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Algorithms
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Multi-Objective and Multi-Level Optimization: Algorithms and Applications
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Multi-Objective and Multi-Level Optimization: Algorithms and Applications

A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Combinatorial Optimization, Graph, and Network Algorithms".

Deadline for manuscript submissions: closed (30 April 2023) | Viewed by 10526

Special Issue Editors

Prof. Dr. Massimiliano Caramia

E-Mail Website
Guest Editor
Department of Enterprise Engineering, University of Rome "Tor Vergata", 00133 Roma, Italy
Interests: scheduling; graph theory; optimization; mathematical modeling; supply chain optimization; logistics; transportation; production systems
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Junzo Watada

E-Mail Website
Guest Editor
Graduate School of Information, Production and Systems, Waseda University, Kitakyushu 808-0135, Japan
Interests: artificial intelligence; image processing; soft computing, including meta heuristics, fuzzy systems, rough set analysis; model building; optimization; data analytics; big data mining; management engineering; financial engineering
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Decision-making in real world applications often require the consideration more than one objective to find effective solutions. When (conflicting) objectives are associated with either a single decision-maker or cooperative decision-makers, this typically leads to multi-objective optimization; here, optional solutions do not have the same image value, as it happens in single-objective optimization, but are non-dominated, equivalent, and allow the definition of the Pareto front. When objectives are associated with different non-cooperative decision-makers, we fall into the game theory arena; furthermore, when objectives and/or decision makers have a hierarchy among them, this asks to cope with nested optimization problems and, therefore, multi-level optimization.

All these problems are computationally hard to solve, and their resolution typically involves reformulating the latter into several single-objective problems or one single-objective problem by introducing additional (non-linear) constraints. Moreover, to limit the computational burden, before their resolution, it is worthwhile to reduce the number of objectives to a very limited (significative) number by applying proper methodologies.

The aim of this Special Issue is to collect original manuscripts dealing with multi-objective and multi-level optimization; we sought original papers presenting innovative applications and/or contributing to the theory.

Prof. Dr. Massimiliano Caramia
Prof. Dr. Junzo Watada
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.

Published Papers (6 papers)

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Editorial

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3 pages, 160 KiB  
Editorial
“Multi-Objective and Multi-Level Optimization: Algorithms and Applications”: Foreword by the Guest Editor
by Massimiliano Caramia
Algorithms 2023, 16(9), 425; https://doi.org/10.3390/a16090425 - 05 Sep 2023
Cited by 1 | Viewed by 1048
Abstract
Decision making in real-world applications frequently calls for taking into account multiple goals to come up with viable solutions [...] Full article
(This article belongs to the Special Issue Multi-Objective and Multi-Level Optimization: Algorithms and Applications)

