The proposed method shows encouraging results and almost obtains the best results in all consumption scenarios. Full article
(This article belongs to the Special Issue Mathematical Modelling and Multi-Criteria Optimisation in Engineering)
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16 pages, 5506 KiB  
Article
Transmitter Module Optimization for Wireless Power Transfer Systems with Single Transmitter to Multiple Receivers
by Joungha Lee and Seung Beop Lee
Mathematics 2021, 9(22), 2928; https://doi.org/10.3390/math9222928 - 17 Nov 2021
Viewed by 2039
Abstract
Most of the coil designs for wireless power transfer (WPT) systems have been developed based on the “single transmitter to a single receiver (S-S)” WPT systems by the empirical design approaches, partial domain searches, and shape optimization methods. Recently, the layout optimizations of [...] Read more.
Most of the coil designs for wireless power transfer (WPT) systems have been developed based on the “single transmitter to a single receiver (S-S)” WPT systems by the empirical design approaches, partial domain searches, and shape optimization methods. Recently, the layout optimizations of the receiver coil for S-S WPT systems have been developed using gradient-based optimization, fixed-grid (FG) representation, and smooth boundary (SB) representation. In this paper, the new design optimization of the transmitter module for the “single transmitter to multiple receivers (S-M)” WPT system with the resonance optimization for the S-M WPT system is proposed to extremize the total power transfer efficiency while satisfying the load voltage (i.e., rated power) required by each receiver and the total mass used for the transmitter coil. The proposed method was applied to an application model (e.g., S-M WPT systems with two receiver modules). Using the sensitivity of design variables with respect to the objective function (i.e., total power transfer efficiency) and constraint functions (i.e., load voltage of each receiver module and transmitter coil mass) at each iteration of the optimization process, the proposed method determines the optimal transmitter module that can maximize the total power transfer efficiency while several constraints are satisfied. Finally, the optimized transmitter module for the S-M WPT system was demonstrated through comparison with experiments under the same conditions as the simulation environment. Full article
(This article belongs to the Special Issue Mathematical Modelling and Multi-Criteria Optimisation in Engineering)
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6 pages, 249 KiB  
Article
A Note on On-Line Ramsey Numbers for Some Paths
by Tomasz Dzido and Renata Zakrzewska
Mathematics 2021, 9(7), 735; https://doi.org/10.3390/math9070735 - 29 Mar 2021
Cited by 1 | Viewed by 2076
Abstract
We consider the important generalisation of Ramsey numbers, namely on-line Ramsey numbers. It is easiest to understand them by considering a game between two players, a Builder and Painter, on an infinite set of vertices. In each round, the Builder joins two non-adjacent [...] Read more.
We consider the important generalisation of Ramsey numbers, namely on-line Ramsey numbers. It is easiest to understand them by considering a game between two players, a Builder and Painter, on an infinite set of vertices. In each round, the Builder joins two non-adjacent vertices with an edge, and the Painter colors the edge red or blue. An on-line Ramsey number r˜(G,H) is the minimum number of rounds it takes the Builder to force the Painter to create a red copy of graph G or a blue copy of graph H, assuming that both the Builder and Painter play perfectly. The Painter’s goal is to resist to do so for as long as possible. In this paper, we consider the case where G is a path P4 and H is a path P10 or P11. Full article
(This article belongs to the Special Issue Mathematical Modelling and Multi-Criteria Optimisation in Engineering)
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