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Central mitigation does not necessarily provide the most economical solution to voltage-sag problems. Distributed mitigation with strategically placed compensation devices should provide a better alternative. Placement studies of this nature usually involve extensive evaluations of candidate compensation schemes, which can become unmanageable for large systems with stochastic voltage-sag data. A probability-based technique known as the weighted sampling method is proposed to simplify the problem. The technique is applied to a distribution system to optimize the cost of placing series compensation. The cost has two components: device cost and cost reduction to consumers due to implementation of the device(s). Series compensation devices being optimized are the two distinctly different dynamic voltage restorer and thyristor voltage regulator. These devices are placed and optimized to best complement each other. To achieve reliable and fast convergence, a genetic algorithm with innovative coding is proposed. A 34-node distribution system is studied with a wide range of voltage-sag data and consumer tolerance characteristics.