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Advanced Optimization Methods and Applications
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Advanced Optimization Methods and Applications

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

Deadline for manuscript submissions: closed (31 January 2023) | Viewed by 31962

Special Issue Editors

Dr. Adrian Deaconu

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, Faculty of Mathematics and Computer Science, Transilvania University of Brasov, 50003 Brasov, Romania
Interests: graphs theory; combinatorial optimization; network optimization; inverse problems and inverse optimization
Special Issues, Collections and Topics in MDPI journals
Dr. Petru Adrian Cotfas

E-Mail Website
Guest Editor
Electrical Engineering and Computer Science Faculty, Transilvania University of Brasov, Eroilor, nr. 29, 500036 Brasov, Romania
Interests: photovoltaic systems; hybrid systems characterization; concentrated light systems; hybrid system reliability
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Daniel Tudor Cotfas

E-Mail Website
Guest Editor
Electrical Engineering and Computer Science Faculty, Transilvania University of Brasov, Eroilor, nr. 29, 500036 Brasov, Romania
Interests: photovoltaic systems; hybrid systems; energy harvesting; modeling of the photovoltaic cells and panels
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

You are invited to submit papers related to all aspects of optimization algorithms, graph theory, network optimization, location problems, fuzzy optimization, optimal control, machine learning, artificial intelligence, and parallel programming from both theoretical and applied perspectives.

Optimization methods are finding more and more applications in all domains, and play an essential role when dealing with real-life problems. Algorithms for such problems are being continuously developed and improved in order to obtain higher-quality solutions within a reasonable time frame. Metaheuristic methods inspired from the behavior of populations of different groups of people or from the behavior of swarms of animals or insects are currently used to solve optimization problems where optimal solutions cannot be obtained using exact methods in a reasonable amount of time.

Dr. Adrian Deaconu
Prof. Dr. Petru Adrian Cotfas
Prof. Dr. Daniel Tudor Cotfas
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

  • optimization algorithms
  • heuristics and metaheuristics
  • approximation algorithms
  • network optimization
  • location problems
  • fuzzy optimization
  • combinatorial optimization
  • inverse optimization problems
  • robust optimization
  • graph theory
  • optimal control
  • forecasting
  • machine learning
  • artificial intelligence
  • parallel programming
  • mathematical optimization
  • optimization applications

Published Papers (21 papers)

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Editorial

Jump to: Research

7 pages, 636 KiB  
Editorial
Advanced Optimization Methods and Applications
by Adrian Marius Deaconu, Daniel Tudor Cotfas and Petru Adrian Cotfas
Mathematics 2023, 11(9), 2205; https://0-doi-org.brum.beds.ac.uk/10.3390/math11092205 - 08 May 2023
Viewed by 1296
Abstract
Optimization methods are finding more applications in all domains, as they play an essential role when dealing with real-life problems [...] Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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Research

