Enhanced NSGA-II algorithm based on novel hybrid crossover operator to optimise water supply and ecology of Fenhe reservoir operation

Reservoir-operation optimisation is a crucial aspect of water-resource development and sustainable water process management. This study addresses bi-objective optimisation problems by proposing a novel crossover evolution operator, known as the hybrid simulated binary and improved arithmetic crossover (SBAX) operator, based on the simulated binary cross (SBX) and arithmetic crossover operators, and applies it to the Non-dominated Sorting Genetic Algorithms-II (NSGA-II) algorithm to improve the algorithm. In particular, the arithmetic crossover operator can obtain an optimal solution more precisely within the solution space, whereas the SBX operator can explore a broader range of potential high-quality solutions. Considering the advantages of both operators, this study introduces an improved arithmetic operator to reduce the risk of local convergence inherent in conventional arithmetic operators. Subsequently, two strategies for the SBAX operator are discussed: SBX operator + new arithmetic operator and new arithmetic operator + SBX operator. The convergence of the bi-objective Pareto solution set is evaluated based on the generation and inverted generational distances. This method is used for the collaborative optimisation of the water supply and ecological operation of the Fenhe Reservoir, where its effectiveness is demonstrated. A comparative analysis of the bi-objective optimisation schemes obtained using different crossover operators indicates the following: (1) the NSGA-II algorithm based on the SBAX operator achieves a convergence efficiency that is 14.25-41.95% higher than that of the conventional NSGA-II algorithm; (2) the reservoir operation indices of the scheduling scheme derived from the NSGA-II algorithm based on the SBAX operator significantly outperform those obtained using the conventional NSGA-II algorithm. The optimal strategy reduces the annual average water abandonment by 11.2-14.52 million m³. This study provides a novel approach for bi-objective optimisation and sustainable reservoir management.