Abstract: It is shown that genetic algorithms can be used successfully in problems of definite integral calculation especially when an integrand has a primitive which can't be expressed analytically through elementary functions. A testing of the program, which uses the genetic algorithm developed by authors, showed that the best results are reached if the size of population makes 30-50 chromosomes, approximately 40-60% of its take a part in crossover, and the program stops if the population's leader didn't change during 5-10 generations. An answer of genetic algorithm is more exact than answer received by the classical numerical methods, even if a quantity of partition’s points into segment is small or if an integrand is quickly oscillating. So genetic algorithms can compete both on the accuracy of calculations and on operating time with well-known classical numerical methods such as midpoint approximation, top-left corner approximation, top-right corner approximation, trapezoidal rule, Simpson's rule.

Keywords: definite integral, integral sum, numerical integration, genetic algorithm, fitness-function.

ACM Classification Keywords: F.1.2 COMPUTATION BY ABSTRACT DEVICES: Models of computation – Probabilistic computation. G.1.6 NUMERICAL ANALYSIS: Optimization – Stochastic programming.

Link:

NUMERICAL INTEGRATION BY GENETIC ALGORITHMS

Vladimir Morozenko, Irina Pleshkova

http://www.foibg.com/ijita/vol20/ijita20-03-p07.pdf