The fastest network message oneway spreading problem with bounds of transitive messages was introduced.The problem was formulated with strict mathematics.The corresponding simulated evolutionary algorithm was provided.Through analysing the characteristics of the problem,induding the features of decision variables,the special pattern of the spatial and temporal impacts of decisionmakings and the distribution features of network messages,the optimization model of the problem was built.Taking advantage of the binary feature of decision variables and the relative independence of the pattern of single round information interchanging,the reproduction operator,the crossover operator and the mutation operator of genetic algorithm were designed,that can be manipulated flexibly.So the simulated evolutionary solution of the model was achieved.The numerical example demonstrates the effectiveness of the model and the algorithm.The main extensible research directions with regard to the problem were summed up.