I have a question regarding how the load that cannot be met by primary renewable devices (like a wind turbine or PV array) is met. According to the load following strategy, it seems that multiple devices (generators, batteries, etc.) can meet a given demand simultaneously and optimally.  By this I mean that the load can be shared in an optimal way across multiple devices.  Is the objective function for this optimization included in the online documentation? How does the system perform this optimization for each hour so quickly?

HOMER does perform an optimization within each time step, in which it considers every combination of dispatchable power sources (generators, grid, battery).  HOMER assumes that each dispatchable source has a fixed and marginal cost of electricity.  (Non-linear cost curves would increase the complexity, which might explain some of the speed difference between HOMER and your Matlab model.)

It searches for the combination of generators that can supply the required AC and DC loads and the required AC and DC operating reserve (spinning reserve) at the least cost.  It tries to take all costs into account, including fuel, O&M, replacement, as well as the average cost incurred in the charging of the battery in preceding time steps.  It also has to worry about generators running out of fuel or being scheduled on or off.