The use of continuous genetic algorithm as a novel numerical solver for two-point boundary value problems

الملخص EN

In this paper, the author introduces continuous geneticas easily accepted in the engineering application field.

Third, the proposed methodology has an implicit parallel nature which points to its implementation on parallel machines.

Numerical examples presented in the paper illustrate the applicability and generality of the proposed method.

The effects of various GA operators and control parameters on the convergence speed of the proposed algorithm are also explored.

It is observed that the rank-based selection scheme results in the fastest convergence speed where the rank-based ratio is inversely proportional to the population size used.

Generational replacement schemes outperform overlapping schemes where the number of elite parents that are passed to the next generation is about one-tenth of the population size.

The effects that different crossover rates, mutation rates and population sizes have on the algorithm's convergence speed are also investigated.

Numerical results show that the algorithm works best with relatively high crossover probabilities within the range [0.7, 1] while the best mutation probabilities are close to unity.

A moderate population size is needed to ensure adequate diversity within the population.

At the same time, a reasonable upper limit on the population size is needed to reduce computations.