Multi-objective differential evolution algorithm for environmental-economic power dispatch problem

This paper presents a multi-objective evolutionary algorithm for environmental\economic power dispatch (EEPD) problem. The multi-objective evolutionary algorithm based on differential evolution (MODE). In this algorithm, the differential evolution (DE) concept for the single objective optimization is extended to multi-objective optimization. The EEPD problem is formulated as a true nonlinear constrained multi-objective optimization problem with competing objectives. The proposed approach employs a diversity-preserving technique to overcome the premature convergence and search bias problems and produce a well-distributed Pareto-optimal set of non-dominated solutions. A hierarchical clustering algorithm is also imposed to provide the decision maker with a representative and manageable Pareto-optimal set. Moreover, fuzzy set theory is employed to extract the best compromise non-dominated solution. Several optimization runs of the proposed approach have been carried out on IEEE 30-bus test system. The results demonstrate the capabilities of the proposed approach to generate well-distributed Pareto-optimal solutions for the multi-objective EEPD problem and the comparison with the results reported in the literature demonstrates the superiority of the proposed approach and confirms its potential to solve the multi-objective EEPD problem.