This paper presents an integrated approach that combines goal-attainment (GA) and adaptive polynomial networks (APN) to real-time biobjective power dispatch. The goals considered are fuel cost and the environmental impact of multiple emissions. The complicated relationships between the input (power demand and operator's economic and emission preferences) and the output (power generated by each generator) can be efficiently modeled by the APN. Moreover, the APN can rapidly provide an accurate estimate of the real-time dispatch results for the power demand and the operator's preferences. The effectiveness of the proposed approach has been demonstrated by the IEEE 30-bus six-generator and the practical Taipower 388-bus 27-generator systems. Test results reveal that the proposed approach achieves significant savings in computation time and reduces the complexity of the real-time power dispatch. Furthermore, the proposed APN outperforms the artificial neural networks (ANNs) method, in both developing the model and estimating the power generated by each generator.