An Evolutionary Framework for Bi-objective Dynamic Economic and Environmental Dispatch Problems

A dynamic economic and environmental dispatch (DEED) problem is a challenging bi-objective optimization problem that simultaneously minimizes both operating costs and gas emissions. To solve it, several evolutionary algorithms (EAs) have been used, each of which has pros and cons, with one performing better in an early stage of evolution and another later. In this paper, to solve such problems, an evolutionary framework is designed based on two EAs, a genetic algorithm (GA) and differential evolution (DE), dynamically configures the better of the two during the evolution. In it, two sub-populations are performed, one for each of GA and DE, and their sizes updated in each generation according to the respective algorithm’s performance in previous generations. Moreover, a heuristic is employed to improve the performance of the proposed algorithm by repairing infeasible individuals towards feasible directions. To demonstrate its performance, two renewable-based DEED problems are solved using the proposed and state-of-the-art algorithms. An analysis of the simulation results reveals that the proposed algorithm is the best of those considered, with the heuristic enhancing its performances.