Voltage sags are some of the most serious quality problems of electricity faced by both concessionaires as consumers of Electric Power System. Constant monitoring is essential to identify the disturbances in a distribution system, however the costs involved make impossible the complete monitoring system, as only a limited number of monitors are available to cover the largest possible number of events. Thus, it is clear that the determination of the equipment installation points is a crucial factor for the success of the monitoring plan. In this paper an approach to optimized allocation of quality monitors electricity in distribution systems is presented. We used techniques of multi-objective evolutionary optimization, specifically Non-Dominated Sorting Genetic Algorithm II algorithm -NSGA-II to solve the problem of allocation monitors. The model adopted in the problem formulation considers only those aspects related to voltage sags, therefore, considered the objectives were to maximize the amount of subsidence observed by monitors distributed in the system and reduce the cost of monitoring. The occurrence of single-phase, two-phase and three-phase faults were considered in the proposed methodology and the conduct of the frequencies of each of the fault types were modeled using the Monte Carlo method. The presented approach was subjected to IEEE test 13 and 34 nodes feeders, simulated in DigSILENT Power Factory 15.1 software. The results allow the user the choice of monitoring solution that best fits their technical and financial reality, thus demonstrating the good efficiency of the proposed methodology.