Сравнение генетических алгоритмов MOGA и NSGA-II на задаче оптимизации формы рабочего колеса гидротурбины

Abstract

Проведено сравнение генетических алгоритмов MOGA и NSGA-II на тестовых задачах и задаче оптимизации формы рабочего колеса гидротурбины. Рассмотрен модифицированный алгоритм NSGA-IIm, в котором операторы рекомбинации и мутации заимствованы из MOGA. Для сравнения скорости сходимости алгоритмов использована метрика, характеризующая расстояние от приближенного фронта Парето до точного. Представлены результаты решения тестовой задачи Purpose. The main goal of this article is to compare two popular multi-objective genetic algorithms MOGA and NSGA-II by solving test problems and a practical problem of hydraulic turbine runner optimization. Modification of NSGA-II called NSGA-IIm is also considered. The major problem is to compare convergence rates of approximate solution to the exact Pareto front. Methodology. The genetic algorithms MOGA and NSGA-II are described in detail. The modified algorithm NSGA-IIm is NSGA-II with the recombination and mutation operators taken from the MOGA algorithm. The known problems ZDT3 (2 objectives, 30 and 12 parameters, no constraints) and OSY (2 objectives, 6 parameters, 6 constraints) are taken as test problems. These algorithms are compared by solving runner optimization problem with 24 free parameters and 2 or 3 objectives. To compare the algorithms, a metric characterizing the distance from the approximate Pareto front to the exact one is introduced. Since the algorithms are stochastic in nature, the value of the metric was averaged over 100 runs of the algorithm. In the two-objective runner optimization problem the metric value was averaged over 3 runs of the algorithm. Findings. Solving the test problems, it was found that in the first 50 generations the MOGA algorithm converges faster than other algorithms, but after 50 generations the NSGA-II algorithm has shown the best result. The MOGA algorithm gives an approximate front containing more solutions than NSGA-II. When solving the two-objective and the three-objective runner optimization problem the similar results were obtained. The approximate Pareto front, obtained by the MOGA algorithm, is distributed more uniformly than other algorithms and contains a larger number of solutions. The advantage of the algorithms NSGA-II and NSGA-IIm is a slightly better definition of extreme values of target functionals. However, the obtained differences are not very significant. Originality/value. Obtained results show that both MOGA and NSGA-II are very similar in terms of convergence rate and can be applied for solving complex engineering problems.