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Abstract: Under the development of computing network convergence, considering the computing and network resources of multiple providers as a whole in the computing Force Network (CFN) has gradually become a new trend. However, since each computing and network resource provider (CNRP) only considers its interest and competes with other CNRPs, introducing multiple CNRPs will create the problem of a lack of trust and difficulty in unified scheduling. In addition, concurrent users have different requirements, so there is an urgent need to study how to optimally match users and CNRPs on a many-to-many basis, thus improving user satisfaction and ensuring and improving the utilization of limited resources. In this paper, firstly, we adopt a reputation model based on the beta distribution function to measure the credibility of CNRPs and propose a performance-based reputation update model. Then, we formalize the problem into a constrained multi-objective optimization problem and find the feasible solutions using a modified fast and elitist non-dominated sorting genetic algorithm (NSGA-II). We also conduct extensive simulation experiments to evaluate the proposed algorithm; the simulation results demonstrate that the proposed model and the problem formulation are valid and, based on which NSGA-II algorithm is effective and which can find the Pareto set of CFN, increases user satisfaction and resource utilization. Moreover, a set of solutions provided by the Pareto set give us more choices of the many-to-many matching of users and CNRPs problem according to the actual situation.