An efficient algorithm via a novel one-parameter filled function based on general univariate functions for unconstrained global optimization

Abstract

The global optimization algorithm based on filled function is considered to be effective for solving global optimization problems, attracting significant attention from scholars due to its strong ability to escape from local minimizers. The performance of this algorithm is directly affected by the properties of the filled function adopted. To improve computational efficiency, a new general form of filled function proposed one-parameter is provided in this paper, which is constructed from the general forms of two unary functions with monotonic properties. Theoretical results demonstrate that the newly-defined function satisfies the definition of filled function, and exhibits better mathematical properties. Based on these properties, a novel filled function algorithm for unconstrained global optimization problems is given. The advantage of this algorithm is that it only needs to minimize the filled function instead of alternately minimizing the objective function and the filled function, which theoretically reduces the number of iterations, and to search the optimal solution of the filled function in the whole search space rather than the neighbourhood of the current local optimal solution, which reduces the search blind spots. The comparison results show that our algorithm has dominant superiority in computational speed and accuracy as well as stability.