Jump to: Editorial

29 pages, 5828 KiB  
Article
Application of Advanced Optimized Soft Computing Models for Atmospheric Variable Forecasting
by Rana Muhammad Adnan, Sarita Gajbhiye Meshram, Reham R. Mostafa, Abu Reza Md. Towfiqul Islam, S. I. Abba, Francis Andorful and Zhihuan Chen
Mathematics 2023, 11(5), 1213; https://0-doi-org.brum.beds.ac.uk/10.3390/math11051213 - 01 Mar 2023
Cited by 12 | Viewed by 1221
Abstract
Precise Air temperature modeling is crucial for a sustainable environment. In this study, a novel binary optimized machine learning model, the random vector functional link (RVFL) with the integration of Moth Flame Optimization Algorithm (MFO) and Water Cycle Optimization Algorithm (WCA) is examined [...] Read more.
Precise Air temperature modeling is crucial for a sustainable environment. In this study, a novel binary optimized machine learning model, the random vector functional link (RVFL) with the integration of Moth Flame Optimization Algorithm (MFO) and Water Cycle Optimization Algorithm (WCA) is examined to estimate the monthly and daily temperature time series of Rajshahi Climatic station in Bangladesh. Various combinations of temperature and precipitation were used to predict the temperature time series. The prediction ability of the novel binary optimized machine learning model (RVFL-WCAMFO) is compared with the single optimized machine learning models (RVFL-WCA and RVFL-MFO) and the standalone machine learning model (RVFL). Root mean square errors (RMSE), the mean absolute error (MAE), the Nash–Sutcliffe efficiency (NSE), and the determination coefficient (R2) statistical indexes were utilized to access the prediction ability of the selected models. The proposed binary optimized machine learning model (RVFL-WCAMFO) outperformed the other single optimized and standalone machine learning models in prediction of air temperature time series on both scales, i.e., daily and monthly scale. Cross-validation technique was applied to determine the best testing dataset and it was found that the M3 dataset provided more accurate results for the monthly scale, whereas the M1 dataset outperformed the other two datasets on the daily scale. On the monthly scale, periodicity input was also added to see the effect on prediction accuracy. It was found that periodicity input improved the prediction accuracy of the models. It was also found that precipitation-based inputs did not provided very accurate results in comparison to temperature-based inputs. The outcomes of the study recommend the use of RVFL-WCAMFO in air temperature modeling. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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21 pages, 1617 KiB  
Article
An Inverse Optimal Value Approach for Synchronously Optimizing Activity Durations and Worker Assignments with a Project Ideal Cost
by Lili Zhang, Zhengrui Chen, Dan Shi and Yanan Zhao
Mathematics 2023, 11(5), 1178; https://0-doi-org.brum.beds.ac.uk/10.3390/math11051178 - 27 Feb 2023
Cited by 2 | Viewed by 1070
Abstract
Most companies survive the pain of cost and schedule overruns because of inaccurate project activity time settings. In order to deliver a project with a target cost and on schedule, this research proposes an inverse optimal value approach to optimize activity durations and [...] Read more.
Most companies survive the pain of cost and schedule overruns because of inaccurate project activity time settings. In order to deliver a project with a target cost and on schedule, this research proposes an inverse optimal value approach to optimize activity durations and the corresponding worker assignments synchronously to make the optimal project cost infinitely close to an ideal cost. The leader model reflects cost orientation and adjustability of activity durations, the follower model reflects the complexity of activity sequence, critical path completion time, cost pressure, skill matching, energy consumption, and other costs. Through upper-level and lower-level feedback and interaction of activity durations and worker assignments it is possible to deliver a project with an ideal cost. With considerations of the mathematical model characteristics of bi-level programming, nonlinearity, NP hard, and MAX functions, an improved genetic algorithm combining adaptive artificial fish swarms is designed. From the comparison results of random examples and an actual example, the error rate of the optimal value of the improved algorithm is acceptable. Numerical experiments show that the inverse optimal approach can deliver a project without delay and with an ideal cost. The inverse optimization method is more in line with the idea of target management, and can help managers achieve the purpose of cost control. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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17 pages, 557 KiB  
Article
Low-Rank Matrix Completion via QR-Based Retraction on Manifolds
by Ke Wang, Zhuo Chen, Shihui Ying and Xinjian Xu
Mathematics 2023, 11(5), 1155; https://0-doi-org.brum.beds.ac.uk/10.3390/math11051155 - 26 Feb 2023
Cited by 3 | Viewed by 1217
Abstract
Low-rank matrix completion aims to recover an unknown matrix from a subset of observed entries. In this paper, we solve the problem via optimization of the matrix manifold. Specially, we apply QR factorization to retraction during optimization. We devise two fast algorithms based [...] Read more.
