scholarly journals Hybridization of Grasshopper Optimization Algorithm With Genetic Algorithm for Solving System of Non-Linear Equations

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 220944-220961
Author(s):  
M. A. El-Shorbagy ◽  
Adel M. El-Refaey
Keyword(s):  
Genetic Algorithm ◽  
Optimization Algorithm ◽  
Linear Equations ◽  
Grasshopper Optimization Algorithm ◽  
Non Linear ◽  
Grasshopper Optimization ◽  
Non Linear Equations

scholarly journals Modified Grasshopper Optimization Algorithm Based Genetic Algorithm for Global Optimization Problems: The System of Nonlinear Equations Case Study

2021 ◽  
Author(s):  
Hala A. Omar ◽  
Mohammed El-Shorbagy
Keyword(s):  
Genetic Algorithm ◽  
Optimization Algorithm ◽  
Local Minimum ◽  
Optimization Problems ◽  
Search Space ◽  
System Of Nonlinear Equations ◽  
Grasshopper Optimization Algorithm ◽  
Speed Up ◽  
Grasshopper Optimization

Abstract Grasshopper optimization algorithm (GOA) is one of the promising optimization algorithms for optimization problems. But, it has the main drawback of trapping into a local minimum, which causes slow convergence or inability to detect a solution. Several modifications and combinations have been proposed to overcome this problem. In this paper, a modified grasshopper optimization algorithm (MGOA) based genetic algorithm (GA) is proposed to overcome this problem. Modifications rely on certain mathematical assumptions and varying the domain of the Cmax control parameter to escape from the local minimum and move the search process to a new improved point. Parameter C is one of the most important parameters in GOA where it balances the exploration and exploitation of the search space. These modifications aim to lead to speed up the convergence rate by reducing the repeated solutions and the number of iterations. The proposed algorithm will be tested on the 19 main test functions to verify and investigate the influence of the proposed modifications. In addition, the algorithm will be applied to solve 5 different cases of nonlinear systems with different types of dimensions and regularity to show the reliability and efficiency of the proposed algorithm. Good results were achieved compared to the original GOA.

scholarly journals Variable Search Space Converging Genetic Algorithm for Solving System of Non-linear Equations

2020 ◽  
Vol 30 (1) ◽  
pp. 142-164 ◽  
Author(s):  
Venkatesh SS ◽  
Deepak Mishra
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problems ◽  
Fitness Function ◽  
Linear Equations ◽  
Search Space ◽  
New Variant ◽  
Non Linear ◽  
Coarse Search ◽  
Non Linear Equations ◽  
Digit Length

Abstract This paper introduce a new variant of the Genetic Algorithm whichis developed to handle multivariable, multi-objective and very high search space optimization problems like the solving system of non-linear equations. It is an integer coded Genetic Algorithm with conventional cross over and mutation but with Inverse algorithm is varying its search space by varying its digit length on every cycle and it does a fine search followed by a coarse search. And its solution to the optimization problem will converge to precise value over the cycles. Every equation of the system is considered as a single minimization objective function. Multiple objectives are converted to a single fitness function by summing their absolute values. Some difficult test functions for optimization and applications are used to evaluate this algorithm. The results prove that this algorithm is capable to produce promising and precise results.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

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