Multiobjective Grey Prediction Evolution Algorithm for Environmental/Economic Dispatch Problem

The environmental/economic dispatch (EED) problem, as one of the most important optimization problems in power systems operations, is a highly constrained, nonlinear, multiobjective optimization problem. Multiobjective evolutionary algorithms have become effective tools for solving the EED problem. To obtain higher quality Pareto solutions for EED as well as further improve the uniformity and diversity of the Pareto set, this paper proposes a novel multiobjective evolutionary algorithm, namely multiobjective grey prediction evolution algorithm (MOGPEA). The MOGPEA first develops a novel grey prediction evolution algorithm (GPEA) based on the even grey model (EGM(1,1)). Unlike other evolutionary algorithms, the GPEA considers the population series of evolutionary algorithms as a time series and uses the EGM(1,1) model to construct an exponential function as a reproduction operator for obtaining offspring. In addition, the MOGPEA adopts two learning strategies to improve the uniformity and diversity of the Pareto optimal solutions of the EED. One is a leader-updating strategy based on the maximum distance of each solution in an external archive, and the other is a leader-guiding strategy based on one solution of each external archive. To validate the effectiveness of the MOGPEA, a standard IEEE 30-bus 6-generator test system (with/without considering losses) is studied with fuel cost and emission as two conflicting objectives to be simultaneously optimized. The experimental results are compared with those obtained using a number of algorithms reported in the literature. The results reveal that the MOGPEA generates superior Pareto optimal solutions of the multiobjective EED problem. Matlab_Codes of this article can be found in https://github.com/Zhongbo-Hu/Prediction-Evolutionary-Algorithm-HOMEPAGE.