在python中获得由GLPK求解器为LP计算的前10个次优解

Question

I am trying to use GLPK for solving an LP problem. My problem is the routing problem in a computer network. Given network topology and each link capacity and the traffic demand matrix for each source-destination pair in the network, I want to minimize maximum link utilization in the network. This is an LP problem and I know how to use GLPK to get the optimum solution.

My problem is that I want to get the sub-optimal solutions also. Is there any way that I can get say top 10 suboptimal solutions by GLPK?

Best

Answer 1

For a pure LP (with only continuous variables), the concept of finding " next best " solutions is very difficult (just move an epsilon away, and you have another solution). We can define this differently: find "next best" corner points (aka bases). This is not so easy to do, but there is a somewhat complex way by encoding bases using binary variables ( link ).

If the problem is actually a MIP (with binary variables) it is easier to find "next best" solutions. Some advanced solvers have built-in facilities for this (called: solution pool ). Note: glpk does not have this option. Alternatively, we can also do this by adding a cut that forbids the best-found solution and then resolve ( link ). In this case we exploited some structure. A general cut for 0-1 variables is derived here . This can also be done for general integer variables, but then things get a bit messy.