Differential Evolution Algorithm With The Fitness-distance Archiving Mechanism For Dynamic Optimization Problems

Many optimization problems in reality are dynamically changing,and their objective functions change over time,causing the optimal solutions to change continuously,making it difficult for static optimization algorithms to adapt to this dynamic environment.To meet this challenge,several dynamic optimization algorithms have been proposed in recent years,and by designing different types of dynamic environment handling methods,the algorithms are equipped with the ability to track the continuously changing optimal solutions.In these related works,a significant number of algorithms exploit the correlation between successive environments to design archiving mechanisms as dynamic environment processing methods.However,existing archiving mechanisms have two additional shortcomings: 1)When constructing archives,only the fitness information of individuals is considered,while the distance information between individuals is ignored,making the excellent individuals on the same peak to be saved repeatedly;2)When using archives,only the archived individuals are utilized after the environment changes,resulting in the beneficial information of archived individuals not being fully utilized.To this end,this paper designs a fitness-distance archiving mechanism,providing two implementations from the perspective of single and dual archiving,respectively,which takes into account both fitness and distance information when constructing archives,and utilizes archived individuals both before and after environmental changes.The main work and contributions of this paper are as follows:(1)A differential evolution algorithm based on a single-archive with fitnessdistance is proposed,named DIGDE.In DIGDE,a multi-population mechanism is firstly used to search each region separately,and a predefined threshold is used to judge whether the subpopulation converges or not,and then the optimal individuals of the subpopulation that converge to different peaks are archived,so that the archived individuals have good adaptability and a distance can be maintained between individuals.When using archiving,before the environment changes,the oppositionbased strategy is used to expand the search range of the population,while when the environment changes,new individuals are generated by a Gaussian perturbation strategy for guiding the search.In addition,in order to further improve the search ability of the algorithm,two different mutation strategies are adaptively adopted according to the population search range.In order to verify the performance of DIGDE,a large number of experiments are carried out on the well-known moving peak benchmark problem,and the performance is compared with five well-known dynamic optimization algorithms.The results show that DIGDE has strong competitiveness.(2)A differential evolution algorithm based on a dual-archive with fitness-distance is proposed,named FDADE.Unlike DIGDE,two archives are designed in FDADE at the same time,and corresponding archives are constructed for the fitness information and distance information of individuals,respectively.The excellent individuals with better fitness are saved in the fitness archive,while the excellent individuals meeting the distance requirement are saved in the distance archive.When using archives,a dualarchive cooperative strategy is designed to use different archives utilization at different stages of the algorithm to balance the exploration and exploitation capabilities of the algorithm before the environment changes,and when the environment changes,a dualarchive bootstrap strategy is designed for generating populations in the new environment,which enables the algorithm to preserve the search experience and helps to further accelerate the convergence of the algorithm.Extensive experiments have been conducted on well-known moving peak benchmark problems to compare the performance with DIGDE based on a single-archive mechanism and five well-known dynamic optimization algorithms,and the results show that FDADE performs better.(3)In order to further verify the performance of the algorithm in this paper in solving the actual dynamic optimization problem,relevant experiments are carried out on the dynamic economic dispatch problem of electric power.In this problem,the performance of the optimization algorithm is challenged by the different load demands at different time periods and the existence of valve point effect and climbing rate limitation of the generator set,which makes the objective function of optimization have high dimensional and nonlinear difficulties.In this paper,the problem is solved from the perspective of dynamic optimization.In the experiment,the generation cost of five generating units under 24 time periods is solved,and the results are compared with four dynamic optimization algorithms and one static optimization algorithm,and the results show that the algorithm in this paper can obtain the best results.