Abstract
Differential evolution (DE) has been widely applied to complex global optimization problems. Different search strategies have been designed to find the optimum conditions in a fitness landscape. However, none of these strategies works well over all possible fitness landscapes. Since the fitness landscape associated with a complex global optimization problem usually consists of various local landscapes, each search strategy is efficient in a particular type of fitness landscape. A reasonable approach is to combine several search strategies and integrate their advantages to solve global optimization problems. This paper presents a new self-feedback strategy differential evolution (SFSDE) algorithm based on fitness landscape analysis of single-objective optimization problem. In the SFSDE algorithm, in the analysis of the fitness landscape features of fitness-distance correlation, a self-feedback operation is used to iteratively select and evaluate the mutation operators of the new SFSDE algorithm. Moreover, mixed strategies and self-feedback transfer are combined to design a more efficient DE algorithm and enhance the search range, convergence rate and solution accuracy. Finally, the proposed SFSDE algorithm is implemented to optimize soil water textures, and the experimental results show that the proposed SFSDE algorithm reduces the difficulty in estimating parameters, simplifies the solution process and provides a novel approach to calculate the parameters of the Van Genuchten equation. In addition, the proposed algorithm exhibits high accuracy and rapid convergence and can be widely used in the parameter estimation of such nonlinear optimization models.
Highlights
The fitness landscape is a new theory proposed by the theoretical biologist Sewall Wright that regards evolution as a process of movement or adaptive migration in a threedimensional landscape with basins and valleys (Wright 1932)
The fitness landscape predicts the performance of the algorithm, and the study of the fitness landscape will aid in the design of improved evolutionary algorithms
The self-feedback strategy differential evolution (SFSDE) algorithm is compared with methods in three other references and three standard differential evolution (DE) methods
Summary
The fitness landscape is a new theory proposed by the theoretical biologist Sewall Wright that regards evolution as a process of movement or adaptive migration in a threedimensional landscape with basins and valleys (Wright 1932). The concept of the fitness landscape was initially used for biological evolution optimization dynamics, which has a very important role in the analysis and understanding of evolutionary algorithms. When the evolutionary algorithm is used to solve complex optimization problems, the corresponding landscape of fitness is usually complex. Each point in the landscape represents a possible gene combination, and the height of each point denotes the fitness. Due to differences in the fitness of different gene combinations, these features present a rugged landscape of mountains and valleys, which we call a fitness landscape. The fitness landscape is a commonly used metaphor for expressing the features of evolutionary algorithms in solving complex problems. We discuss the concept of a fitness landscape and analyze and extract the features of such a landscape, which will help scholars design and optimize the performance of evolutionary algorithms
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