  The Environmental and Economic Dispatch problem (EEDP)is a nonlinear
Multi-objective Optimization Problem (MOP) which simultaneously satisfies
multiple contradictory criteria, and it's a nonsmooth problem when valvepoint
effects, multi-fuel effects and prohibited operating zones have been
considered. It is an important optimization task in fossil fuel fired power
plant operation for allocating generation among the committed units such that
fuel cost and pollution (emission level) are optimized simultaneously while
satisfying all operational constraints. In this paper, we use smoothing
functions with the gradient consistency property to approximate the nonsmooth
multi-objective Optimization problem. Our approach is based on the smoothing
method. In fact, we explain the convergence analysis of smoothing method by
using approximate Karush-Kuhn-Tucker condition, which is necessary for a point
to be a local weak efficient solution and is also sufficient under convexity
assumptions. Finally, we give an application of our approach for solving the
bi-objective EEDP.
