Topic Editors

Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucuresti, Romania

Advances in Optimization and Nonlinear Analysis Volume II

Abstract submission deadline
closed (10 January 2024)
Manuscript submission deadline
closed (10 March 2024)
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Topic Information

Dear Colleagues,

This Topic aims to publish research studies on optimization and nonlinear analysis by investigating the well-posedness and optimal solutions in new classes of (multiobjective) variational (control) problems governed by multiple and/or path-independent curvilinear integral cost functionals and mixed and/or isoperimetric constraints involving first- and second-order partial differential equations. Additionally, some applications of fractional calculus in this regard are considered. In consequence, I cordially invite you to publish your results on this topic or related subjects (variational inequalities, equilibrium problems, fixed point problems, evolutionary problems, and so on) in this Topic.

Dr. Savin Treanţă
Topic Editor

Keywords

  • fractional calculus
  • well-posedness
  • optimization problems
  • control problems
  • variational and nonlinear problems
  • equilibrium problems
  • partial differential equations
  • partial differential inequations
  • isoperimetric constraints
  • variational inequalities
  • interval-valued problems

Participating Journals

Journal Name Impact Factor CiteScore Launched Year First Decision (median) APC
Algorithms
algorithms
1.8 4.1 2008 15 Days CHF 1600
Automation
automation
- 2.9 2020 20.6 Days CHF 1000
Axioms
axioms
1.9 - 2012 21 Days CHF 2400
Entropy
entropy
2.1 4.9 1999 22.4 Days CHF 2600
Fractal and Fractional
fractalfract
3.6 4.6 2017 20.9 Days CHF 2700
Mathematical and Computational Applications
mca
1.9 - 1996 28.8 Days CHF 1400

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Published Papers (9 papers)

