Finding Multiple Solutions
Answered
Hi,
I have read that with Gurobi the output of multiple solutions is possible. With the following code I wanted to be able to obtain the optimal as well as other possible good solutions.
model.setParam('Method',1)
model.setParam('PoolSolutions',20)
model.setParam('PoolSearchMode',2)
model.optimize()
With the following query I get that only 1 "nSolutions" have been found and the number of "Solution" is None.
# Print number of solutions stored
nSolutions = model.SolCount
print('Number of solutions found: ' + str(nSolutions))
Solution=model.setParam('SolutionNumber',0)
print('Solution:' + str(Solution))
I interpret this to mean that only one optimal solution for my optimization can be determined by the solver. And there are no other "good" solutions to my problem? Is that correct?
Could this be due to the complexity of my optimization that no further solutions can be found? I would have assumed that no matter how complex the optimization is, the solver can also determine and output further non-optimal solutions.
Thanks in advance.
Julia
-
Hi Julia,
Regarding the retrieving of solutions, please note that the setParam function does not return the solution. It only sets the solution which you will get via the Xn and the PoolObjVal attributes. Please refer to the documentation on Retrieving Solutions and the poolsearch.py example for more details.
Could this be due to the complexity of my optimization that no further solutions can be found? I would have assumed that no matter how complex the optimization is, the solver can also determine and output further non-optimal solutions.
Could you post the log file snippet showing the solution process? It is possible that your model has exactly 1 feasible solution (even if it is rather unlikely).
Best regards,
Jaromił0 -
Hi Jaromil,
thank you very much for your feedback!
I am aware that I cannot output the solution with setParam.
First, I would like to query the number of stored solutions with SolCount. Since only one solution (=the optimal solution?) was counted there, I wanted to ask first if it is possible that only one solution exists in my optimization.The following is my log file:
Gurobi 9.1.2 (win64) logging started Tue Aug 24 12:22:39 2021
Changed value of parameter LogFile to Log
Prev: Default:
Changed value of parameter Method to 1
Prev: -1 Min: -1 Max: 5 Default: -1
Changed value of parameter PoolSolutions to 50
Prev: 10 Min: 1 Max: 2000000000 Default: 10
Changed value of parameter PoolSearchMode to 2
Prev: 0 Min: 0 Max: 2 Default: 0
Gurobi Optimizer version 9.1.2 build v9.1.2rc0 (win64)
Thread count: 6 physical cores, 12 logical processors, using up to 12 threads
Optimize a model with 4323 rows, 3849 columns and 699251 nonzeros
Model fingerprint: 0x123a83c8
Coefficient statistics:
Matrix range [1e-04, 2e+00]
Objective range [4e+00, 3e+02]
Bounds range [0e+00, 0e+00]
RHS range [1e+00, 8e+01]
Presolve removed 8 rows and 2 columns
Presolve time: 0.16s
Presolved: 4315 rows, 3847 columns, 697806 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 2.6704171e+03 2.392500e+02 0.000000e+00 0s
2196 2.0185177e+04 0.000000e+00 0.000000e+00 1s
Solved in 2196 iterations and 0.71 seconds
Optimal objective 2.018517748e+04Thank you in advance and best regards,
Julia0 -
Hi Julia,
Your problem is an LP. LPs generally have exactly one optimal solution. The Solution Pool feature is designed for MIPs and will not provide you multiple optimal solutions for LPs.
The rare cases where an LP has infinitely many optimal solutions are hard to handle and require manual algorithms and/or heuristics to get multiple solution points. As an example, one approach may focus on the computation of all vertices of the optimal facet (which is in general very expensive).
Best regards,
Jaromił0
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