Novel filled function algorithm without parameters for unconstrained global optimization

<p style="text-align:center;"> <strong>(Communicated by Changjun Yu)</strong> <p style="text-align:justify;"> Many optimization problems modelled from actual problems have multiple global or local minimizers, which makes traditional optimization algorithms easily plunge into the local minimizer. The filled function algorithm is an effective method for such problems, which transforms the objective function into a filled function with special properties at the current local minimizer. By iteratively minimizing the objective and the filled function, the filled algorithm can gradually discover better local minimizers until the global minimizer is obtained. Hence, constructing new forms of filled function is a popular research direction, which can improve the performance of the filled function algorithm. A new parameter-free filled function with some advantages is constructed and the corresponding theoretical analyses are conducted in this paper. Firstly, its local minimizers are those of the objective function. Secondly, the current local minimizer of the objective function is the global maximizer of the proposed filled function. Based on the proposed filled function, a new global optimization algorithm without parameters to tune is given, which can avoid alternately solving the objective function and the filled function. The new algorithm is applied to solve several test functions with satisfactory experimental results, which show that the proposed algorithm is more efficient compared to the existing filled function algorithm.