Multiobjective Brainstorm Optimization with Diversity Preservation Mechanism for Nonlinear Equation Systems

Author(s):  
Yi Zhao ◽  
Zelin Zhu
Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1661
Author(s):  
Mohamed Abdel-Basset ◽  
Reda Mohamed ◽  
Safaa Saber ◽  
S. S. Askar ◽  
Mohamed Abouhawwash

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.


2017 ◽  
Vol 47 (11) ◽  
pp. 2817-2830 ◽  
Author(s):  
Yunong Zhang ◽  
Yinyan Zhang ◽  
Dechao Chen ◽  
Zhengli Xiao ◽  
Xiaogang Yan

1984 ◽  
Vol 7 (4) ◽  
pp. 793-802 ◽  
Author(s):  
A. J. Hughes Hallett

Most models in economics and the applied sciences are solved by first order iterative techniques, usually those based on the Gauss-Seidel algorithm. This paper examines the convergence of multiparameter extrapolations (accelerations) of first order iterations, as an improved approximation to the Newton method for solving arbitrary nonlinear equation systems. It generalises my earlier results on single parameter extrapolations. Richardson's generalised method and the deflation method for detecting successive solutions in nonlinear equation systems are also presented as multiparameter extrapolations of first order iterations. New convergence results are obtained for those methods.


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