HHMODE: a global–local co‑evolutionary hyper‑heuristic algorithm for coordinated pump scheduling in urban water distribution systems

In urban water distribution systems, the scientific design of pump group scheduling strategies directly affects both water supply safety and operational cost-effectiveness. However, the operation of pump groups involves coupling conflicts among multiple objectives and complex operational constraints, making it difficult for traditional methods to effectively solve the scheduling optimization problem. Meanwhile, the continuous rise in urban water demand and energy prices introduces new challenges to achieving efficient and energy-saving pump operation. To address this issue, a multi-objective collaborative pump group scheduling model is proposed, fully considering the regulation function of the clear water pool. Based on this, a global–local co-evolutionary hyper-heuristic algorithm is developed. In the intake-supply collaborative optimization model, an adaptive time-division strategy is designed for intake flow planning, which reduces the load on intake pumps by smoothing flow distribution. In the hyper-heuristic optimization algorithm, a hybrid adaptive triggering mechanism is designed to dynamically coordinate the cooperative co-evolution of global optimization and local search. Meanwhile, a multi-armed bandit strategy is employed to adaptively select local search operators online, thereby efficiently identifying the best individuals within promising search regions. Validated on a real-world pump scheduling case, the proposed algorithm achieves superior optimization performance, reducing total energy consumption by 20.02% and decreasing the number of pump switching operations by 44% compared with the on-site scheduling strategy, and it is capable of producing accurate pump scheduling plans within a limited number of iterations. Furthermore, it exhibits superior performance on standard benchmark functions, demonstrating strong applicability.