Research On Hybrid Differential Evolution Algorithms And Their Applications For Earth-Moon Low-Energy Transfer Trajectory Design

As the first step of deep space exploration,lunar exploration has been attracting much attention.For long-term unmanned driving tasks,time is no longer an important consideration,while reducing energy consumption is crucial.Therefore,low energy transfer trajectory design is necessary in this situation.When only energy consumption is considered,the Earth-Moon low-energy transfer trajectory design problem can be regarded as a typical single-objective numerical optimization problem.However,the characteristics on the search space of the Earth-Moon low-energy transfer trajectory design problem varies in regions.There are many local optimal solutions in the entire search space,some local optimal solutions change smoothly and have large attracting basins,and the regions where high-quality solutions are located are sensitive and small in attracting basins,which put forward certain requirements on both the global search ability and the local search ability of the optimization algorithm.Differential Evolution algorithm is a kind of population based stochastic numerical optimization method,which is easy to implement because of its simple structure and easy to use with few control parameters.It has always been favored for single-objective optimization problems.However,as an optimization algorithm with search as the core,the most fundamental problem faced by Differential Evolution algorithms is the balance between the exploration ability in the global and exploitation ability at the local.Compared with its outstanding performance in the exploration ability,the convergence speed of Differential Evolution algorithm is relatively slow during the later stage of the evolution,and the exploitation ability in a small local area is relatively insufficient.At the same time,Differential Evolution algorithm has a large number of evolution operators,and different operators have different effects on the exploration and exploitation.The setting of its control parameters also depends on specific optimization problems and different stages of evolution.At present,although the adaptive strategies of the scaled factor and crossover factor are becoming more and more perfect,there are still relatively few studies on adaptive control of the population size.In view of the above reasons,this article will study the hybrid differential evolution algorithm from the level of algorithm,the level of evolution operator and the level of evolution strategy.In summary,the main research contents and innovations of this article are as follows.(1)Aiming at the problem of slow convergence and relatively insufficient local search ability of Differential Evolution algorithm in the later stage of evolution,a Differential Evolution with Mix Strategies and Population Restart is proposed.Firstly,at the algorithm level,the Differential Evolution algorithm is hybiridized with the local search algorithm Sequence Quadratic Programming.Secondly,the Differential Evolution algorithm adopts two types of mutation crossover operators in stages.At the same time,it also introduces a population restart strategy in consideration of the different search results of the local search algorithm.Through experiments and analysis on the standard test set,the improved strategy in this algorithm is conducive to improving the local search capability of the differential evolution algorithm and speeding up the convergence speed of the algorithm.(2)In view of the different effects of different mutation/crossover operators and population size settings on the exploration and explotation abilities,a Population EntropyBased Adaptive Differential Evolution with Multiple Strategies is proposed.The algorithm first defines the method to calculate the population entropy,and judge the population distribution state at each stage of the evolution according to the changes of the population entropy,so as to adopt mutation/crossover operators and adjust the population size in a targeted manner.Through experimental analysis,it is verified that the corresponding strategy in the algorithm is effective to further balance the exploration and development capabilities of the differential evolution algorithm.(3)Aiming at the influence of mutation operator and population initialization strategy on the exploration and development capabilities of differential evolution algorithm,a Uniform Initialization-Based Adaptive Differential Evolution with Multiple Strategies is proposed.First of all,the uniform initialization strategy is adopted in the early stage of evolution to spread the population as much as possible to the entire search space,so as to give full play to the exploration capabilities of the algorithm in the early stage of evolution.Secondly,a basic mutation operator is adopted in the early stage of evolution,and as the evolution progresses,a floating mutation operator and a random population jumping strategy are adopted according to the update of the optimal solution at different stages of evolution.Through experimental analysis,the algorithm can effectively play the exploration ability in the early stage of evolution,and can effectively improve the development ability in the later stage of the evolution,thereby further improving the search result.(4)At present,the earth-moon low-energy transfer trajectory design problem is mainly solved by some deterministic numerical optimization methods and classic stochastic optimization methods.However,considering the multiple local optimums,space sensitivity of the high-quality solutions region in the search space,and some local optimal solution regions with large attractive basins,the use of hybrid differential evolution algorithm will be more advantageous,and for the changing characteristics of the entire search space,the use of adaptive control parameters will also be more favorable.The algorithms in(1),(2)and(3)are applied to the Earth-Moon low-energy transfer trajectory design.At the same time,the two-dimensional and three-dimensional physical models based on the problem are discussed separately.And under different search space settings,the analysis of the stability and stress resistance of these three algorithms on the earth-moon low-energy transfer trajectory design problem is realized.The performances of these three algorithms in different situations are also discussed.