An interactive evolutionary improved whale algorithm and its convergence analysis

Aiming at the disadvantages of the whale algorithm, such as poor stability, slow convergence speed and easy to fall into local extremum, a two-population interactive evolutionary whale algorithm with roulette selection and the quadratic interpolation mechanism is proposed. The roulette selection mechanism is introduced in the searching and foraging stage, which effectively avoids the problem that the poor solution is selected several times and ensures the convergence performance of the algorithm. In the evolutionary structure and solution process of the algorithm, the population of two different evolutionary mechanisms and the continuous information interaction between them are used to balance and adjust the global search and local search ability of the algorithm effectively. The quadratic interpolation strategy is used to update the position of the whale individuals after the evolution update of the two populations and before the information exchange, which increases the diversity of the population, and then the optimal selection of new positions improves the convergence rate of the algorithm. Then the algorithm flow is given and the convergence of the algorithm is proved using the probability measure method. Finally, six representative algorithms are used to simulate different characteristic functions in the CEC2017 test function suite in multiple dimensions. The results show that the improved algorithm has better convergence speed, optimization precision and solution stability, and has good convergence performance. © 2023 Northeast University. All rights reserved.