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In recent years, higher-order boundary value problems (BVPs) have received much attention from researchers and scientists due to the fact that most phenomena in engineering, physiology and astrophysics are modeled by higher-order BVPs. Although there are various analytical and numerical methods for solving higher-order boundary value problems, these classical methods have their own disadvantages such as the initial approximation, low accuracy and a large number of required integrals. Therefore, many researchers are interested in exploring alternative methods to those traditional techniques; some of which are metaheuristic algorithms.
The genetic programming (GP), which is one of the metaheuristic algorithms, belongs to the population-based techniques and simulates the Darwin's principle in evolution and natural selection.
Many research literatures dealing with higher-order boundary value problems, including:
The power series approximation method (Njoseh & Mamadu, 2016) that has been proposed for the numerical solution of a generalized linear and non-linear higher order BVPs. The homotopy analysis method (Siddiqi and Iftikhar, 2013a) is used for solving seventh-, eighth-, and tenth-order BVPs to obtain the approximate solutions. Siddiqi and Ifikhar (2013b) used the variation of parameter method to find the analytical solutions of the seventh-order BVPs. The non-polynomial spline technique to solve the eighth-order boundary value problem is presented by Siddiqi and Twizell (2007).
Inc & Evans (2004) introduced the solutions of the eighth-order boundary value problems depending on the Adomian decomposition method.
Golbabai and Javidi (2007) employed the homotopy perturbation method (HPM) to solve the eighth-order boundary value problems. Malik et al. (2013, 2014) applied an evolutionary computing scheme of hybrid genetic algorithm for solving biochemical reaction and singular boundary value problems arising in physiology. Arqub et al. (2012, 2014) implemented the continuous genetic algorithm to get the numerical solutions of boundary value problems. Sabir et al. (2019) proposed a hybrid combination of the genetic algorithm (GA) and the interior point method (IPA) to solve Lane-Emden problems. Entesar et al. (2019) presented a new hybrid technique which combined the homotopy analysis method (HAM) with the genetic algorithm for solving fractional partial differential equations. Kharrat et al. (2020a) extended the application of the genetic algorithm for solving singular boundary-initial value problems arising in physiology applications. Navarro and Aguayo (2018) solved ordinary differential equations depending on the genetic algorithms and the Taylor series matrix method to solve ordinary differential equations. Hussain and Abdul-Abbass (2018) suggested a modified genetic algorithm for ordinary and partial differential equations. A genetic programming scheme, which is applied to obtain the solution of boundary value problems for nonlinear partial differential equations arising in hydrodynamic applications, was also proposed by Kharrat et al. (2020b). Saber et al. (2021) implemented an integrated intelligent computing platform to solve the second order nonlinear differential equations numerically.