add support for retrieving multiple solutions (solution pool) from MILP solvers

[maxale]

Some MILP solvers support computing multiple solutions (called solution pool) to a given MILP problem, but Sage lacks the ability to retrieve more than one solution from the solver (the existing .solve() method produces only one solution).

Here is some info on how multiple solutions can be produced in Gurobi and CPLEX solvers:

• Gurobi: https://www.gurobi.com/documentation/9.5/refman/finding_multiple_solutions.html

  • add support for solution pool sage-numerical-backends-gurobi#6

• CPLEX: https://www.ibm.com/docs/en/icos/20.1.0?topic=optimization-solution-pool-generating-keeping-multiple-solutions

  • add support for solution pool sage-numerical-backends-cplex#1

Component: linear programming

Issue created by migration from https://trac.sagemath.org/ticket/34183

[mkoeppe]

comment:1

The most likely route for Sage to improve its MIP interface is to go through CVXPY (#33920).

So a good step would be to investigate whether CVXPY provides this feature and if not, to work on getting it added.