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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. INDEX TERMS Environmental/economic dispatch, evolutionary algorithm, EGM(1,1) model, grey prediction.

The collective decision optimization algorithm (CDOA) is a new stochastic population-based evolutionary algorithm which simulates the decision behavior of human. In this paper, a multiobjective collective decision optimization algorithm (MOCDOA) is first proposed to solve the environmental/economic dispatch (EED) problem. MOCDOA uses three novel learning strategies, that is, a leader-updating strategy based on the maximum distance of each solution in an external archive, a wise random perturbation strategy based on the sparse mark around a leader, and a geometric center-updating strategy based on an extreme point. The proposed three learning strategies benefit the improvement of the uniformity and the diversity of Pareto optimal solutions. Several experiments have been carried out on the IEEE 30-bus 6-unit test system and 10-unit test system to investigate the performance of MOCDOA. In terms of extreme solutions, compromise solution, and three metrics (SP, HV, and CM), MOCDOA is compared with other existing multiobjective optimization algorithms. It is demonstrated that MOCDOA can generate the well-distributed and the high-quality Pareto optimal solutions for the EED problem and has the potential to solve the multiobjective optimization problems of other power systems.

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