Possibly use complete enumeration to solve MIPs with very few binary variables #3011

A user has observed that his MIP with only one binary variable takes 0.4s to solve by his own complete enumeration, but the MIP solver running with defaults takes >20s. With the options

• presolve = off (this helps to get 7 secs off)
• mip_heuristic_run_feasibility_jump = false (this help to reduce the by another 5 secs)
• mip_heuristic_effort = 0
• mip_detect_symmetry = false
• mip_heuristic_run_rins = false
• mip_heuristic_run_rens = false
• mip_heuristic_run_root_reduced_cost = false

the MIP time is still 10.2s

It would seem to be worth performing complete enumeration of MIPs with only a very few binary variables. Whilst few MIPs passed to HiGHS will have this property, the MIP solver generates smaller sub-MIPs when running certain primal heuristics, and these might have very few binary variables.