How to get multiple solution

Hi Yang Du,

I assume that you either work with a feasibility problem, where finding any solution would lead to immediate termination, or with an optimization problem where the first solution the solver finds happens to be an optimal one. Also in the latter case, the solver will prune the search space s.t. all potential other feasible solutions become cut off and spend the remaining time proving the optimality of the said solution. There is a way, though, how you can make the solver also consider suboptimal parts of the search space and this is by the MIPADDCUTOFF control:

https://www.fico.com/fico-xpress-optimization/docs/latest/solver/optimizer/HTML/MIPADDCUTOFF.html

As documented, setting it to (large) negative values will enforce (large) progression steps in a sequence of incumbent solutions. By default, it is set to a small negative value, which represents minimum progress between one solution and the next.

Setting it to a POSITIVE value, however, will make the solver also accept solutions that are worse than the best one seen so far (worse by at most MIPADDCUTOFF) and might be what you are looking for in your application.

Note that of course depending on your problem it might happen that

a) the solution to your problem is unique, in which case there is simply no way to get another solution or

b) there are MANY alternative optima. In this case, you might want to set a MAXMIPSOL limit

Best regards,

Timo