Hybrid Artificial Bee Colony Algorithm for Solving Nonlinear System of Equations

Abstract

The paper presents a hybrid algorithm for solving nonlinear system of equations through combining Artificial Bee Colony algorithm and Particle Swarm Optimization algorithm together. Numerical computations show that the hybrid algorithm has feasibility and validity in solving nonlinear system of equations.

A Multi-Simplex Imperialist Competitive Paradigm for Solving Nonlinear Physical Systems

“…Abdollahi et al [24] used the standard imperialist competitive algorithm (ICA), Oliveira et al [25] proposed a variant of simulated annealing algorithm with fuzzy rules adaptations, Wu et al [26] used a new variant of the Social emotional optimization for solving nonlinear systems of equations. Other applications of metaheuristics for nonlinear systems include invasive weed optimization algorithm [27], polarization technique [28], cuckoo optimization algorithm [29], genetic algorithm [30][31][32], artificial bee colony algorithm [33] and multi-population parallel ICA [34] their successful applications, there also exist two main challenges for metaheuristics that are (i) maintaining balance between exploration and exploitation (ii) avoiding large computational cost. Abdollahi et al [35] highlighted that in most of the previous applications [1,[21][22][23][24][25][26]29,30,33,36,37] of metaheuristics to nonlinear systems large population sizes were used which resulted in high computation costs and slow convergence.…”

“…Other applications of metaheuristics for nonlinear systems include invasive weed optimization algorithm [27], polarization technique [28], cuckoo optimization algorithm [29], genetic algorithm [30][31][32], artificial bee colony algorithm [33] and multi-population parallel ICA [34] their successful applications, there also exist two main challenges for metaheuristics that are (i) maintaining balance between exploration and exploitation (ii) avoiding large computational cost. Abdollahi et al [35] highlighted that in most of the previous applications [1,[21][22][23][24][25][26]29,30,33,36,37] of metaheuristics to nonlinear systems large population sizes were used which resulted in high computation costs and slow convergence. To cope with these drawbacks, it is needed to construct an effective and reliable combination of local and global search algorithms for solving nonlinear systems of equations.…”

A Hybrid Approach for Solving Systems of Nonlinear Equations Using Harris Hawks Optimization and Newton’s Method

“…As a result, the hybrid will inherit the advantages and alleviates the weaknesses of both algorithms [27]. Some examples of hybridizing PBAs are the hybrid of the ABC and PSO [28], hybrid GA [29], [30], hybrid FA [31], hybrid PSO [32], hybrid KHA [33], hybrid ABC [34], and many others [36] - [40].…”

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

“…There are many PBAs [31][32][33][34][35][36][37][38] that were used to solve SNLEs such as GA, PSO, ABC, CSA and FA. In [31] Chang proposed an improved real-coded GA for parameters estimation of the nonlinear system.…”

“…They modified the way of updating each particle to overcome the problems of the basic PSO method such as trapping in local minima and slowing convergence. In addition, In [36], Jia and He presented a hybrid algorithm for solving SNLEs through combining ABC algorithm and PSO together. The principle of the hybrid algorithm is using the advantages of both algorithms to ameliorate the defect of slumping into premature or into local optimum.…”