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In this paper, the generator contributions to the transmission system are determined by an evolutionary computation technique. Evaluating the contributions of generators to the power flows in transmission lines is formulated as a multiobjective optimization problem and calculated using a parallel vector evaluated particle swarm optimization (VEPSO) algorithm. Specifically, the contributions are modeled by particles of swarms whose positions are optimally determined while satisfying all multiobjectives and other physical and operating constraints. The VEPSO method is parallelized by distributing the swarms in a number of networked PCs. The proposed parallel VEPSO algorithm accounts for nonlinear characteristics of the generators and transmission lines. The applicability of the proposed parallel VEPSO algorithm in accessing the generator contributions is demonstrated and compared with analytical methods for four different systems: three-bus, six-bus, IEEE 30-bus, and 136-bus test systems. The experimental results show that the proposed parallel VEPSO algorithm is capable of obtaining precise solutions compared to analytical methods while considering nonlinear characteristics of the systems.