Originally posted by: rocarvaj

Hello,
When I add MIP starts to CPLEX using CPXaddmipstarts and then optimize, CPLEX reports something like:

3 of 200 MIP starts provided solutions.
MIP start 'm6' defined initial solution with objective 56048.0000.
...

I would like to know if the number of MIP starts reports (3, in this case) is the total number of feasible solutions out the solutions provided by the user or something else. I ask this because in the example above, I'm pretty sure all those 200 solutions are feasible (you can always argue that I have to double check). In fact, I've tried the following: Give CPLEX the same MIP start twice and it reports: "1 of 2 MIP starts provided solutions". Does CPLEX stay with some of the solutions and does not count solutions that are equal or similar (in some sense)?

Also, in the example above, right after CPLEX solves the B&B root node it reports it has 208 solutions. Does this mean that CPLEX keeps al of the solutions anyway.

Thanks,
Rodolfo
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Originally posted by: SystemAdmin

CPLEX tests all MIP starts that you provide but only reports those as "defining an initial solution" that improve the incumbent. That means, if you have two MIP starts m1 and m2 with objective function values o1 and o2 and o1 is better than o2, then CPLEX will not report m2 (since it first processed m1 and m2 is no better than that). So the number of MIP start solutions reported by CPLEX depends on the order of the MIP starts. If you order your MIP starts by decreasing objective function value (for a minimization problem) then CPLEX should report all of them (unless there are MIP starts with the same objective).
By default CPLEX keeps the solutions (and may use them as starting point in local improvement heuristics). You can control the number of solutions that CPLEX keeps by CPX_PARAM_SOLNPOOLCAPACITY. More details about this can be found in solution pool chapter of the user manual.
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