Improved Multi-objective Butterfly Optimization Algorithm and its Application in Cascade Reservoirs Optimal Operation Considering Ecological Flow

Traditional reservoir operations often take power production as the main purpose. However, blindly maximizing power production will prompt the reservoirs to work continuously at high water levels, leading to lower water release and possible damage to the river ecosystem. In this paper, a multi-objective optimal operation model was established for a cascade reservoir system, with the goals of maximizing power production and ecological benefit. The ecological benefit was defined based on a suitable interval of ecological flow, which was calculated by the Tennant and flow duration curve methods. To efficiently solve the model, a multi-objective butterfly optimization algorithm was proposed by coupling the improved initial population strategy, dynamic switching probability strategy, archive elite solution-guided evolution, and polynomial mutation strategy. This algorithm was compared with three popular multi-objective optimization algorithms on benchmark functions and a cascade reservoir operation problem in the lower reaches of the Yalong River. Results showed that the proposed algorithm achieved the maximum hydropower production, with 82.5, 76.4 and 64.2 billion kW‧h in the wet, normal and dry years. It also obtained the highest ecological benefit values, which were 0.76, 0.80 and 0.86 in the wet, normal and dry years, respectively. The proposed algorithm has the potential to solve multi-objective optimization problems. Under different inflow scenarios, a certain competitive relationship between targets was witnessed. As the decrease of inflow, the competition tended to intensify.