Abstract: The filled function method, as an effective approach for solving global optimization problems involving multivariable and multimodal functions, finds the global optimal solution or approximate global optimal solution by alternately minimizing the objective function and the filled function. Its optimization performance is directly related to the properties of the filled function employed. Consequently, constructing novel filled functions with good mathematical properties has always been a significant hot research. However, existing filled functions present the following issues: they with discontinuity and non-differentiability are not easily solvable; they contain many parameters that are difficult to control and adjust; they include exponential or logarithmic terms affecting the efficiency of the algorithm. To address these shortcomings, the F-C function for solving unconstrained global optimization problems is introduced by combining the filled function with the cross function. Based on this definition, a new single-parameter F-C function is constructed, and the parameter is easily adjustable during the iterative process. By the theoretical properties analysis, a new global optimization F-C function method using the F-C function is proposed, which breaks the solving framework of traditional filled function algorithms, reduces the numbers of solving the objective function, and improves computational efficiency. The effectiveness and feasibility of the F-C function algorithm are verified through several numerical computations. Finally, the F-C function algorithm is applied to optimize parameters in cutting temperature experiments. The numerical experiment results showed that the proposed algorithm has better fitting effect compared with previous findings.

Key words: global optimization, filled function, cross function, F-C function, cutting temperature