Adaptive hybrid optimization method for valley functions in weight minimization problems for wind turbine blades

Abstract

The article proposes an adaptive method for finding the minimum of an arbitrary smooth multivariable function. The method has been used to solve the benchmark optimization problem of a valley function. The essence of the proposed algorithm lies in the sequential approach to the bottom of the valley and the subsequent movement in the direction of decreasing the objective function. The comparison of the results of calculating the minimum point of the function is performed by using both non-gradient and gradient methods, namely: Powell, Hook-Jeeves, the steepest descent method and the method developed. It has been found that the effectiveness of the proposed method is greater than the usual search algorithms, but it is not without its drawbacks. The method that represents a number of hybrid methods, which form a hybrid coalition is proposed. The proposed hybrid algorithm does not provide a satisfactory result in the "single" search. The search algorithm reaches a point where all the values of the function at the surrounding points are greater than the values at the obtained point, and the algorithm cannot overcome the barrier. To solve the problem, it is necessary to take the obtained point as a new starting point and repeat the algorithm for finding the minimum of the function, that is, use the multistart method. The proposed method has been used to solve the problem of optimizing the blade of a wind turbine, which was reduced to the problem of unconditional optimization by using the method of penalty functions, but the goal function had a significantly valley structure. The optimal values of section thicknesses have been obtained, which makes it possible to build a blade with improved characteristics.