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This paper considers a phasor measurement unit (PMU) placement problem requiring simultaneous optimization of two conflicting objectives, such as minimization of the number of PMUs and maximization of the measurement redundancy. The objectives are in conflict, for the improvement of one of them leads to deterioration of another. Consequently, instead of a unique optimal solution, there exists a set of the best trade-offs between competing objectives, the so-called Pareto-optimal solutions. A specially tailored nondominated sorting genetic algorithm (NSGA) for the PMU placement problem is proposed as a methodology to find these Pareto-optimal solutions. The algorithm is combined with the graph-theoretical procedure and a simple GA to reduce the initial number of the PMU candidate locations. The NSGA parameters are carefully set by performing a number of trial runs and evaluating the NSGA performances based on the number of distinct Pareto-optimal solutions found in the particular run and the distance of the obtained Pareto front from the optimal one. Illustrative results on the 39-bus and 118-bus IEEE systems are presented.