An improved self-adaptive grey wolf optimizer for the daily optimal operation of cascade pumping stations.

Cascade pumping stations play a particularly important role in a water diversion project, and even a small increase in pumping efficiency would bring considerable economic and social benefits. In order to optimize the daily operation of cascade pumping stations to minimize the total daily cost and maximize the efficiency, an improved self-adaptive Grey Wolf optimizer (IAGWO) is proposed. The parameter A of IAGWO is dynamically adjusted to reduce the percentage of wolves moving out of the feasible area (AGWO), and the Inverse Parabolic Spread Distribution, which can maintain the diversity and bring wolves back into the feasible region, is used to further improve the accuracy. The proposed IAGWO and AGWO algorithms are tested using 23 benchmark functions, and the results show that the exploration of the proposed IAGWO and AGWO algorithms is augmented and their exploitation is competitive compared with other algorithms examined in this study. Moreover, a strategy is proposed to dynamically adjust the feasible region of variables in order to reduce unnecessary search for the optimization model of daily cost. The proposed IAGWO and AGWO algorithms are applied to a cascade pumping station system consisting of six pumping stations. Compared to the present scheme, the optimized schemes by IAGWO, AGWO, GWO and PSO can save 0.80268%, 0.80189%, 0.77369% and 0.45331% of daily operating expenses, respectively, which show that the proposed algorithms can obtain more efficient and economic solutions for the daily operation of cascade pumping stations.