Low-rank matrix completion aims to recover an unknown matrix from a subset of observed entries. In this paper, we solve the problem via optimization of the matrix manifold. Specially, we apply QR factorization to retraction during optimization. We devise two fast algorithms based on steepest gradient descent and conjugate gradient descent, and demonstrate their superiority over the promising baseline with the ratio of at least 24%. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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19 pages, 363 KiB  
Article
Scheduling of Jobs with Multiple Weights on a Single Machine for Minimizing the Total Weighted Number of Tardy Jobs
by Shuen Guo, Hao Lang and Hanxiang Zhang
Mathematics 2023, 11(4), 1013; https://0-doi-org.brum.beds.ac.uk/10.3390/math11041013 - 16 Feb 2023
Cited by 1 | Viewed by 819
Abstract
We consider the scheduling of jobs with multiple weights on a single machine for minimizing the total weighted number of tardy jobs. In this setting, each job has m weights (or equivalently, the jobs have m weighting vectors), and thus we have m [...] Read more.
We consider the scheduling of jobs with multiple weights on a single machine for minimizing the total weighted number of tardy jobs. In this setting, each job has m weights (or equivalently, the jobs have m weighting vectors), and thus we have m criteria, each of which is to minimize the total weighted number of tardy jobs under a corresponding weighting vector of the jobs. For this scheduling model, the feasibility problem aims to find a feasible schedule such that each criterion is upper bounded by its threshold value, and the Pareto scheduling problem aims to find all the Pareto-optimal points and for each one a corresponding Pareto-optimal schedule. Although the two problems have not been studied before, it is implied in the literature that both of them are unary NP-hard when m is an arbitrary number. We show in this paper that, in the case where m is a fixed number, the two problems are solvable in pseudo-polynomial time, the feasibility problem admits a dual-fully polynomial-time approximation scheme, and the Pareto-scheduling problem admits a fully polynomial-time approximation scheme. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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24 pages, 3639 KiB  
Article
Black Widow Optimization Algorithm Used to Extract the Parameters of Photovoltaic Cells and Panels
by Manoharan Madhiarasan, Daniel T. Cotfas and Petru A. Cotfas
Mathematics 2023, 11(4), 967; https://0-doi-org.brum.beds.ac.uk/10.3390/math11040967 - 13 Feb 2023
Cited by 5 | Viewed by 1480
Abstract
The metaheuristic algorithms and their hybridization have been utilized successfully in the past to extract the parameters of photovoltaic (PV) cells and panels. The novelty of the paper consists of proposing the black widow optimization algorithm (BWOA) for the first time to identify [...] Read more.
The metaheuristic algorithms and their hybridization have been utilized successfully in the past to extract the parameters of photovoltaic (PV) cells and panels. The novelty of the paper consists of proposing the black widow optimization algorithm (BWOA) for the first time to identify the parameters of the two photovoltaic cells RTC France, amorphous silicon (aSi), and two photovoltaic panels PWP201, PVM 752 GaAs. The single-diode model (SDM) and double-diode model (DDM) for analyzing the PVs are considered. The performance of the BWOA is verified using four statistical tests: the root mean square error, which is the primary tool, the mean relative error, the mean bias error, and the coefficient of determination. The research results of this study are as follows: BWOA gave the same results, or very slightly better, for RTC and PWP201 for SDM in comparison with the best algorithms from the specialized literature; for all the other cases, BWOA has substantially better results, especially for PVM 752 GaAs, where the improvements in RMSE are: 16.5%, for PWP201: 6.25%, and for aSi: 5.3%, all for the DDM; the computing time is around 2 s, which is one of the lowest durations. A consistent study is made to optimize the accuracy and computational time in function of the number of iterations and population. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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20 pages, 554 KiB  
Article
Generalizations of Higher-Order Duality for Multiple Objective Nonlinear Programming under the Generalizations of Type-I Functions
by Mohamed Abd El-Hady Kassem and Huda M. Alshanbari
Mathematics 2023, 11(4), 889; https://0-doi-org.brum.beds.ac.uk/10.3390/math11040889 - 09 Feb 2023
Cited by 2 | Viewed by 764
Abstract
In this study, we introduce new generalizations of higher-order type-I functions and higher-order pseudo-convexity type-I functions. The application of the notion of sublinear functionals to these generalizations of higher-order type-I and higher-order pseudo-convexity type-I functions is crucial to our main findings. Furthermore, under [...] Read more.
In this study, we introduce new generalizations of higher-order type-I functions and higher-order pseudo-convexity type-I functions. The application of the notion of sublinear functionals to these generalizations of higher-order type-I and higher-order pseudo-convexity type-I functions is crucial to our main findings. Furthermore, under these generalizations of the higher-order type-I and higher-order pseudo-convexity type-I functions, we established and studied six new types of higher-order duality models and programs for multiple objective nonlinear programming problems. In addition, we use these generalizations of higher-order type-I functions and higher-order pseudo-convexity type-I functions, to formulate and prove the theorems of weak duality, strong duality, and strict converse duality for these new six types of higher-order model programs. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