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17 pages, 3527 KiB  
Article
Proportional-Integral-Derivative Controller Based-Artificial Rabbits Algorithm for Load Frequency Control in Multi-Area Power Systems
by Ragab El-Sehiemy, Abdullah Shaheen, Ahmed Ginidi and Saad F. Al-Gahtani
Fractal Fract. 2023, 7(1), 97; https://doi.org/10.3390/fractalfract7010097 - 16 Jan 2023
Cited by 34 | Viewed by 2745
Abstract
A major problem in power systems is achieving a match between the load demand and generation demand, where security, dependability, and quality are critical factors that need to be provided to power producers. This paper proposes a proportional–integral–derivative (PID) controller that is optimally [...] Read more.
A major problem in power systems is achieving a match between the load demand and generation demand, where security, dependability, and quality are critical factors that need to be provided to power producers. This paper proposes a proportional–integral–derivative (PID) controller that is optimally designed using a novel artificial rabbits algorithm (ARA) for load frequency control (LFC) in multi-area power systems (MAPSs) of two-area non-reheat thermal systems. The PID controller incorporates a filter with such a derivative coefficient to reduce the effects of the accompanied noise. In this regard, single objective function is assessed based on time-domain simulation to minimize the integral time-multiplied absolute error (ITAE). The proposed ARA adjusts the PID settings to their best potential considering three dissimilar test cases with different sets of disturbances, and the results from the designed PID controller based on the ARA are compared with various published techniques, including particle swarm optimization (PSO), differential evolution (DE), JAYA optimizer, and self-adaptive multi-population elitist (SAMPE) JAYA. The comparisons show that the PID controller’s design, which is based on the ARA, handles the load frequency regulation in MAPSs for the ITAE minimizations with significant effectiveness and success where the statistical analysis confirms its superiority. Considering the load change in area 1, the proposed ARA can acquire significant percentage improvements in the ITAE values of 1.949%, 3.455%, 2.077% and 1.949%, respectively, with regard to PSO, DE, JAYA and SAMPE-JAYA. Considering the load change in area 2, the proposed ARA can acquire significant percentage improvements in the ITAE values of 7.587%, 8.038%, 3.322% and 2.066%, respectively, with regard to PSO, DE, JAYA and SAMPE-JAYA. Considering simultaneous load changes in areas 1 and 2, the proposed ARA can acquire significant improvements in the ITAE values of 60.89%, 38.13%, 55.29% and 17.97%, respectively, with regard to PSO, DE, JAYA and SAMPE-JAYA. Full article
(This article belongs to the Topic Advances in Optimization and Nonlinear Analysis Volume II)
(This article belongs to the Section Engineering)
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26 pages, 7792 KiB  
Article
Non-Linear Analysis of Novel Equivalent Circuits of Single-Diode Solar Cell Models with Voltage-Dependent Resistance
by Mahendiran Vellingiri, Muhyaddin Rawa, Sultan Alghamdi, Abdullah A. Alhussainy, Ahmed S. Althobiti, Martin Calasan, Mihailo Micev, Ziad M. Ali and Shady H. E. Abdel Aleem
Fractal Fract. 2023, 7(1), 95; https://doi.org/10.3390/fractalfract7010095 - 14 Jan 2023
Cited by 4 | Viewed by 2127
Abstract
The most commonly used model of solar cells is the single-diode model, with five unknown parameters. First, this paper proposes three variants of the single-diode model, which imply the voltage dependence of the series resistance, parallel resistance, and both resistors. Second, analytical relationships [...] Read more.
The most commonly used model of solar cells is the single-diode model, with five unknown parameters. First, this paper proposes three variants of the single-diode model, which imply the voltage dependence of the series resistance, parallel resistance, and both resistors. Second, analytical relationships between the current and the voltage expressed were derived using the Lambert W function for each proposed model. Third, the paper presents a hybrid algorithm, Chaotic Snake Optimization (Chaotic SO), combining chaotic sequences with the snake optimization algorithm. The application of the proposed models and algorithm was justified on two well-known solar photovoltaic (PV) cells—RTC France solar cell and Photowatt-PWP201 module. The results showed that the root-mean-square-error (RMSE) values calculated by applying the proposed equivalent circuit with voltage dependence of both resistors are reduced by 20% for the RTC France solar cell and 40% for the Photowatt-PWP201 module compared to the standard single-diode equivalent circuit. Finally, an experimental investigation was conducted into the applicability of the proposed models to a solar laboratory module, and the results obtained proved the relevance and effectiveness of the proposed models. Full article
(This article belongs to the Topic Advances in Optimization and Nonlinear Analysis Volume II)
(This article belongs to the Section Engineering)
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13 pages, 418 KiB  
Article
New Fractional Integral Inequalities Pertaining to Center-Radius (cr)-Ordered Convex Functions
by Soubhagya Kumar Sahoo, Hleil Alrweili, Savin Treanţă and Zareen A. Khan
Fractal Fract. 2023, 7(1), 81; https://doi.org/10.3390/fractalfract7010081 - 11 Jan 2023
Cited by 1 | Viewed by 1510
Abstract
In this work, we use the idea of interval-valued convex functions of Center-Radius (cr)-order to give fractional versions of Hermite–Hadamard inequality. The results are supported by some numerical estimations and graphical representations considering some suitable examples. The results are novel in [...] Read more.
