Improvement And Application Of Discrete Firework Algorithm

There are many optimization problems in scientific research and real life,which are usually divided into continuous optimization problems and discrete optimization problems.Discrete problems are simple in form and have many characteristics and advantages that continuous problems do not have.Therefore,continuous problems are often converted into discrete problems for research.Discrete fireworks algorithm(DFWA)is a swarm intelligence algorithm to solve discrete problems proposed by Professor Tan Ying of Peking University after the pioneering paper "Fireworks algorithm for optimization" in 2010,and applied to the traveling salesman problem.problem,TSP).With the continuous improvement of the fireworks algorithm,it has shown excellent optimization ability in continuous optimization problems,but the research on discrete fireworks algorithms in the path optimization problem is still lacking.Therefore,in view of its limitations of being easily trapped into a local optimum and the randomness of the selection strategy,this paper proposes a discrete fireworks algorithm based on an improved selection strategy.The research work mainly includes:(1)In view of the instability of the elite selection strategy of the discrete firework algorithm,a combination of deterministic selection and random selection is proposed.The improved algorithm removes parent fireworks from the candidate population,selects only among the children's spark population,and improves the roulette strategy to multi-wheel roulette.Because the uniform mutation operation only accepts better solutions,the probability of selecting to high-quality populations is increased to some extent.The new selection strategy can not only enhance the global search speed in the early stage of the algorithm,but also improve the optimization ability.(2)This paper proposes to adjust the number of offspring selection through dynamic parameters.The number of children in the early iterations increases with the number of iterations and an increase factor to appropriately increase the number of children and expand the search range.The parameters affected by the number of iterations make it easier for individuals with lower fitness to be selected.The optimal solution has stabilized in the middle and late stages of the iteration,and it does not require too many children to repeat the operation.Therefore,appropriately increasing the selection probability of individuals with large fitness can prevent precocity in the algorithm search process.(3)In order to verify the practicability of the improved algorithm,this article applies it to the TSP problem.Experiments are performed at 34 simulated locations.The sum of path distances is used as the fitness function,and it is compared with genetic algorithms and ant colony algorithms.To further verify the performance of the proposed improved discrete firework algorithm,the algorithm was applied to the TSP standard data set for testing on Matlab R2016 a software,and it was run 50 times each with GA,PSO,and ACO,from the algorithm convergence,stability and accuracy.Compared.(4)In order to extend the application space of the algorithm,this paper analyzes the multi-traveling salesman problem,mathematically models the four cases of single origin and multiple origins with or without closed loop,and applies the improved algorithm to MTSP.The process mainly includes establishing mathematical models for four MTSP situations,compiling simulation programs,and comparing experiments to verify the performance of the algorithm.