31 pages, 932 KiB  
Article
Two-Stage Optimization Methods to Solve the DNA-Sample Allocation Problem
by Diego Noceda-Davila, Silvia Lorenzo-Freire and Luisa Carpente
Mathematics 2022, 10(22), 4359; https://0-doi-org.brum.beds.ac.uk/10.3390/math10224359 - 19 Nov 2022
Cited by 1 | Viewed by 972
Abstract
This paper deals with new methods capable of solving the optimization problem concerning the allocation of DNA samples in plates in order to carry out the DNA sequencing with the Sanger technique. These methods make it possible to work with independent subproblems of [...] Read more.
This paper deals with new methods capable of solving the optimization problem concerning the allocation of DNA samples in plates in order to carry out the DNA sequencing with the Sanger technique. These methods make it possible to work with independent subproblems of lower complexity, obtaining solutions of good quality while maintaining a competitive time cost. They are compared with the ones introduced in the literature, obtaining interesting results. All the comparisons among the methods in the literature and the laboratory results have been made with real data. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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17 pages, 323 KiB  
Article
Quasi Efficient Solutions and Duality Results in a Multiobjective Optimization Problem with Mixed Constraints via Tangential Subdifferentials
by Mohsine Jennane, El Mostafa Kalmoun, Lahoussine Lafhim and Anouar Houmia
Mathematics 2022, 10(22), 4341; https://0-doi-org.brum.beds.ac.uk/10.3390/math10224341 - 18 Nov 2022
Cited by 1 | Viewed by 803
Abstract
We take up a nonsmooth multiobjective optimization problem with tangentially convex objective and constraint functions. In employing a suitable constraint qualification, we formulate both necessary and sufficient optimality conditions for (local) quasi efficient solutions in terms of tangential subdifferentials. Furthermore, under generalized convexity [...] Read more.
We take up a nonsmooth multiobjective optimization problem with tangentially convex objective and constraint functions. In employing a suitable constraint qualification, we formulate both necessary and sufficient optimality conditions for (local) quasi efficient solutions in terms of tangential subdifferentials. Furthermore, under generalized convexity assumptions, we state strong, weak and converse duality relations of Wolfe and Mond–Weir types. We give a number of examples to illustrate the new concepts and main results of this paper. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
15 pages, 1134 KiB  
Article
A VNS-Based Matheuristic to Solve the Districting Problem in Bicycle-Sharing Systems
by Guillermo Cabrera-Guerrero, Aníbal Álvarez, Joaquín Vásquez, Pablo A. Maya Duque and Lucas Villavicencio
Mathematics 2022, 10(22), 4175; https://0-doi-org.brum.beds.ac.uk/10.3390/math10224175 - 08 Nov 2022
Cited by 2 | Viewed by 1160
Abstract
A matheuristic approach that combines a reduced variable neighbourhood search (rVNS) algorithm and a mathematical programming (MP) solver to solve a novel model for the districting problem in a public bicycle-sharing system is presented. The problem is modelled as an integer programming problem. [...] Read more.
A matheuristic approach that combines a reduced variable neighbourhood search (rVNS) algorithm and a mathematical programming (MP) solver to solve a novel model for the districting problem in a public bicycle-sharing system is presented. The problem is modelled as an integer programming problem. While the rVNS algorithm aims to find a high-quality set of centres for the repositioning zones, the MP solver computes the optimal allocation network of the stations to the centres of the repositioning zones. We use a predefined grid to reduce the search space the rVNS needs to explore. The proposed approach obtains promising results for small and medium-sized instances, and is also able to handle large-sized models. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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31 pages, 1727 KiB  
Article
Feature Selection Using Artificial Gorilla Troop Optimization for Biomedical Data: A Case Analysis with COVID-19 Data
by Jayashree Piri, Puspanjali Mohapatra, Biswaranjan Acharya, Farhad Soleimanian Gharehchopogh, Vassilis C. Gerogiannis, Andreas Kanavos and Stella Manika
Mathematics 2022, 10(15), 2742; https://0-doi-org.brum.beds.ac.uk/10.3390/math10152742 - 03 Aug 2022
Cited by 45 | Viewed by 2248
Abstract
Feature selection (FS) is commonly thought of as a pre-processing strategy for determining the best subset of characteristics from a given collection of features. Here, a novel discrete artificial gorilla troop optimization (DAGTO) technique is introduced for the first time to handle FS [...] Read more.
Feature selection (FS) is commonly thought of as a pre-processing strategy for determining the best subset of characteristics from a given collection of features. Here, a novel discrete artificial gorilla troop optimization (DAGTO) technique is introduced for the first time to handle FS tasks in the healthcare sector. Depending on the number and type of objective functions, four variants of the proposed method are implemented in this article, namely: (1) single-objective (SO-DAGTO), (2) bi-objective (wrapper) (MO-DAGTO1), (3) bi-objective (filter wrapper hybrid) (MO-DAGTO2), and (4) tri-objective (filter wrapper hybrid) (MO-DAGTO3) for identifying relevant features in diagnosing a particular disease. We provide an outstanding gorilla initialization strategy based on the label mutual information (MI) with the aim of increasing population variety and accelerate convergence. To verify the performance of the presented methods, ten medical datasets are taken into consideration, which are of variable dimensions. A comparison is also implemented between the best of the four suggested approaches (MO-DAGTO2) and four established multi-objective FS strategies, and it is statistically proven to be the superior one. Finally, a case study with COVID-19 samples is performed to extract the critical factors related to it and to demonstrate how this method is fruitful in real-world applications. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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9 pages, 347 KiB  
