A new bio-inspired optimization algorithm called artificial hummingbird algorithm (AHA) is proposed in this work to solve optimization problems. The AHA algorithm simulates the special flight skills and intelligent foraging strategies of hummingbirds in nature. Three kinds of flight skills utilized in foraging strategies, including axial, diagonal, and omnidirectional flights, are modeled. In addition, guided foraging, territorial foraging, and migrating foraging are implemented, and a visit table is constructed to model the memory function of hummingbirds for food sources. AHA is validated using two sets of numerical test functions, and the results are compared with those obtained from various algorithms. The comparisons demonstrate that AHA is more competitive than other meta-heuristic algorithms and determine high-quality solutions with fewer control parameters. Additionally, the performance of AHA is validated on ten challenging engineering design cases studies. The results show the superior effectiveness of AHA in terms of computational burden and solution precision compared with the existing optimization techniques in literature. The study also explores the application of AHA in hydropower operation design to further demonstrate its potential in practice. The source code of AHA is publicly available at https://seyedalimirjalili.com/aha and https://www.mathworks.com/matlabcentral/fileexchange/101133-artificial-hummingbird-algorithm?s_tid=srchtitle.