An improved differential evolution algorithm for the economic load dispatch problems with or without valve-point effects

This paper presents an improved differential evolution (IDE) algorithm for economic load dispatch (ELD) problems with or without valve-point effects (VPE). The proposed IDE is different from the traditional differential evolution (DE) algorithm in three aspects: first, two mutation operators are used to generate mutant vectors; second, a dynamical crossover rate is used to update trail vectors; third, a useful population randomization is adopted to overcome the premature convergence. In addition, a modified repair process is introduced to handle the constraint violations. Eight cases are selected to testify the performance of four DE approaches on solving ELD problems. According to our empirical results, IDE makes slight improvements on the objective function values from the literature. However, it can always find the solutions satisfying the equality constraints. Most importantly, the IDE can achieve much smaller variances than other DEs on the majority of the test problems, indicating that it has strong stability on solving ELD problems.