Adaptive Amplitude And Differential Variation Enhance Fireworks Algorithm

There are many optimization problems in reality,so there are many optimization algorithms,including classical optimization algorithms and swarm intelligence optimization algorithms.The former adopts the method of deterministic rules.In recent years,the popular swarm intelligence optimization algorithm uses the probability transfer method,that is,uses various random factors combined with meta-heuristics to make many individuals in the group search the solution space in parallel at the same time and individuals collaborate and compete to achieve effective search during the search process.Swarm intelligence algorithm has the characteristics of high randomness,strong self-adaptability,parallel search and good robustness,so it is widely used to solve complex optimization problems.Fireworks algorithm is also a kind of swarm intelligence algorithms.In this paper,we proposed some improved ideas and schemes for enhancing fireworks algorithm,then proposed multi-target fireworks algorithm for the improved enhanced fireworks algorithm.The specific work contents and innovative research are as follows:1)Adaptive explosion amplitude and differential mutation.Even though the enhanced fireworks algorithm improves many defects of the fireworks algorithm,it still has its own shortcomings,such as the way to calculate the explosion amplitude is not ideal,the search speed is slow and the optimization effect is not good enough for some test functions.Therefore,we proposed the maximum explosion amplitude as a simulated annealing factor to make the explosion amplitude change adaptively with the change of iteration times.It can focus on global search in the early iteration stage and then focus on local search in the late iteration stage.To solve the problem that the algorithm is easy to fall into local optimal solution,we use differential mutation to make the particles jump out of the local optimal solution range.The enhanced fireworks algorithm with adaptive explosion amplitude and differential variation can greatly speed up the solution speed of the test function,and the solution accuracy is also improved to some extent.We make an experimental comparison with the original fireworks algorithm and the enhanced fireworksalgorithm on 10 Benchmark functions.Experiments show that the improved algorithm is obviously better than the enhanced fireworks algorithm.2)Based on the above algorithms,we proposed a dual mutation enhanced fireworks algorithm with adaptive explosion amplitude.Different from above,the new algorithm selects sparks and sorts them after generating explosive sparks in each iteration process.That is,the first half of the sparks in the ranking are focused on global search,so as to jump out of the local optimal solution while the second half of the sparks are focused on local fine search.The two mutation modes run parallel search independently.We compare the new algorithm with the original fireworks algorithm,the enhanced fireworks algorithm and the enhanced fireworks algorithm with adaptive explosion amplitude and differential variation on 10 Benchmark functions.The experiments show that the improved algorithm is obviously better than orther algorithms.3)Finally,We applied the improved enhanced Firework Algorithm to multi-objective problems and proposed a multi-target fireworks algorithm based on NSGA-?.The density of each reference point in NSGA-? is taken as the adaptive function value of the fireworks algorithm,that is,when the density of the reference points associated with individuals in the population is large,the explosion amplitude of fireworks is larger and fewer sparks are generated,whereas more sparks are generated and the explosion amplitude is smaller.Experiments show that the multi-target fireworks algorithm based on NSGA-? has excellent performance.