Applying genetic algorithms for solving nonlinear algebraic equations

Pourrajabian, Abolfazl; Ebrahimi, Reza; Mirzaei, Mehran; Shams, Mehrzad

doi:10.1016/j.amc.2013.05.057

Cited by 43 publications

(34 citation statements)

References 11 publications

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“…Consider the following system of equations: (1) We rewrite the system (1) as the following set of constraints…”

Section: Preliminariesmentioning

confidence: 99%

“…can be used as a precondition for checking the constraints at some X i . Namely, the constraints should not be checked at any substitution X i for which proposition (1) holds. Observe if the substitution X i does not satisfy proposition (1)…”

Section: Proofmentioning

confidence: 99%

“…Researchers have proposed many methods for solving systems of equations [1] [7] [8] (see [5] for a good discussion of these methods). These methods either solve the equations directly by applying numerical methods [4] [9][10] [11] [17] [23] or solve them indirectly by transforming the system of equations into problem optimization [2] [3][4] [5] [12] [16] [19] [22].…”

Section: Introductionmentioning

confidence: 99%

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Probability-Directed Problem Optimization Technique for Solving Systems of Linear and Non-Linear Equations

Al-Muhammed¹

2019

Computer Science &Amp; Information Technology (CS &Amp; IT )

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Although many methods have been proposed for solving linear or nonlinear systems of equations, there is always a pressing need for more effective and efficient methods. Good methods should produce solutions with high precision and speed. This paper proposed an innovative method for solving systems of linear and nonlinear equations. This method transforms the problem into an optimization problem and uses a probability guided search technique for solving this optimization problem, which is the solution for the system of equations. The transformation results in an aggregate violation function and a criterion function. The aggregation violation function is composed of the constraints that represent the equations and whose satisfaction is a solution for the system of equations. The criterion function intelligently guides the search for the solution to the aggregate violation function by determining when the constraints must be checked; thereby avoiding unnecessary, timeintensive checks for the constraints. Experiments conducted with our prototype implementation showed that our method is effective in finding solutions with high precision and efficient in terms of CPU time.

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“…Consider the following system of equations: (1) We rewrite the system (1) as the following set of constraints…”

Section: Preliminariesmentioning

confidence: 99%

Section: Proofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Probability-Directed Problem Optimization Technique for Solving Systems of Linear and Non-Linear Equations

Al-Muhammed¹

2019

Computer Science &Amp; Information Technology (CS &Amp; IT )

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show abstract

“…where i ∈ ℝ and each F i : ℝ → ℝ is a nonlinear real function. Pourrajabian et al (2013), solving of NAEs is a prominent problem in science and engineering. According to Liu & Atluri (2008a), we have a new method to reformulate of the complementarity problem (4) as the system of NAEs like as the equation below…”

Section: Introductionmentioning

confidence: 99%

An ordinary differential equation approach for nonlinear programming and nonlinear complementary problem

Nurhidayat

Zhang

Chu-Chin

et al. 2020

Int. J. Ind. Optim.

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We consider an ordinary differential equation (ODE) approach for solving non- linear programming (NLP) and nonlinear complementary problem (NCP). The Karush- Kuhn Tucker (KKT) optimality conditions can be converted to NCP. Based on the Fischer-Burmeister (FB) function and the Natural-Residual (NR) function are obtained the new NCP-functions. A special technique is employed to reformulate of the NCP as the system of nonlinear algebraic equations (NAEs) later on reformulated once more by force. of an original time-like function into an ODE. Afterwards, a group preserving scheme (GPS) is a package to reformulate an ODE into the new numerical equation in a way the ODEs system is designed into a nonlinear dynamical system (NDS) and is continued to a discovery the new numerical equation through activating the Lorentz group SO0(n, 1) and its Lie algebra so(n, 1). Lastly, the fictitious time integration method (FTIM) is utilized into this new numerical equation to determine an approximation solution at the numerical experiments area.

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“…Evolutionary algorithms have been applied to a wide variety of engineering problems [1], and they have also been applied to mathematics problems. For instance, Jong and Spears [2] showed that Genetic Algorithms (GA) can be used to solve NP-Complete problems, [3] applied a GA to a geometry problem, and [4] solved nonlinear algebraic equations by using a GA. Here we have successfully applied a Rank Genetic Algorithm (Rank GA) [5] to the graph theory problem of finding the rainbow connection number of a graph ( ( )).…”

Section: Introduction and Definitionsmentioning

confidence: 99%

Rainbow Connectivity Using a Rank Genetic Algorithm: Moore Cages with Girth Six

Cervantes‐Ojeda

Gómez

González-Moreno

et al. 2019

Journal of Applied Mathematics

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A rainbow t-coloring of a t-connected graph G is an edge coloring such that for any two distinct vertices u and v of G there are at least t internally vertex-disjoint rainbow (u,v)-paths. In this work, we apply a Rank Genetic Algorithm to search for rainbow t-colorings of the family of Moore cages with girth six (t;6)-cages. We found that an upper bound in the number of colors needed to produce a rainbow 4-coloring of a (4;6)-cage is 7, improving the one currently known, which is 13. The computation of the minimum number of colors of a rainbow coloring is known to be NP-Hard and the Rank Genetic Algorithm showed good behavior finding rainbow t-colorings with a small number of colors.

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Applying genetic algorithms for solving nonlinear algebraic equations

Cited by 43 publications

References 11 publications

Probability-Directed Problem Optimization Technique for Solving Systems of Linear and Non-Linear Equations

Probability-Directed Problem Optimization Technique for Solving Systems of Linear and Non-Linear Equations

An ordinary differential equation approach for nonlinear programming and nonlinear complementary problem

Rainbow Connectivity Using a Rank Genetic Algorithm: Moore Cages with Girth Six

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