Research On Optimization Method For Differential Evolution And Its Application To Flight Conflict Resolution

Intelligent optimization technology,as an important research direction in the field of artificial intelligence,has become one of the most important means of solving many complex optimization problems due to its advantages of global search and efficient parallelism.As an important branch of intelligent optimization technology,Differential Evolution(DE)is a population-based global search method,which has the advantages of simple principle,few control parameters,high optimization performance,and good robustness.It provides a new idea for solving the high-dimensional complex optimization problem of flight conflict resolution.However,DE has the problems of slow convergence speed and low convergence accuracy when solving high-dimensional complex optimization problems,thus limiting its practicality.In view of this,this thesis conducts the research on relevant optimization methods to address the existing problems of DE,and studies the construction of flight conflict resolution method on this basis.The main efforts are as follows:(1)To address the problem that improper population size setting of DE is likely to cause an imbalance between convergence speed and population diversity,which makes it difficult to ensure the convergence and stability of the algorithm,a population size reduction method with individual similarity(PRS)is proposed.The method utilizes a linear differential decrease strategy and an individual similarity-based elimination mechanism to ensure the number and quality of the population in each generation,thus further accelerating population convergence while ensuring search diversity.Meanwhile,since the population size directly affects the individual selection in the mutation strategy,thus affecting the individual mutation process,PRS introduces an elite-oriented strategy to appropriately adjust the individual selection method,which can provide a clear guidance for individual evolution,avoid search blindness,and accelerate convergence speed.Wilcoxon and Nemenyi tests with significance levels of 5% and10% on the IEEE CEC2014 test set consisting of 30 benchmark functions with different characteristics are performed.The experimental results show that the proposed PRS method can effectively give attention to both convergence speed and solution quality,significantly improve the optimization performance of the basic DE and improved DE algorithms,and obviously outperform other population size reduction methods.(2)To address the problem of mutation strategy selection for DE,a backtracking differential evolution with multi-mutation strategies autonomy and collaboration(b DE-Ms AC)is proposed from the perspective of balancing global exploration and local exploitation,which aims to meet the demand for search capability at different evolutionary stages by integrating the advantages of different mutation strategies.The algorithm uses the elite-oriented strategy to improve five mutation strategies,and constructs the global exploration strategy domain(GED)and local exploitation strategy domain(LED),while introducing a mechanism of multimutation strategies autonomy and collaboration to achieve the complementary advantages and co-evolution between GED and LED.Considering the influence of control parameters in the mutation strategy on the individual search process,a control parameter adaptation strategy based on individual similarity and individual evolutionary state is designed to improve the applicability and convergence of the algorithm.In addition,an evolution backtracking strategy is introduced to adaptively intervene in the evolutionary process of the population,and the population can trace back to the generation with maximum best fitness descent and then change the search direction,thus enhancing the search ability of the algorithm.The experimental results indicate that the proposed b DE-Ms AC can effectively integrate the search advantages of different mutation strategies to balance exploration and exploitation of different evolutionary stages,and has stronger competitiveness.(3)Aiming at the problem that the population diversity of DE is affected by population structure,a differential evolution with variable leader-adjoint populations(v LADE)is proposed from the perspective of multi-population collaboration.The algorithm uses a variable leaderadjoint population model to divide the entire population into a leader population and an adjoint population,and assigns different mutation strategies according to their role positions.The leader population focuses on exploitation and employs a new DE/current-best-rand/1 mutation strategy to improve the convergence speed,thus ensuring its dominant position throughout the population;While the adjoint population focuses on exploration and adopts an improved DE/rand/1 mutation strategy that can not only promote its rapid evolution toward promising regions but also enhance population diversity.The two populations evolve synergistically through individual exchange and sharing,while maintaining independent and autonomous evolution.The experimental results show that v LADE can effectively regulate the population diversity during the evolutionary process by utilizing the advantage of multi-population collaboration,enhancing the global exploration and local exploitation of the algorithm.(4)The flight conflict resolution problem has high requirements on the performance of the conflict resolution method,and it is difficult to effectively solve the problems of premature convergence and evolution stagnation that limit the practicality of DE by only adopting a single improvement method as described above,thus failing to guarantee the conflict resolution effect and quality.To this end,an enhanced leader-adjoint differential evolution algorithm(LADE)is proposed by combining the advantages of the above-mentioned improved methods.The algorithm adopts a heterogeneous dual-population strategy constructed by the leader-adjoint model to divide the population in each generation into leader population and adjoint population,and utilizes the population size reduction method to improve convergence.Based on the collaboration advantage of multi-mutation strategies,two mutation strategies with stronger exploration ability are assigned to the leader population to enhance search diversity and avoid premature convergence;Also,two mutation strategies with stronger exploitation ability are assigned to the adjoint population to accelerate convergence and avoid evolution stagnation.The experimental results on 10-dimensional,30-dimensional,50-dimensional,and 100-dimensional IEEE CEC2017 benchmark functions demonstrate that the proposed algorithm has stronger convergence performance and exhibits stronger competitiveness;The simulation results on a test set consisting of 22 low,medium,and high-dimensional real-world optimization problems indicate that LADE is able to obtain faster search speed and higher solution quality,and has strong practicality.(5)Research on the application of LADE algorithm to flight conflict resolution is carried out.Firstly,considering the strong correlation and collaboration among multiple aircraft,a multi-objective flight conflict resolution optimization model based on the shortest total route length,shortest offset distance,and minimum flight delay is constructed.Meanwhile,the interval number analytic hierarchy process(IAHP)is used to determine the weight of each objective,ensuring the optimal comprehensive cost of conflict resolution.Secondly,since DE uses real-number coding to optimize in continuous space,it is difficult to solve the discrete optimization problem of flight conflict resolution.Therefore,based on the resolution strategies of heading adjustment,speed adjustment,and altitude adjustment,an individual coding scheme is designed using integer encoding,and the basic operations of DE are discretized.Then,flight scenarios with different conflict characteristics are designed according to the flight conflict category,and the discrete LADE is used to perform conflict resolution experiments under different conflict resolution schemes.The results demonstrate that LADE can achieve 100%resolution success rate in different flight conflict scenarios,and in particular,it is able to obtain higher solution accuracy within 200 generations by utilizing the altitude adjustment scheme.Overall,LADE is an efficient flight conflict resolution method,and shows competitive advantages in terms of convergence speed,solution accuracy,and robustness,effectively reducing the conflict resolution cost and achieving multi-aircraft collaborative resolution;Meanwhile,the rationality and effectiveness of the conflict resolution optimization model are verified.