In this work, we use the idea of interval-valued convex functions of Center-Radius (cr)-order to give fractional versions of Hermite–Hadamard inequality. The results are supported by some numerical estimations and graphical representations considering some suitable examples. The results are novel in the context of cr-convex interval-valued functions and deal with differintegrals of the p+s2 type. We believe this will be an important contribution to spurring additional research. Full article
(This article belongs to the Topic Advances in Optimization and Nonlinear Analysis Volume II)
(This article belongs to the Section Engineering)
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24 pages, 744 KiB  
Article
New Class Up and Down λ-Convex Fuzzy-Number Valued Mappings and Related Fuzzy Fractional Inequalities
by Muhammad Bilal Khan, Hatim Ghazi Zaini, Gustavo Santos-García, Muhammad Aslam Noor and Mohamed S. Soliman
Fractal Fract. 2022, 6(11), 679; https://doi.org/10.3390/fractalfract6110679 - 16 Nov 2022
Cited by 11 | Viewed by 1773
Abstract
The fuzzy-number valued up and down λ-convex mapping is originally proposed as an intriguing generalization of the convex mappings. The newly suggested mappings are then used to create certain Hermite–Hadamard- and Pachpatte-type integral fuzzy inclusion relations in fuzzy fractional calculus. It is [...] Read more.
The fuzzy-number valued up and down λ-convex mapping is originally proposed as an intriguing generalization of the convex mappings. The newly suggested mappings are then used to create certain Hermite–Hadamard- and Pachpatte-type integral fuzzy inclusion relations in fuzzy fractional calculus. It is also suggested to revise the Hermite–Hadamard integral fuzzy inclusions with regard to the up and down λ-convex fuzzy-number valued mappings (U∙D λ-convex F-N∙V∙Ms). Moreover, Hermite–Hadamard–Fejér has been proven, and some examples are given to demonstrate the validation of our main results. The new and exceptional cases are presented in terms of the change of the parameters i and α in order to assess the accuracy of the obtained fuzzy inclusion relations in this study. Full article
(This article belongs to the Topic Advances in Optimization and Nonlinear Analysis Volume II)
(This article belongs to the Section Engineering)
18 pages, 340 KiB  
Article
Optimality Guidelines for the Fuzzy Multi-Objective Optimization under the Assumptions of Vector Granular Convexity and Differentiability
by Jianke Zhang, Yueyue Wang, Quanxi Feng and Lifeng Li
Fractal Fract. 2022, 6(10), 600; https://doi.org/10.3390/fractalfract6100600 - 15 Oct 2022
Cited by 1 | Viewed by 1326
Abstract
In this research, we investigate a novel class of granular type optimality guidelines for the fuzzy multi-objective optimizations based on guidelines of vector granular convexity and granular differentiability. Firstly, the concepts of vector granular convexity is introduced to the vector fuzzy-valued function. Secondly, [...] Read more.
In this research, we investigate a novel class of granular type optimality guidelines for the fuzzy multi-objective optimizations based on guidelines of vector granular convexity and granular differentiability. Firstly, the concepts of vector granular convexity is introduced to the vector fuzzy-valued function. Secondly, several properties of vector granular convex fuzzy-valued functions are provided. Thirdly, the granular type Karush-Kuhn-Tucker(KKT) optimality guidelines are derived for the fuzzy multi-objective optimizations. Full article
(This article belongs to the Topic Advances in Optimization and Nonlinear Analysis Volume II)
(This article belongs to the Section Engineering)
13 pages, 1770 KiB  
Article
Improved Biogeography-Based Optimization Algorithm Based on Hybrid Migration and Dual-Mode Mutation Strategy
by Lisheng Wei, Qian Zhang and Benben Yang
Fractal Fract. 2022, 6(10), 597; https://doi.org/10.3390/fractalfract6100597 - 14 Oct 2022
Cited by 3 | Viewed by 1871
Abstract
To obtain high-quality Pareto optimal solutions and to enhance the searchability of the biogeography-based optimization (BBO) algorithm, we present an improved BBO algorithm based on hybrid migration and a dual-mode mutation strategy (HDBBO). We first adopted a more scientific nonlinear hyperbolic tangent mobility [...] Read more.
To obtain high-quality Pareto optimal solutions and to enhance the searchability of the biogeography-based optimization (BBO) algorithm, we present an improved BBO algorithm based on hybrid migration and a dual-mode mutation strategy (HDBBO). We first adopted a more scientific nonlinear hyperbolic tangent mobility model instead of the conventional linear migration model which can obtain a solution closer to the global minimum of the function. We developed an improved hybrid migration operation containing a micro disturbance factor, which has the benefit of strengthening the global search ability of the algorithm. Then, we used the piecewise application of Gaussian mutation and BBO mutation to ensure that the solution set after mutation was also maintained at a high level, which helps strengthen the algorithm’s search accuracy. Finally, we performed a convergence analysis on the improved BBO algorithm and experimental research based on 11 benchmark functions. The simulation results showed that the improved BBO algorithm had superior advantages in terms of optimization accuracy and convergence speed, which showed the feasibility of the improved strategy. Full article
(This article belongs to the Topic Advances in Optimization and Nonlinear Analysis Volume II)
(This article belongs to the Section Engineering)