Article
Equilibrium in a Bargaining Game of Two Sellers and Two Buyers
by Jiawei Li, Tianxiang Cui and Graham Kendall
Mathematics 2022, 10(15), 2705; https://0-doi-org.brum.beds.ac.uk/10.3390/math10152705 - 30 Jul 2022
Cited by 2 | Viewed by 1438
Abstract
The uniqueness of equilibrium in bargaining games with three or more players is a problem preventing bargaining theory from general real world applications. We study the uniqueness of bargaining equilibrium in a bargaining game of two sellers and two buyers, which has instances [...] Read more.
The uniqueness of equilibrium in bargaining games with three or more players is a problem preventing bargaining theory from general real world applications. We study the uniqueness of bargaining equilibrium in a bargaining game of two sellers and two buyers, which has instances in real-world markets. Each seller (or buyer) wants to reach an agreement with a buyer (or seller) on the division of a pie in the bargaining game. A seller and a buyer will receive their agreed divisions if they can reach an agreement. Otherwise, they receive nothing. The bargaining game includes a finite number of rounds. In each round, a player can propose an offer or accept an offer. Each player has a constant discounting factor. Under the assumption of complete information, we prove that the equilibrium of this bargaining game is the same division of two pies. The ratio of division as a function of the discount factors of all players is also deduced. The result can be extended to a bargaining game of n-sellers and n-buyers, which reveals the relevance of bargaining equilibrium to the general equilibrium of a market. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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34 pages, 15562 KiB  
Article
A Feature Selection Based on Improved Artificial Hummingbird Algorithm Using Random Opposition-Based Learning for Solving Waste Classification Problem
by Mona A. S. Ali, Fathimathul Rajeena P. P. and Diaa Salama Abd Elminaam
Mathematics 2022, 10(15), 2675; https://0-doi-org.brum.beds.ac.uk/10.3390/math10152675 - 29 Jul 2022
Cited by 16 | Viewed by 2095 | Correction
Abstract
Recycling tasks are the most effective method for reducing waste generation, protecting the environment, and boosting the overall national economy. The productivity and effectiveness of the recycling process are strongly dependent on the cleanliness and precision of processed primary sources. However, recycling operations [...] Read more.
Recycling tasks are the most effective method for reducing waste generation, protecting the environment, and boosting the overall national economy. The productivity and effectiveness of the recycling process are strongly dependent on the cleanliness and precision of processed primary sources. However, recycling operations are often labor intensive, and computer vision and deep learning (DL) techniques aid in automatically detecting and classifying trash types during recycling chores. Due to the dimensional challenge posed by pre-trained CNN networks, the scientific community has developed numerous techniques inspired by biology, swarm intelligence theory, physics, and mathematical rules. This research applies a new meta-heuristic algorithm called the artificial hummingbird algorithm (AHA) to solving the waste classification problem based on feature selection. However, the performance of the AHA is barely satisfactory; it may be stuck in optimal local regions or have a slow convergence. To overcome these limitations, this paper develops two improved versions of the AHA called the AHA-ROBL and the AHA-OBL. These two versions enhance the exploitation stage by using random opposition-based learning (ROBL) and opposition-based learning (OBL) to prevent local optima and accelerate the convergence. The main purpose of this paper is to apply the AHA-ROBL and AHA-OBL to select the relevant deep features provided by two pre-trained models of CNN (VGG19 & ResNet20) to recognize a waste classification. The TrashNet dataset is used to verify the performance of the two proposed approaches (the AHA-ROBL and AHA-OBL). The effectiveness of the suggested methods (the AHA-ROBL and AHA-OBL) is compared with that of 12 modern and competitive optimizers, namely the artificial hummingbird algorithm (AHA), Harris hawks optimizer (HHO), Salp swarm algorithm (SSA), aquila optimizer (AO), Henry gas solubility optimizer (HGSO), particle swarm optimizer (PSO), grey wolf optimizer (GWO), Archimedes optimization algorithm (AOA), manta ray foraging optimizer (MRFO), sine cosine algorithm (SCA), marine predators algorithm (MPA), and rescue optimization algorithm (SAR). A fair evaluation of the proposed algorithms’ performance is achieved using the same dataset. The performance analysis of the two proposed algorithms is applied in terms of different measures. The experimental results confirm the two proposed algorithms’ superiority over other comparative algorithms. The AHA-ROBL and AHA-OBL produce the optimal number of selected features with the highest degree of precision. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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33 pages, 7092 KiB  
