一类新的单参数F-C函数及其应用  

A New Class of Single Parameter F-C Functions and Its Application

作　　者：李硕 尚有林[1] 屈德强 LI Shuo;SHANG Youlin;QU Deqiang(School of Mathematics and Statistics,Henan University of Science and Technology,Luoyang 471023;Business School,University of Shanghai for Science and Technology,Shanghai 200093)

机构地区：[1]河南科技大学数学与统计学院,洛阳471023 [2]上海理工大学管理学院,上海200093

出　　处：《工程数学学报》2024年第3期494-506,共13页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(12071112,11471102);河南省高等学校重点科研项目计划基础研究专项(20ZX001).

摘　　要：填充函数法作为可以有效求解多变量、多极值函数的全局最优化方法,通过交替求解目标函数和填充函数找到问题的全局最优解或近似全局最优解,其寻优能力与所采用的填充函数性质有直接关系。因此,构造具有良好数学性质的填充函数新形式一直都是填充函数法的重要研究领域。然而,当前已有的填充函数存在以下问题:填充函数不连续不可微;参数过多难以控制和调整;包含指数项或对数项。为解决上述不足,将填充函数和跨越函数相结合,引入求解无约束全局优化问题的F-C函数定义。根据此定义,构造一类新的单参数F-C函数,此参数在迭代过程中易于调节。在分析该函数理论性质的基础上,提出新的全局优化F-C函数方法,该算法打破传统填充函数算法的求解框架,成功减少求解目标函数的次数,提高计算效率。通过数值计算验证F-C函数算法的有效性和可行性。最后,用F-C函数算法对切削温度实验中的参数进行优化,并与已有结果进行比较,数值试验结果表明该算法具有更好的拟合效果。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.

关 键 词：全局最优化 填充函数 跨越函数 F-C函数 切削温度 

分 类 号：O221.2[理学—运筹学与控制论]