32. Multi-objective Firefly Algorithm for Hierarchical Mutation Learning

In response to the problem that the traditional multi-objective firefly algorithm has insufficient exploration capability, poor convergence and easy to fall into local optimum, this paper proposes a multi-objective firefly algorithm for hierarchical mutation learning (MOFA-HML). Firstly, the population is stratified by non-dominated sorting of sequential search strategy (ENS-SS), so that the dominated solution in the latter layer learns from the individuals in the former layer to ensure fast and accurate convergence of the population, and the differential evolution operation is performed on the non-dominated individuals in the population, and the distribution space of the non-dominated solutions is more extensive to improve the exploration ability of the algorithm; the mutation operation is performed on the population to guide the local development of the algorithm and improve the solution accuracy of the algorithm; finally, by the inter-individual Euclidean distance to screen firefly individuals and maintain the distributivity of the population. On 12 test problems of ZDT and UF series, MOFA-HML is compared with 5 classical algorithms and 7 recent algorithms, and the results show that MOFA-HML has excellent exploration ability, good convergence and distributivity of solutions.