A class of one-parameter filled functions with the same local minima as the objective function for global optimization problems

Abstract

As an effective global optimization method, the filled function algorithm obtains the optimal solution of optimization problems by alternately minimizing the objective function and filled function. One development direction of the filled function method is to construct the filled function with good properties, which directly affects the efficiency of the algorithm and has attracted the attention of scholars. This paper presents a class of one-parameter filled function that is easy to adjust. It is proved theoretically that the filled function is continuously differentiable and has the same local minimizers as the objective function, and these minimizers are all better than the current local minimizer of the objective function. Meanwhile, some natures of the constructed filled function are conducted as followed by a new algorithm is presented. The new filled function algorithm optimizes the iterative framework of the conventional filled function method, improving the efficiency and decreasing the computational cost. The numerical experiments of the new algorithm on several optimization issues are reported with satisfactory computational results, verifying the feasibility and efficiency of the algorithm.