Article
An Efficient Heap Based Optimizer Algorithm for Feature Selection
by Mona A. S. Ali, Fathimathul Rajeena P. P. and Diaa Salama Abd Elminaam
Mathematics 2022, 10(14), 2396; https://0-doi-org.brum.beds.ac.uk/10.3390/math10142396 - 08 Jul 2022
Cited by 4 | Viewed by 1665
Abstract
The heap-based optimizer (HBO) is an innovative meta-heuristic inspired by human social behavior. In this research, binary adaptations of the heap-based optimizer B_HBO are presented and used to determine the optimal features for classifications in wrapping form. In addition, [...] Read more.
The heap-based optimizer (HBO) is an innovative meta-heuristic inspired by human social behavior. In this research, binary adaptations of the heap-based optimizer B_HBO are presented and used to determine the optimal features for classifications in wrapping form. In addition, HBO balances exploration and exploitation by employing self-adaptive parameters that can adaptively search the solution domain for the optimal solution. In the feature selection domain, the presented algorithms for the binary Heap-based optimizer B_HBO are used to find feature subsets that maximize classification performance while lowering the number of selected features. The textitk-nearest neighbor (textitk-NN) classifier ensures that the selected features are significant. The new binary methods are compared to eight common optimization methods recently employed in this field, including Ant Lion Optimization (ALO), Archimedes Optimization Algorithm (AOA), Backtracking Search Algorithm (BSA), Crow Search Algorithm (CSA), Levy flight distribution (LFD), Particle Swarm Optimization (PSO), Slime Mold Algorithm (SMA), and Tree Seed Algorithm (TSA) in terms of fitness, accuracy, precision, sensitivity, F-score, the number of selected features, and statistical tests. Twenty datasets from the UCI repository are evaluated and compared using a set of evaluation indicators. The non-parametric Wilcoxon rank-sum test was used to determine whether the proposed algorithms’ results varied statistically significantly from those of the other compared methods. The comparison analysis demonstrates that B_HBO is superior or equivalent to the other algorithms used in the literature. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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27 pages, 577 KiB  
Article
A Variable Neighborhood Search Approach for the Dynamic Single Row Facility Layout Problem
by Gintaras Palubeckis, Armantas Ostreika and Jūratė Platužienė
Mathematics 2022, 10(13), 2174; https://0-doi-org.brum.beds.ac.uk/10.3390/math10132174 - 22 Jun 2022
Cited by 2 | Viewed by 1381
Abstract
The dynamic single row facility layout problem (DSRFLP) is defined as the problem of arranging facilities along a straight line during a multi-period planning horizon with the objective of minimizing the sum of the material handling and rearrangement costs. The material handling cost [...] Read more.
The dynamic single row facility layout problem (DSRFLP) is defined as the problem of arranging facilities along a straight line during a multi-period planning horizon with the objective of minimizing the sum of the material handling and rearrangement costs. The material handling cost is the sum of the products of the flow costs and center-to-center distances between facilities. In this paper, we focus on metaheuristic algorithms for this problem. The main contributions of the paper are three-fold. First, a variable neighborhood search (VNS) algorithm for the DSRFLP is proposed. The main version of VNS uses an innovative strategy to start the search from a solution obtained by constructing an instance of the single row facility layout problem (SRFLP) from a given instance of the DSRFLP and applying a heuristic algorithm for the former problem. Second, a fast local search (LS) procedure is developed. The innovations of this procedure are two-fold: (i) the fast insertion and swap neighborhood exploration techniques are adapted for the case of the dynamic version of the SRFLP; and (ii) to reduce the computational time, the swap operation is restricted on pairs of facilities of equal lengths. Provided the number of planning periods is a constant, the neighborhood exploration procedures for n facilities have only O(n2) time complexity. The superiority of these procedures over traditional LS techniques is also shown by performing numerical tests. Third, computational experiments on DSRFLP instances with up to 200 facilities and three or five planning periods are carried out to validate the effectiveness of the VNS approach. The proposed VNS heuristic is compared with the simulated annealing (SA) method which is the state of the art algorithm for the DSRFLP. Experiments show that VNS outperforms SA by a significant margin. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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31 pages, 10645 KiB  
Article
A Developed Frequency Control Strategy for Hybrid Two-Area Power System with Renewable Energy Sources Based on an Improved Social Network Search Algorithm
by Mohamed Khamies, Salah Kamel, Mohamed H. Hassan and Mohamed F. Elnaggar
Mathematics 2022, 10(9), 1584; https://0-doi-org.brum.beds.ac.uk/10.3390/math10091584 - 07 May 2022
Cited by 4 | Viewed by 1291
Abstract
