3. Method Of Test Functions In Combination With Method Of Nonlinear Capacity

2018 ◽  
pp. 55-70
Keyword(s):  
Test Functions ◽  
Nonlinear Capacity

scholarly journals The BV solution of the parabolic equation with degeneracy on the boundary

2016 ◽  
Vol 14 (1) ◽  
pp. 272-282
Author(s):  
Huashui Zhan ◽  
Shuping Chen
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Well Posedness ◽  
Test Functions ◽  
The Stability

AbstractConsider a parabolic equation which is degenerate on the boundary. By the degeneracy, to assure the well-posedness of the solutions, only a partial boundary condition is generally necessary. When 1 ≤ α < p – 1, the existence of the local BV solution is proved. By choosing some kinds of test functions, the stability of the solutions based on a partial boundary condition is established.

Salp swarm algorithm with crossover scheme and Lévy flight for global optimization

2021 ◽  
pp. 1-12
Author(s):  
Heming Jia ◽  
Chunbo Lang
Keyword(s):  
Global Optimization ◽  
Heuristic Algorithm ◽  
Experimental Results ◽  
High Dimensional ◽  
Lévy Flight ◽  
Test Functions ◽  
Levy Flight ◽  
Salp Swarm Algorithm ◽  
Swarm Algorithm ◽  
Accuracy And Stability

Salp swarm algorithm (SSA) is a meta-heuristic algorithm proposed in recent years, which shows certain advantages in solving some optimization tasks. However, with the increasing difficulty of solving the problem (e.g. multi-modal, high-dimensional), the convergence accuracy and stability of SSA algorithm decrease. In order to overcome the drawbacks, salp swarm algorithm with crossover scheme and Lévy flight (SSACL) is proposed. The crossover scheme and Lévy flight strategy are used to improve the movement patterns of salp leader and followers, respectively. Experiments have been conducted on various test functions, including unimodal, multimodal, and composite functions. The experimental results indicate that the proposed SSACL algorithm outperforms other advanced algorithms in terms of precision, stability, and efficiency. Furthermore, the Wilcoxon’s rank sum test illustrates the advantages of proposed method in a statistical and meaningful way.

scholarly journals Blowing-up solutions of the time-fractional dispersive equations

2021 ◽  
Vol 10 (1) ◽  
pp. 952-971
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Mokhtar Kirane ◽  
Berikbol T. Torebek
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Nonlinear Capacity ◽  
Blowing Up ◽  
De Vries ◽  
Initial Boundary Value

Abstract This paper is devoted to the study of initial-boundary value problems for time-fractional analogues of Korteweg-de Vries, Benjamin-Bona-Mahony, Burgers, Rosenau, Camassa-Holm, Degasperis-Procesi, Ostrovsky and time-fractional modified Korteweg-de Vries-Burgers equations on a bounded domain. Sufficient conditions for the blowing-up of solutions in finite time of aforementioned equations are presented. We also discuss the maximum principle and influence of gradient non-linearity on the global solvability of initial-boundary value problems for the time-fractional Burgers equation. The main tool of our study is the Pohozhaev nonlinear capacity method. We also provide some illustrative examples.

scholarly journals A Modified Niching Crow Search Approach to Well Placement Optimization

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 857
Author(s):  
Jahedul Islam ◽  
Md Shokor A. Rahaman ◽  
Pandian M. Vasant ◽  
Berihun Mamo Negash ◽  
Ahshanul Hoqe ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Search Algorithm ◽  
Gravitational Search Algorithm ◽  
Multimodal Optimization ◽  
Test Functions ◽  
Well Placement ◽  
Suggested Approach ◽  
Placement Optimization ◽  
Well Placement Optimization ◽  
Search Approach

Well placement optimization is considered a non-convex and highly multimodal optimization problem. In this article, a modified crow search algorithm is proposed to tackle the well placement optimization problem. This article proposes modifications based on local search and niching techniques in the crow search algorithm (CSA). At first, the suggested approach is verified by experimenting with the benchmark functions. For test functions, the results of the proposed approach demonstrated a higher convergence rate and a better solution. Again, the performance of the proposed technique is evaluated with well placement optimization problem and compared with particle swarm optimization (PSO), the Gravitational Search Algorithm (GSA), and the Crow search algorithm (CSA). The outcomes of the study revealed that the niching crow search algorithm is the most efficient and effective compared to the other techniques.

scholarly journals A Hybrid Whale Optimization Algorithm for Global Optimization

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1477
Author(s):  
Chun-Yao Lee ◽  
Guang-Lin Zhuo
Keyword(s):  
Global Optimization ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Whale Optimization Algorithm ◽  
Initial Population ◽  
Test Functions ◽  
Benchmark Test ◽  
Thermal Exchange ◽  
Whale Optimization ◽  
Benchmark Test Functions

This paper proposes a hybrid whale optimization algorithm (WOA) that is derived from the genetic and thermal exchange optimization-based whale optimization algorithm (GWOA-TEO) to enhance global optimization capability. First, the high-quality initial population is generated to improve the performance of GWOA-TEO. Then, thermal exchange optimization (TEO) is applied to improve exploitation performance. Next, a memory is considered that can store historical best-so-far solutions, achieving higher performance without adding additional computational costs. Finally, a crossover operator based on the memory and a position update mechanism of the leading solution based on the memory are proposed to improve the exploration performance. The GWOA-TEO algorithm is then compared with five state-of-the-art optimization algorithms on CEC 2017 benchmark test functions and 8 UCI repository datasets. The statistical results of the CEC 2017 benchmark test functions show that the GWOA-TEO algorithm has good accuracy for global optimization. The classification results of 8 UCI repository datasets also show that the GWOA-TEO algorithm has competitive results with regard to comparison algorithms in recognition rate. Thus, the proposed algorithm is proven to execute excellent performance in solving optimization problems.