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14 pages, 316 KiB  
Article
Some H-Godunova–Levin Function Inequalities Using Center Radius (Cr) Order Relation
by Waqar Afzal, Mujahid Abbas, Jorge E. Macías-Díaz and Savin Treanţă
Fractal Fract. 2022, 6(9), 518; https://doi.org/10.3390/fractalfract6090518 - 14 Sep 2022
Cited by 30 | Viewed by 1892
Abstract
Interval analysis distinguishes between different types of order relations. As a result of these order relations, convexity and nonconvexity contribute to different kinds of inequalities. Despite this, convex theory is commonly known to rely on Godunova–Levin functions because their properties make it more [...] Read more.
Interval analysis distinguishes between different types of order relations. As a result of these order relations, convexity and nonconvexity contribute to different kinds of inequalities. Despite this, convex theory is commonly known to rely on Godunova–Levin functions because their properties make it more efficient for determining inequality terms than convex ones. The purpose of this study is to introduce the notion of cr-h-Godunova–Levin functions by using total order relation between two intervals. Considering their properties and widespread use, center-radius order relation appears to be ideally suited for the study of inequalities. In this paper, various types of inequalities are introduced using center-radius order (cr) relation. The cr-order relation enables us firstly to derive some Hermite–Hadamard (H.H) inequalities, and then to present Jensen-type inequality for h-Godunova–Levin interval-valued functions (GL-IVFS) using a Riemann integral operator. This kind of convexity unifies several new and well-known convex functions. Additionally, the study includes useful examples to support its findings. These results confirm that this new concept is useful for addressing a wide range of inequalities. We hope that our results will encourage future research into fractional versions of these inequalities and optimization problems associated with them. Full article
(This article belongs to the Topic Advances in Optimization and Nonlinear Analysis Volume II)
(This article belongs to the Section Engineering)
24 pages, 1007 KiB  
Article
Hermite–Hadamard, Fejér and Pachpatte-Type Integral Inequalities for Center-Radius Order Interval-Valued Preinvex Functions
by Soubhagya Kumar Sahoo, Muhammad Amer Latif, Omar Mutab Alsalami, Savin Treanţă, Weerawat Sudsutad and Jutarat Kongson
Fractal Fract. 2022, 6(9), 506; https://doi.org/10.3390/fractalfract6090506 - 10 Sep 2022
Cited by 14 | Viewed by 1826
Abstract
The objective of this manuscript is to establish a link between the concept of inequalities and Center-Radius order functions, which are intriguing due to their properties and widespread use. We introduce the notion of the CR (Center-Radius)-order interval-valued preinvex function with the help [...] Read more.
The objective of this manuscript is to establish a link between the concept of inequalities and Center-Radius order functions, which are intriguing due to their properties and widespread use. We introduce the notion of the CR (Center-Radius)-order interval-valued preinvex function with the help of a total order relation between two intervals. Furthermore, we discuss some properties of this new class of preinvexity and show that the new concept unifies several known concepts in the literature and also gives rise to some new definitions. By applying these new definitions, we have amassed many classical and novel special cases that serve as applications of the key findings of the manuscript. The computations of cr-order intervals depend upon the following concept B=Bc,Br=B¯+B̲2,B¯B̲2. Then, for the first time, inequalities such as Hermite–Hadamard, Pachpatte, and Fejér type are established for CR-order in association with the concept of interval-valued preinvexity. Some numerical examples are given to validate the main results. The results confirm that this new concept is very useful in connection with various inequalities. A fractional version of the Hermite–Hadamard inequality is also established to show how the presented results can be connected to fractional calculus in future developments. Our presented results will motivate further research on inequalities for fractional interval-valued functions, fuzzy interval-valued functions, and their associated optimization problems. Full article
(This article belongs to the Topic Advances in Optimization and Nonlinear Analysis Volume II)
(This article belongs to the Section Engineering)
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9 pages, 296 KiB  
Article
Results on the Existence of Solutions Associated with Some Weak Vector Variational Inequalities
by Savin Treanţă
Fractal Fract. 2022, 6(8), 431; https://doi.org/10.3390/fractalfract6080431 - 7 Aug 2022
Cited by 3 | Viewed by 1268
Abstract
In this paper, by considering the notions of the invex set, Fréchet differentiability, invexity and pseudoinvexity for the involved functionals of curvilinear integral type, we establish some relations between the solutions of a class of weak vector variational inequalities and (weak) efficient solutions [...] Read more.
In this paper, by considering the notions of the invex set, Fréchet differentiability, invexity and pseudoinvexity for the involved functionals of curvilinear integral type, we establish some relations between the solutions of a class of weak vector variational inequalities and (weak) efficient solutions of the associated control problem. Full article
(This article belongs to the Topic Advances in Optimization and Nonlinear Analysis Volume II)
(This article belongs to the Section Engineering)
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