Research

Jump to: Editorial

27 pages, 476 KiB  
Article
The Porcupine Measure for Comparing the Performance of Multi-Objective Optimization Algorithms
by Christiaan Scheepers and Andries Engelbrecht
Algorithms 2023, 16(6), 283; https://doi.org/10.3390/a16060283 - 31 May 2023
Cited by 1 | Viewed by 1381
Abstract
In spite of being introduced over twenty-five years ago, Fonseca and Fleming’s attainment surfaces have not been widely used. This article investigates some of the shortcomings that may have led to the lack of adoption of this performance measure. The quantitative measure based [...] Read more.
In spite of being introduced over twenty-five years ago, Fonseca and Fleming’s attainment surfaces have not been widely used. This article investigates some of the shortcomings that may have led to the lack of adoption of this performance measure. The quantitative measure based on attainment surfaces, introduced by Knowles and Corne, is analyzed. The analysis shows that the results obtained by the Knowles and Corne approach are influenced (biased) by the shape of the attainment surface. Improvements to the Knowles and Corne approach for bi-objective Pareto-optimal front (POF) comparisons are proposed. Furthermore, assuming M objective functions, an M-dimensional attainment-surface-based quantitative measure, named the porcupine measure, is proposed for comparing the performance of multi-objective optimization algorithms. A computationally optimized version of the porcupine measure is presented and empirically analyzed. Full article
(This article belongs to the Special Issue Multi-Objective and Multi-Level Optimization: Algorithms and Applications)
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30 pages, 6634 KiB  
Article
A Pixel-Wise k-Immediate Neighbour-Based Image Analysis Approach for Identifying Rock Pores and Fractures from Grayscale Image Samples
by Pradeep S. Naulia, Arunava Roy, Junzo Watada and Izzatdin B. A. Aziz
Algorithms 2023, 16(1), 42; https://doi.org/10.3390/a16010042 - 09 Jan 2023
Cited by 3 | Viewed by 2169
Abstract
The purpose of the current study is to propose a novel meta-heuristic image analysis approach using multi-objective optimization, named ‘Pixel-wise k-Immediate Neighbors’ to identify pores and fractures (both natural and induced, even in the micro-level) in the wells of a hydrocarbon reservoir, which [...] Read more.
The purpose of the current study is to propose a novel meta-heuristic image analysis approach using multi-objective optimization, named ‘Pixel-wise k-Immediate Neighbors’ to identify pores and fractures (both natural and induced, even in the micro-level) in the wells of a hydrocarbon reservoir, which presents better identification accuracy in the presence of the grayscale sample rock images. Pores and fractures imaging is currently being used extensively to predict the amount of petroleum under adequate trap conditions in the oil and gas industry. These properties have tremendous applications in contaminant transport, radioactive waste storage in the bedrock, and CO2 storage. A few strategies to automatically identify the pores and fractures from the images can be found in the contemporary literature. Several researchers employed classification technique using support vector machines (SVMs), whereas a few of them adopted deep learning systems. However, in these cases, the reported accuracy was not satisfactory in the presence of grayscale, low quality (poor resolution and chrominance), and irregular geometric-shaped images. The classification accuracy of the proposed multi-objective method outperformed the most influential contemporary approaches using deep learning systems, although with a few restrictions, which have been articulated later in the current work. Full article
(This article belongs to the Special Issue Multi-Objective and Multi-Level Optimization: Algorithms and Applications)
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11 pages, 1769 KiB  
Article
Algorithmic Design of Geometric Data for Molecular Potential Energy Surfaces
by Ahyssa R. Cruz and Walter C. Ermler
Algorithms 2023, 16(1), 6; https://doi.org/10.3390/a16010006 - 21 Dec 2022
Cited by 1 | Viewed by 1349
Abstract
A code MolecGeom, based on algorithms for stepwise distortions of bond lengths, bond angles and dihedral angles of polyatomic molecules, is presented. Potential energy surfaces (PESs) are curated in terms of the energy for each molecular geometry. PESs based on the Born–Oppenheimer [...] Read more.
A code MolecGeom, based on algorithms for stepwise distortions of bond lengths, bond angles and dihedral angles of polyatomic molecules, is presented. Potential energy surfaces (PESs) are curated in terms of the energy for each molecular geometry. PESs based on the Born–Oppenheimer approximation, by which the atomic nuclei within a molecule are assumed stationary with respect to the motion of its electrons, are calculated. Applications requiring PESs involve the effects of nuclear motion on molecular properties. These include determining equilibrium geometries corresponding to stationary and saddle point energies, calculating reaction rates and predicting vibrational spectra. This multi-objective study focuses on the development of a new method for the calculation of PESs and the analysis of the molecular geometry components in terms of incremental changes that provide comprehensive sampling while preserving the precision of PES points. MolecGeom is applied to generate geometric data to calculate PESs for theoretical calculations of vibrational-rotational spectra of water and formaldehyde. An ab initio PES comprising 525 and 2160 intramolecular nuclear configurations results in vibrational frequencies in agreement with experiment, having errors less than 0.08% and 0.8%, respectively. Vinyl alcohol, with a total of 14 internal coordinates, generates a PES of 1458 unique geometries. Ascorbic acid, with 54 internal coordinates, generates a 1,899,776 point PES. Full article
(This article belongs to the Special Issue Multi-Objective and Multi-Level Optimization: Algorithms and Applications)
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11 pages, 1303 KiB  
Article
Thermal Conductivity of Low-GWP Refrigerants Modeling with Multi-Object Optimization
by Mariano Pierantozzi, Sebastiano Tomassetti and Giovanni Di Nicola
Algorithms 2022, 15(12), 482; https://doi.org/10.3390/a15120482 - 17 Dec 2022
Cited by 2 | Viewed by 1226
Abstract
In this paper, the procedure of finding the coefficients of an equation to describe the thermal conductivity of refrigerants low in global warming potential (GWP) is transformed into a multi-objective optimization problem by constructing a multi-objective mathematical model based on the Pareto approach. [...] Read more.
In this paper, the procedure of finding the coefficients of an equation to describe the thermal conductivity of refrigerants low in global warming potential (GWP) is transformed into a multi-objective optimization problem by constructing a multi-objective mathematical model based on the Pareto approach. For the first time, the NSGAII algorithm was used to describe a thermophysical property such as thermal conductivity. The algorithm was applied to improve the performance of existing equations. Two objective functions were optimized by using the NSGAII algorithm. The average absolute relative deviation was minimized, while the coefficient of determination was maximized. After the minimization process, the optimal solution located on the Pareto frontier was chosen through a comparative analysis between ten selection methods available in the literature. The procedure generated a new set of coefficients of the studied equation that decreased its average absolute relative deviation by 0.24%, resulting in better performance over the entire database and for fluids with a high number of points. Finally, the system model was compared with existing literature models to evaluate its suitability for predicting the thermal conductivity of low-GWP refrigerants. Full article
(This article belongs to the Special Issue Multi-Objective and Multi-Level Optimization: Algorithms and Applications)
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25 pages, 5609 KiB  
Article
Integrated Design of a Supermarket Refrigeration System by Means of Experimental Design Adapted to Computational Problems
by Daniel Sarabia, María Cruz Ortiz and Luis Antonio Sarabia
Algorithms 2022, 15(11), 417; https://doi.org/10.3390/a15110417 - 07 Nov 2022
Cited by 1 | Viewed by 1761
Abstract
In this paper, an integrated design of a supermarket refrigeration system has been used to obtain a process with better operability. It is formulated as a multi-objective optimization problem where control performance is evaluated by six indices and the design variables are the [...] Read more.
In this paper, an integrated design of a supermarket refrigeration system has been used to obtain a process with better operability. It is formulated as a multi-objective optimization problem where control performance is evaluated by six indices and the design variables are the number and discrete power of each compressor to be installed. The functional dependence between design and performance is unknown, and therefore the optimal configuration must be obtained through a computational experimentation. This work has a double objective: to adapt the surface response methodology (SRM) to optimize problems without experimental variability as are the computational ones and show the advantage of considering the integrated design. In the SRM framework, the problem is stated as a mixture design with constraints and a synergistic cubic model where a D-optimal design is applied to perform the experiments. Finally, the multi-objective problem is reduced to a single objective one by means of a desirability function. The optimal configuration of the power distribution of the three compressors, in percentage, is (50,20,20). This solution has an excellent behaviour with respect to the six indices proposed, with a significant reduction in time oscillations of controlled variables and power consumption compared with other possible power distributions. Full article
(This article belongs to the Special Issue Multi-Objective and Multi-Level Optimization: Algorithms and Applications)
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