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AI InsightThe solution found in this paper shows that though genetic algorithm can be used to solve polynomials, other methods like Newton-Ralpson, Secant, Regula-falsi and Bisection can easily guess the solution in a few iterations thereby saving cost and time
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Abstract
A Polynomial Genetic Algorithm (PGA) is a type of evolutionary algorithm used for optimization problems that involve finding the minimum or maximum of a polynomial function. The algorithm is based on the principles of natural selection and genetic recombination and mutation. The algorithm starts by initializing a random population of chromosomes. The fitness of each chromosome is evaluated based on the value of the polynomial function it represents. The fittest chromosomes are selected for reproduction, and their genetic material is combined through crossover and mutation to produce a new generation of chromosomes. One important consideration in using a genetic algorithm for polynomial optimization is the choice of representation for the chromosomes. Binary or integer representations can be used, with each bit or integer representing a coefficient in the polynomial. Alternatively, a floating-point representation can be used, with each chromosome representing a set of coefficients that can be used to construct the polynomial. In summary, to solve a polynomial using a genetic algorithm, we need to define a fitness function that evaluates the fitness of each chromosome based on its ability to represent a good solution to the polynomial, and then use standard genetic algorithm techniques to evolve a population of chromosomes towards a solution. The solution found in this paper shows that though genetic algorithm can be used to solve polynomials, other methods like Newton-Ralpson, Secant, Regula-falsi and Bisection can easily guess the solution in a few iterations thereby saving cost and time