Many-objective optimization with improved shuffled frog leaping algorithm for inter-basin water transfers

Inter-basin water transfers (IBWT) are implemented to re-allocate unevenly distributed water resources. However, many conflicting objectives associated with society, economy, and environment have made the water resources allocation problem in IBWT more complicated than ever before. Thus, there is a continuous need for in-depth research with the latest optimization techniques to secure many-objective allocation of water resources for IBWT. In addition, being troubled of easily falling into local minima and premature convergence in some multi-objective optimization algorithms, it is necessary to explore new alternatives to improve their search quality. Here we propose a many-objective optimization methodology for IBWT, which includes three modules: (1) formulating a many-objective optimization problem based on realistic controls; (2) developing a new multi-objective real-coded quantum inspired shuffled frog leaping algorithm (r-MQSFLA) to solve the optimization problem; (3) utilizing the Analytic Hierarchy Process (AHP)-Entropy method to filter the Pareto solutions. In r-MQSFLA, the real-coded quantum computer and the external archive with dynamic updating mechanism are applied to SFLA. The performance of r-MQSFLA is first compared to that of other multi-objective evolutionary algorithms (MOEAs) in solving mathematical benchmark problems. A case study of the Eastern Route of South-to-North Water Transfer Project in Jiangsu Province, China varying from a normal to an extremely dry year, demonstrates that r-MQSFLA displays approximate performance on some compared algorithms and is improved significantly than MOSFLA in terms of convergence, diversity and reasonable solutions. This study can update the understanding of quantum theory to MOEAs and will provide a reference for better water resources allocation in IBWT under uncertainty.