Returning multiple optimal solutions

[gegen07]

Transferred from gitter
@qszhao

I just chatted with @huanfachen and he mentioned one special case in LSCP/MCLP. It may be possible to have multiple optimal solutions, will we allow the function to return all the optimal solutions or just one?

Problem description:
@jGaboardi

In a very basic situation of LSCP, if there are two facilities (A and B) that are equidistant to all client locations, either facility can be chosen to cover all clients. Therefore the optimal number of facilities selected will be 1, but either A or B could be selected, leading to two equally valid optimal solutions.

[jGaboardi]

This appears to be very difficult to accomplish. Below are some resources for this:

• multiple-optimal-solutions-in-pulp
• finding-all-optimal-lp-solutions
• retrieving-multiple-optimal-solutions-with-pulp
• how-to-generate-multiple-solutions-to-linear-program-in-python