<p>This paper focuses on global optimization problems and proposes a novel One-parameter filled function approach. Global optimization problems, which have extensive applications in fields such as engineering, finance, and management, face the core challenge of multiple local minima in the objective function, making it extremely difficult to find the global minimum. The paper first reviews the basic concepts of global optimization problems and the development of the filled function method, analyzing the advantages and disadvantages of existing filled functions. Based on this, a new One-parameter filled function is constructed. This function is simple in form, easy to adjust, and possesses good mathematical properties, effectively assisting the algorithm in escaping from local optimal solutions to search for the global minimum. The construction process of the new filled function is detailed, and it is rigorously proven to meet the definition requirements of a filled function. Subsequently, a global optimization algorithm based on the new filled function is designed, which includes initialization, local optimization, filled function minimization, and iterative update steps, with detailed descriptions for each step. A series of representative test functions are used for numerical experiments, and the new filled function and algorithm are comprehensively evaluated from multiple indicators such as the number of iterations, computation time, and solution accuracy. The experimental results show that the new filled function exhibits superior performance in global optimization problems, capable of finding the global optimal solution with fewer iterations and demonstrating good robustness for different initial values. Although there are still efficiency bottlenecks in handling large-scale problems, this method provides new ideas and approaches for solving global optimization problems.</p>

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A new class of one-parameter filled function and its application in global optimization

  • Zengfu Chao,
  • Xu Niu

摘要

This paper focuses on global optimization problems and proposes a novel One-parameter filled function approach. Global optimization problems, which have extensive applications in fields such as engineering, finance, and management, face the core challenge of multiple local minima in the objective function, making it extremely difficult to find the global minimum. The paper first reviews the basic concepts of global optimization problems and the development of the filled function method, analyzing the advantages and disadvantages of existing filled functions. Based on this, a new One-parameter filled function is constructed. This function is simple in form, easy to adjust, and possesses good mathematical properties, effectively assisting the algorithm in escaping from local optimal solutions to search for the global minimum. The construction process of the new filled function is detailed, and it is rigorously proven to meet the definition requirements of a filled function. Subsequently, a global optimization algorithm based on the new filled function is designed, which includes initialization, local optimization, filled function minimization, and iterative update steps, with detailed descriptions for each step. A series of representative test functions are used for numerical experiments, and the new filled function and algorithm are comprehensively evaluated from multiple indicators such as the number of iterations, computation time, and solution accuracy. The experimental results show that the new filled function exhibits superior performance in global optimization problems, capable of finding the global optimal solution with fewer iterations and demonstrating good robustness for different initial values. Although there are still efficiency bottlenecks in handling large-scale problems, this method provides new ideas and approaches for solving global optimization problems.