A new filled function method based on adaptive search direction and valley widening for global optimization

Abstract

The filled function methods are a kind of effective method to find the global minimum for optimization problems. However, there exist four limitations to this kind of method: 1) A large number of local minima may take a lot of iterations (time and computation cost) for the methods to find the global minimum. 2) The parameters (if any) in the constructed filled function are difficult to adjust and control. 3) It is hard to select a proper initial point. The initial point can affect the effectiveness of the method greatly. 4) The narrow valleys will make the method difficult to find a more superior minimum. To break the limitations, we use a flatten technique to eliminate a number of local minima firstly. Then we design a new continuously filled function without any adjustable parameter. Moreover, we propose an adaptive strategy for determining the initial points by using uniformly distributed search directions. Furthermore, we propose a narrow valley widening strategy which can make it much easier for the filled function method to get a more superior minimum in the narrow valleys. Based on these strategies, we develop a new effective filled function method. 7 widely used benchmark functions are tested and the performance comparison is made between the developed method and two state-of-the-art filled function methods. The experimental results demonstrate that the developed method in this work is more effective than the compared algorithms for solving global optimization problems.