A novel analytical approach for solving partial differential equations via a tensor product theory of Banach spaces

Alshanti, Waseem Ghazi; Batiha, Iqbal M.; Hammad, Ma’mon Abu

doi:10.1016/j.padiff.2023.100531

Cited by 6 publications

(1 citation statement)

References 9 publications

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“…Problem solving techniques in dealing with optimization problems are classified into two groups: deterministic and stochastic approaches [3]. Deterministic approaches in two classes, gradient-based and non-gradientbased, have effective performance in optimizing convex, linear, continuous, differentiable, and low-dimensional problems [4]. Although, when problems become more complex and especially the dimensions of the problem increase, deterministic approaches are inefficient as they get stuck in local optima [5].…”

Section: Introductionmentioning

confidence: 99%

Pufferfish Optimization Algorithm: A New Bio-Inspired Metaheuristic Algorithm for Solving Optimization Problems

Al-Baik,

Alomari,

Alssayed

et al. 2024

Biomimetics

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A new bio-inspired metaheuristic algorithm named the Pufferfish Optimization Algorithm (POA), that imitates the natural behavior of pufferfish in nature, is introduced in this paper. The fundamental inspiration of POA is adapted from the defense mechanism of pufferfish against predators. In this defense mechanism, by filling its elastic stomach with water, the pufferfish becomes a spherical ball with pointed spines, and as a result, the hungry predator escapes from this threat. The POA theory is stated and then mathematically modeled in two phases: (i) exploration based on the simulation of a predator’s attack on a pufferfish and (ii) exploitation based on the simulation of a predator’s escape from spiny spherical pufferfish. The performance of POA is evaluated in handling the CEC 2017 test suite for problem dimensions equal to 10, 30, 50, and 100. The optimization results show that POA has achieved an effective solution with the appropriate ability in exploration, exploitation, and the balance between them during the search process. The quality of POA in the optimization process is compared with the performance of twelve well-known metaheuristic algorithms. The simulation results show that POA provides superior performance by achieving better results in most of the benchmark functions in order to solve the CEC 2017 test suite compared to competitor algorithms. Also, the effectiveness of POA to handle optimization tasks in real-world applications is evaluated on twenty-two constrained optimization problems from the CEC 2011 test suite and four engineering design problems. Simulation results show that POA provides effective performance in handling real-world applications by achieving better solutions compared to competitor algorithms.

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Section: Introductionmentioning

confidence: 99%

Pufferfish Optimization Algorithm: A New Bio-Inspired Metaheuristic Algorithm for Solving Optimization Problems

Al-Baik,

Alomari,

Alssayed

et al. 2024

Biomimetics

View full text Add to dashboard Cite

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Approximation of three‐dimensional nonlinear wave equations by fundamental solutions and weighted residuals process

Safari

2023

Math Methods in App Sciences

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In this paper, the localized method of fundamental solutions (LMFS) with coupling the dual reciprocity method (DRM) is applied to simulate three‐space dimensional nonlinear wave equations. First, DRM, which is a popular meshless method based on polyharmonic splines (PhS), is applied to obtain the particular solution. After evaluating the particular solution, 3D‐LMFS method can be employed to evaluate the homogeneous solution. The proposed 3D‐LMFS algorithms construct 3D artificial surfaces where source points and then the collocation procedure propose by using the fundamental solutions in each 3D surface. Straightforwardly, a solution to the 3D wave equation is approximated by a sum of the combination of PhS and fundamental solutions using LMFS. Eventually, the scheme has been prosperously tested with selected examples.

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Bobcat Optimization Algorithm: an effective bio-inspired metaheuristic algorithm for solving supply chain optimization problems

Benmamoun,

Khlie,

Bektemyssova

et al. 2024

Sci Rep

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A novel analytical approach for solving partial differential equations via a tensor product theory of Banach spaces

Cited by 6 publications

References 9 publications

Pufferfish Optimization Algorithm: A New Bio-Inspired Metaheuristic Algorithm for Solving Optimization Problems

Pufferfish Optimization Algorithm: A New Bio-Inspired Metaheuristic Algorithm for Solving Optimization Problems

Approximation of three‐dimensional nonlinear wave equations by fundamental solutions and weighted residuals process

Bobcat Optimization Algorithm: an effective bio-inspired metaheuristic algorithm for solving supply chain optimization problems

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