Mixed Strategy Differential Evolution Based On Fitness Landscapes And Their Applications

Nature is the source of inspiration when we solve various problems.For some more complex problems,new and better solutions can be generated based on natural laws.Evolutionary Algorithm(EA)is a general problem solving method based on this idea.EA uses simple coding techniques to represent a variety of complex structures,and guides learning and determines the direction of search by simply evolving a set of representations and natural selection of the survival of the fittest.EAs have been widely used in the fields of biomedicine,optimization problems,intelligent control,artificial intelligence,image processing,pattern recognition,and big data cloud computing.Differential Evolution(DE)that was recognized as highly competitive in the evolutionary algorithm family as early as more than 20 years ago stand out.They solve problems such as single-objective optimization,constrained single-objective optimization,and multi-objective optimization.DE has many excellent performances in the accuracy of the solution,the convergence speed and the robustness.The fitness landscape is derived from evolutionary biology.In evolutionary computation,fitness landscapes are used to describe the relationship between search solution space and fitness.The purpose of fitness landscape is used to understand the behavior of evolutionary algorithms for solving optimization problems.When the evolutionary algorithm solves a complex optimization problem,the corresponding fitness landscape often has complex characteristics such as non-continuity,non-linearity,multi-peak,and high-dimensionality,etc.In order to more intuitively present the topological information of the optimization problem and help to design a better performance evolutionary algorithm,this thesis introduces a new representation and analysis method of fitness landscapes by studying the relationship between fitness and correlation distance,random walk time series,autocorrelation and information entropy of landscape roughness in local fitness landscape.The primary task of this thesis is to seek the relationship between the topological characteristics of the fitness landscape and evolutionary algorithms.In the field of evolutionary computation,people have designed different search strategies to improve the efficiency of evolutionary algorithms.The efficiency of search strategies depends on the problem itself.More specifically,it relies on the characteristics of local fitness landscapes.According to the no-free lunch theorem in evolutionary optimization theory,the algorithm has a good(bad)search strategy during the optimization process,so a natural idea is to combine mixed search strategies and dynamically select these strategies for searching.From the perspective of fitness landscape,the efficiency of a search strategy is closely related to the characteristics of fitness landscape,Following the game theory,this mixed search strategy is the probability distribution in which each individual or population selects a strategy from a strategy library.Therefore,it must adapt to the fitness landscape.Different search strategies are designed to find the optimal solution of fitness landscapes in traditional evolutionary algorithms,but it is impossible to find a search strategy that can be effective in all kinds of fitness landscapes.Because the fitness landscape corresponding to a complex optimization problem is often composed of different local fitness landscape,and each search strategy is usually only valid for certain types of local fitness landscape.In conclusion,this thesis proposes a differential evolution that integrates fitness landscape and mixed search strategy.The algorithm dynamically adjusts the search strategy according to the characteristics of the local fitness landscape representation and analysis,probabilistically selects a search strategy that is most suitable for a specific local fitness landscape from a strategy library,making this mixed search strategy adaptable to various complex optimizations.The research method based on the integration of fitness landscape and mixed search strategy can improve the global search ability and computational performance,several algorithms proposed in this thesis can be widely used to solve various optimization control problems.In view of the above description,this thesis according to different optimization problems puts forward the differential evolution algorithm based on fitness landscape and mixed search strategies.The main work and novelty are as follows:(1)This thesis proposes an algorithm design method that combines the fitness landscape and the mixed search strategy.This method uses various fitness landscape representation methods to analyze the topological characteristics.The relationship between local fitness landscape and mixed search strategies are transformed into a conditional probability distribution.The reinforcement learning is used to learn the optimal hybrid strategy adapted to observe the local landscape.The local fitness landscape strategy is extended to a global search space by a random walk,so as to design a differential evolution suitable for solving various optimization problems.(2)A fitness distance correlation differential evolution(FDCDE)for single-objective optimization problems is presented.According to the theory of fitness distance correlation,the representation and analysis of the correlations between fitness and local landscape distance are quantified.The classification analysis of the optimization problems is carried out by using the fitness distance correlation coefficient and extracting the uni-modal and multimodal landscape features.Using the reinforcement learning strategies to determine the optimal probability distribution from the characteristics of the fitness landscape to the search strategy set.The proposed algorithm solves the single-objective optimization problem more comprehensively,avoids falling into the local optimum and improves the algorithm accuracy and convergence speed.(3)A fitness landscape ruggedness differential evolution(FLRDE)for constrained single-objective optimization problems is proposed.The algorithm strategy is to calculate the characteristics of the fitness autocorrelation function by analyzing the global topology information,adjust the time-series sensitive parameters based on the random walk using the fitness landscape roughness analysis method of information entropy,and calculate the information entropy value by the string of the time series.According to the relationship between the fitness landscape roughness and the optimal solution distribution,design a mixed mutation strategy to determine the optimal probability distribution from fitness landscape roughness to the set of search strategy by information entropy.The proposed algorithm is superior to the traditional evolutionary algorithm in solving the constrained single-objective optimization problems,not only can solve the local optimal problem,but also can accurately calculate the global optimal solution.(4)A hybrid fitness landscape differential evolution(HFLDE)for solving multiobjective optimization problems is presented.The proposed algorithm combines the fitness landscape characteristics representation and analysis methods,analyzes the correlation between multiple fitness landscape and distances,calculates fitness distance correlation coefficients of multiple fitness landscape and predicts the difficulty.According to the relationship between the fitness landscape roughness and the optimal solution distribution,extract the uni-modal and multi-modal landscape features of the information entropy,and combines the reinforcement learning method to determine the optimal probability distribution of the search strategy set of the algorithm,and then guides the search strategy to judge the influence of the objective function search weight,thereby designing the hybrid fitness landscape differential evolution for solving multi-objective optimization problems.The experimental data analysis results show that this proposed algorithm can solve the problem of search redundancy when solving multi-objective optimization problems,effectively improve the performance of the search algorithm in the optimization process.(5)The fitness distance correlation differential evolution is applied to solve the soil moisture management in the precision agriculture.This algorithm is used to fit the Van Genuchten equation parameters,comparing and verifying other existing algorithms.The purpose is to use this evolutionary algorithm that combines fitness landscapes and mixed search strategies to promote and solve other optimization control problems in precision agriculture.