In this paper, an effective frequency control strategy is proposed for emulating sufficient inertia power and improving frequency stability. The developed technique is based on applying virtual inertia control (VIC) with superconducting magnetic energy storage (SMES) instead of a traditional energy storage system [...] Read more.
In this paper, an effective frequency control strategy is proposed for emulating sufficient inertia power and improving frequency stability. The developed technique is based on applying virtual inertia control (VIC) with superconducting magnetic energy storage (SMES) instead of a traditional energy storage system (ESS) to compensate for the system inertia during the high penetration of renewable energy sources, taking into account the role of the controller in the secondary control loop (SCL). Unlike previous studies that depended on the designer experience in selecting the parameters of the inertia gain or the parameters of the SMES technology, the parameters of the proposed strategy are selected using optimization techniques. Moreover, an improved optimization algorithm called Improved Social Network Search algorithm (ISNS) is proposed to select the optimal parameters of the proposed control strategy. Moreover, the ISNS is improved to overcome the demerits of the traditional SNS algorithm, such as low speed convergence and global search capability. Accordingly, the ISNS algorithm is applied to a hybrid two-area power grid to determine the optimal parameters of the proposed control technique as follows: the proportional-integral derivative (PID) controller in the SCL. Additionally, the ISNS is applied to select the optimal control gains of the VIC-based SMES technology (e.g., the inertia gain, the proportional gain of the SMES, and the negative feedback gain of the SMES). Furthermore, the effectiveness of the proposed ISNS algorithm is validated by comparing its performance with that of the traditional SNS algorithm and other well-known algorithms (i.e., PSO, TSA, GWO, and WHO) considering different standard benchmark functions. Formerly, the effectiveness of the proposed frequency control technique was confirmed by comparing its performance with the system performance based on optimal VIC with ESS as well as without VIC considering different operating situations. The simulation results demonstrated the superiority of the proposed technique over other considered techniques, especially during high penetration of renewable power and lack of system inertia. As a result, the proposed technique is credible for modern power systems that take into account RESs. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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22 pages, 389 KiB  
Article
An Online Semi-Definite Programming with a Generalized Log-Determinant Regularizer and Its Applications
by Yaxiong Liu, Ken-ichiro Moridomi, Kohei Hatano and Eiji Takimoto
Mathematics 2022, 10(7), 1055; https://0-doi-org.brum.beds.ac.uk/10.3390/math10071055 - 25 Mar 2022
Cited by 1 | Viewed by 1402
Abstract
We consider a variant of the online semi-definite programming problem (OSDP). Specifically, in our problem, the setting of the decision space is a set of positive semi-definite matrices constrained by two norms in parallel: the L∞ norm to the diagonal entries and [...] Read more.
We consider a variant of the online semi-definite programming problem (OSDP). Specifically, in our problem, the setting of the decision space is a set of positive semi-definite matrices constrained by two norms in parallel: the L∞ norm to the diagonal entries and the Γ-trace norm, which is a generalized trace norm with a positive definite matrix Γ. Our setting recovers the original one when Γ is an identity matrix. To solve this problem, we design a follow-the-regularized-leader algorithm with a Γ-dependent regularizer, which also generalizes the log-determinant function. Next, we focus on online binary matrix completion (OBMC) with side information and online similarity prediction with side information. By reducing to the OSDP framework and applying our proposed algorithm, we remove the logarithmic factors in the previous mistake bound of the above two problems. In particular, for OBMC, our bound is optimal. Furthermore, our result implies a better offline generalization bound for the algorithm, which is similar to those of SVMs with the best kernel, if the side information is involved in advance. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
16 pages, 3990 KiB  
Article
The Modified Viscosity Approximation Method with Inertial Technique and Forward–Backward Algorithm for Convex Optimization Model
by Adisak Hanjing, Limpapat Bussaban and Suthep Suantai
Mathematics 2022, 10(7), 1036; https://0-doi-org.brum.beds.ac.uk/10.3390/math10071036 - 24 Mar 2022
Cited by 6 | Viewed by 1486
Abstract
In this paper, we propose a new accelerated algorithm for finding a common fixed point of nonexpansive operators, and then, a strong convergence result of the proposed method is discussed and analyzed in real Hilbert spaces. As an application, we create a new [...] Read more.
In this paper, we propose a new accelerated algorithm for finding a common fixed point of nonexpansive operators, and then, a strong convergence result of the proposed method is discussed and analyzed in real Hilbert spaces. As an application, we create a new accelerated viscosity forward–backward method (AVFBM) for solving nonsmooth optimization problems of the sum of two objective functions in real Hilbert spaces, and the strong convergence of AVFBM to a minimizer of the sum of two convex functions is established. We also present the application and simulated results of AVFBM for image restoration and data classification problems. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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26 pages, 5456 KiB  