scholarly journals Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1866
Author(s):  
Mohamed Jleli ◽  
Bessem Samet ◽  
Calogero Vetro
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
A Priori Estimates ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Higher Order ◽  
Differential Inequalities ◽  
Structure Of Solutions ◽  
Nonlinear Capacity ◽  
Fractional Differential

Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis of the integral form of the inequality with appropriate choice of test function.

scholarly journals A comparison of optimisation algorithms for high-dimensional particle and astrophysics applications

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Csaba Balázs ◽  
◽  
Melissa van Beekveld ◽  
Sascha Caron ◽  
Barry M. Dillon ◽  
...  
Keyword(s):  
Random Sampling ◽  
Detailed Comparison ◽  
Global Optimisation ◽  
Adaptive Memory ◽  
Test Functions ◽  
Bee Colony ◽  
Covariance Matrix Adaptation ◽  
Global Fit ◽  
Adaptation Evolution ◽  
Optimisation Algorithms

Abstract Optimisation problems are ubiquitous in particle and astrophysics, and involve locating the optimum of a complicated function of many parameters that may be computationally expensive to evaluate. We describe a number of global optimisation algorithms that are not yet widely used in particle astrophysics, benchmark them against random sampling and existing techniques, and perform a detailed comparison of their performance on a range of test functions. These include four analytic test functions of varying dimensionality, and a realistic example derived from a recent global fit of weak-scale supersymmetry. Although the best algorithm to use depends on the function being investigated, we are able to present general conclusions about the relative merits of random sampling, Differential Evolution, Particle Swarm Optimisation, the Covariance Matrix Adaptation Evolution Strategy, Bayesian Optimisation, Grey Wolf Optimisation, and the PyGMO Artificial Bee Colony, Gaussian Particle Filter and Adaptive Memory Programming for Global Optimisation algorithms.

scholarly journals Modified Flower Pollination Algorithm for Global Optimization

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1661
Author(s):  
Mohamed Abdel-Basset ◽  
Reda Mohamed ◽  
Safaa Saber ◽  
S. S. Askar ◽  
Mohamed Abouhawwash
Keyword(s):  
Global Optimization ◽  
Nonlinear Equation ◽  
Differential Evolution ◽  
Flower Pollination Algorithm ◽  
Test Cases ◽  
Test Functions ◽  
Flower Pollination ◽  
New Variant ◽  
Experimental Findings ◽  
Nonlinear Equation Systems

In this paper, a modified flower pollination algorithm (MFPA) is proposed to improve the performance of the classical algorithm and to tackle the nonlinear equation systems widely used in engineering and science fields. In addition, the differential evolution (DE) is integrated with MFPA to strengthen its exploration operator in a new variant called HFPA. Those two algorithms were assessed using 23 well-known mathematical unimodal and multimodal test functions and 27 well-known nonlinear equation systems, and the obtained outcomes were extensively compared with those of eight well-known metaheuristic algorithms under various statistical analyses and the convergence curve. The experimental findings show that both MFPA and HFPA are competitive together and, compared to the others, they could be superior and competitive for most test cases.

scholarly journals On New Classes of Stancu-Kantorovich-Type Operators

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1235
Author(s):  
Bianca Ioana Vasian ◽  
Ștefan Lucian Garoiu ◽  
Cristina Maria Păcurar
Keyword(s):  
Test Functions ◽  
New Class ◽  
Convergence Results ◽  
Error Estimations ◽  
Kantorovich Operators

The present paper introduces new classes of Stancu–Kantorovich operators constructed in the King sense. For these classes of operators, we establish some convergence results, error estimations theorems and graphical properties of approximation for the classes considered, namely, operators that preserve the test functions e0(x)=1 and e1(x)=x, e0(x)=1 and e2(x)=x2, as well as e1(x)=x and e2(x)=x2. The class of operators that preserve the test functions e1(x)=x and e2(x)=x2 is a genuine generalization of the class introduced by Indrea et al. in their paper “A New Class of Kantorovich-Type Operators”, published in Constr. Math. Anal.

scholarly journals Enhancing Ant-Based Algorithms for Medical Image Edge Detection by Admissible Perturbations of Demicontractive Mappings

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 885
Author(s):  
Vasile Berinde ◽  
Cristina Ţicală
Keyword(s):  
Edge Detection ◽  
Medical Image ◽  
Test Functions ◽  
Head Ct ◽  
X Ray ◽  
Numerical Tests ◽  
Image Edge Detection ◽  
Evaluation Of Parameters ◽  
Image Edge ◽  
Demicontractive Mappings

The aim of this paper is to show analytically and empirically how ant-based algorithms for medical image edge detection can be enhanced by using an admissible perturbation of demicontractive operators. We thus complement the results reported in a recent paper by the second author and her collaborators, where they used admissible perturbations of demicontractive mappings as test functions. To illustrate this fact, we first consider some typical properties of demicontractive mappings and of their admissible perturbations and then present some appropriate numerical tests to illustrate the improvement brought by the admissible perturbations of demicontractive mappings when they are taken as test functions in ant-based algorithms for medical image edge detection. The edge detection process reported in our study considers both symmetric (Head CT and Brain CT) and asymmetric (Hand X-ray) medical images. The performance of the algorithm was tested visually with various images and empirically with evaluation of parameters.

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