Load flow analysis is a significant tool for proper planning, operation, and dynamic analysis of a power system that provides the steady-state values of voltage magnitudes and angles at the fundamental frequency. However, due to the absence of a slack bus in an islanded microgrid, modified load flow algorithms should be adopted considering the system frequency as one of the solution variables. This paper proposes the application of nature-inspired hybrid optimization algorithms for solving the load flow problem of islanded microgrids. Several nature-inspired algorithms such as genetic algorithm (GA), differential evolution (DE), flower pollination algorithm (FPA), and grasshopper optimization algorithm (GOA) are separately merged with imperialistic competitive algorithm (ICA) to form four hybrid algorithms named as ICGA, ICDE, ICFPA, and ICGOA. Performances of these algorithms are tested on the 6-bus test system and the modified IEEE 37-bus test system. A comparison among the proposed algorithms is carried out in terms of statistical analysis conducted using SPSS statistics software. From the statistical analysis, it is identified that on an average, ICDE takes less number of iterations and consequently needs less execution time compared with other algorithms in solving the load flow problem of islanded microgrids.