**Tao Bai 1,\*, Xia Liu 1, Yan-ping HA 2, Jian-xia Chang 1, Lian-zhou Wu 1, Jian Wei <sup>1</sup> and Jin Liu <sup>3</sup>**


Received: 23 February 2020; Accepted: 17 March 2020; Published: 24 March 2020

**Abstract:** Given the increasingly worsening ecology issues in the lower Yellow River, the Xiaolangdi reservoir is chosen as the regulation and control target, and the single and multi-objective operation by ecology and power generation in the lower Yellow River is studied in this paper. This paper first proposes the following three indicators: the ecological elasticity coefficient (f1), the power generation elasticity coefficient (f2), and the ecological power generation profit and loss ratio (k). This paper then conducts a multi-target single dispatching study on ecology and power generation in the lower Yellow River. A genetic algorithm (GA) and an improved non-dominated genetic algorithm (NSGA-II) combining constraint processing and feasible space search techniques were used to solve the single-objective model with the largest power generation and the multi-objective optimal scheduling model considering both ecology and power generation. The calculation results show that: (1) the effectiveness of the NSGA-IIcombined with constraint processing and feasible spatial search technology in reservoir dispatching is verified by an example; (2) compared with the operation model of maximizing power generation, the power generation of the target model was reduced by 0.87%, the ecological guarantee rate was increased by 18.75%, and the degree of the impact of ecological targets on the operating results was quantified; (3) in each typical year, the solution spatial distribution and dimensions of the single-target and multi-target models of change are represented by the Pareto-front curve, and a multi-objective operation plan is generated for decision makers to choose; (4) the f1, f2, and k indicators are selected to analyze the sensitivity of the five multi-objective plans and to quantify the interaction between ecological targets and power generation targets. Ultimately, this paper discusses the conversion relationship and finally recommends the best equilibrium solution in the multi-objective global equilibrium solution set. The results provide a decision-making basis for the multi-objective dispatching of the Xiaolangdi reservoir and have important practical significance for further improving the ecological health of the lower Yellow River.

**Keywords:** multi-objective optimal operation model; feasible search space; Pareto-front optimal solution set; loss–benefit ratio of ecology and power generation; elasticity coefficient
