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Increasingly mature computer technology is very conducive to solve the complex optimizations of power system. To effectively deal with the many-objective optimal power flow (MOOPF) problems, a novel NSGA-FA algorithm which alleviates the limitation of local optimum is put forward in this paper. The NSGA-FA algorithm combines the special sorting rule of non-dominated sorting genetic algorithm-III (NSGA-III) and the location-updating mechanism of many-objective firefly algorithm (MFA). Furthermore, the optimal elite guidance (E-guide) mechanism and the non-duplicate elite solution storage (NDES) strategy are proposed to optimize operation-efficiency and solution-diversity of NSGA-FA algorithm. The applicability and preponderance of NSGA-FA algorithm compared with NSGA-III and MFA methods are evaluated by both bi-objective and tri-objective MOOPF experiments on IEEE 30-bus and 57-bus systems. Furthermore, the hyper-volume (HV) metric and the detailed results of five simulation trials intuitively indicate that the presented NSGA-FA algorithm achieves the more preferable Pareto front (PF) with superior-diversity and fast-convergence. In general, the suggested NSGA-FA algorithm provides an innovative idea for the application of computer technology on the economic operation of electric systems. [ABSTRACT FROM AUTHOR]