To solve the economic dispatch problems in power systems

a modified differential evolution algorithm was introduced In the proposed algorithm the non-linear characteristics

such as ramp constraints of the generating units

output restricted zone and non-smooth cost functions are considered.To handle the constraints

the lexicographic order method was employed to ensure the stability and the security of the system by providing feasible solutions.In the algorithm

the concepts of the individual best (pbest) and the global best (gbest) were introduced to DE

which were derived from the particle swarm optimization (PSO) .Moreover

based on the crossover mechanism from the genetic particle swarm optimization

pbest and gbest were used to generate the trail vector with user defined ratios to enhance the local search performance.The simulation results for a practical system with 6 units have shown the effectiveness and the stability of the proposed approach for economic dispatch problems

which are better than those of the genetic algorithm

PSO

and traditional differential evolution.