The economic emission dispatch (EED) is a highly constrained nonlinear multiobjective optimization problem with a convex (or nonconvex) solution space. These characteristics and constraints make the EED a difficult problem to solve. Several approaches for a solution have been proposed, such as deterministic techniques, stochastic techniques, or a combination of both. This work presents the use of an algebraic (deterministic) technique, the numerical polynomial homotopy continuation (NPHC) method, to solve the EED problem. A comparison with the sequential quadratic programming (SQP) algorithm and the nondominated sorting genetic algorithm II (NSGA-II) is also presented. Results show that the NPHC algorithm finds all the roots (solutions) of the problem starting from any initial point and assures an accurate solution with a good convergence time. In addition, the NPHC algorithm provides a more accurate solution than the SQP algorithm and the NSGA-II.