Article
Optimal Reactive Power Dispatch Using a Chaotic Turbulent Flow of Water-Based Optimization Algorithm
by Ahmed M. Abd-El Wahab, Salah Kamel, Mohamed H. Hassan, Mohamed I. Mosaad and Tarek A. AbdulFattah
Mathematics 2022, 10(3), 346; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030346 - 24 Jan 2022
Cited by 24 | Viewed by 2290
Abstract
In this study, an optimization algorithm called chaotic turbulent flow of water-based optimization (CTFWO) algorithm is proposed to find the optimal solution for the optimal reactive power dispatch (ORPD) problem. The ORPD is formulated as a complicated, mixed-integer nonlinear optimization problem, comprising control [...] Read more.
In this study, an optimization algorithm called chaotic turbulent flow of water-based optimization (CTFWO) algorithm is proposed to find the optimal solution for the optimal reactive power dispatch (ORPD) problem. The ORPD is formulated as a complicated, mixed-integer nonlinear optimization problem, comprising control variables which are discrete and continuous. The CTFWO algorithm is used to minimize voltage deviation (VD) and real power loss (P_loss) for IEEE 30-bus and IEEE 57-bus power systems. These goals can be achieved by obtaining the optimized voltage values of the generator, the transformer tap changing positions, and the reactive compensation. In order to evaluate the ability of the proposed algorithm to obtain ORPD problem solutions, the results of the proposed CTFWO algorithm are compared with different algorithms, including artificial ecosystem-based optimization (AEO), the equilibrium optimizer (EO), the gradient-based optimizer (GBO), and the original turbulent flow of water-based optimization (TFWO) algorithm. These are also compared with the results of the evaluated performance of various methods that are used in many recent papers. The experimental results show that the proposed CTFWO algorithm has superior performance, and is competitive with many state-of-the-art algorithms outlined in some of the recent studies in terms of solution accuracy, convergence rate, and stability. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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21 pages, 499 KiB  
Article
Novel Static Multi-Layer Forest Approach and Its Applications
by Ganesh Bhagwat, Shristi Kumari, Vaishnavi Patekar and Adrian Marius Deaconu
Mathematics 2021, 9(21), 2650; https://0-doi-org.brum.beds.ac.uk/10.3390/math9212650 - 20 Oct 2021
Cited by 1 | Viewed by 1903
Abstract
The existing multi-layer tree is of dynamic linked list type which has many limitations and is complicated due to the pointer-node structure. Static array representation gives more flexibility in programming of algorithms and operations like insertion, deletion, and search. It also reduces the [...] Read more.
The existing multi-layer tree is of dynamic linked list type which has many limitations and is complicated due to the pointer-node structure. Static array representation gives more flexibility in programming of algorithms and operations like insertion, deletion, and search. It also reduces the storage space. This paper presents a new method for representing multi-layer forest data structure in array format. It also explains various tree operations, unique data compression algorithm and migration algorithm between traditional approach and the proposed data structure. Most of the fundamental algorithms like those from artificial intelligence that employ decision trees are based on trees/forest data structure. The current paper brings a completely new idea in the representation of these data structures without employing recursion and targeting memory optimizations with reduced code complexities. The applications of forest data structures are many and span over various interdisciplinary areas of Engineering, Medicine, Aviation, Locomotive, Marine, etc. The proposed novel approach not just introduces a new method to look at the tree data structure but also provides the flexibility to adapt to the existing methods as per the user needs. A few such applications in Simulink debugging and the Forest visualisation have been discussed in detail in this paper. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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9 pages, 322 KiB  
Article
Flow Increment through Network Expansion
by Adrian Marius Deaconu and Luciana Majercsik
Mathematics 2021, 9(18), 2308; https://0-doi-org.brum.beds.ac.uk/10.3390/math9182308 - 18 Sep 2021
Cited by 2 | Viewed by 1485
Abstract
The network expansion problem is a very important practical optimization problem when there is a need to increment the flow through an existing network of transportation, electricity, water, gas, etc. In this problem, the flow augmentation can be achieved either by increasing the [...] Read more.
The network expansion problem is a very important practical optimization problem when there is a need to increment the flow through an existing network of transportation, electricity, water, gas, etc. In this problem, the flow augmentation can be achieved either by increasing the capacities on the existing arcs, or by adding new arcs to the network. Both operations are coming with an expansion cost. In this paper, the problem of finding the minimum network expansion cost so that the modified network can transport a given amount of flow from the source node to the sink node is studied. A strongly polynomial algorithm is deduced to solve the problem. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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