Finding multiple feasible solutions using JuMP in julia
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I want to find multiple feasible solutions for a MILP model using Gurobi with JuMP in Julia. According to the documentation, this should be possible. However, I get some odd output when using different objectives for the same model (separately optimising for each objective):
I can only find 1 solution when optimising for objective A but 3 solutions when optimising for objective B. Why don't I get the same number of feasible solutions when optimising for the different objectives?
The methods I used to obtain multiple solutions are the following:
when constructing the model, I add:
set_optimizer_attribute(m, "PoolSearchMode", 2)
set_optimizer_attribute(m, "PoolSolutions", 10)
After solving I added this code:
num_solutions = result_count(m)
-
Do I understand correctly that the difference is only in the objective function, but you get a different number of solutions? Did you also set the parameter PoolGap or PoolGapAbs?
Can you share the log files for both runs?
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Dear Marika,
Yes, I only adapt the objective function and then get a different number of solutions.
I did not set either of the parameters for PoolGap or PoolGapAbs. Would you propose to do so?
This is the solution summary for objective A:Number of solutions found: 1
JuMP.solution_summary(m) = * Solver : Gurobi
* Status
Result count : 1
Termination status : OPTIMAL
Message from the solver:
"Model was solved to optimality (subject to tolerances), and an optimal solution is available."
* Candidate solution (result #1)
Primal status : FEASIBLE_POINT
Dual status : NO_SOLUTION
Objective value : -4.16673e-14
Objective bound : -4.16673e-14
Relative gap : 0.00000e+00
Dual objective value : -4.16673e-14
* Work counters
Solve time (sec) : 8.66302e-01
Barrier iterations : 0
Node count : 1
And this is the solution summary for objective B:Number of solutions found: 3
JuMP.solution_summary(m) = * Solver : Gurobi
* Status
Result count : 3
Termination status : OPTIMAL
Message from the solver:
"Model was solved to optimality (subject to tolerances), and an optimal solution is available."
* Candidate solution (result #1)
Primal status : FEASIBLE_POINT
Dual status : NO_SOLUTION
Objective value : 9.24702e+02
Objective bound : 9.24702e+02
Relative gap : 0.00000e+00
Dual objective value : 9.24702e+02
* Work counters
Solve time (sec) : 1.12726e+00
Barrier iterations : 0
Node count : 10 -
Hi Marloes,
I am not so familiar with Julia. Could you make sure that the parameter PoolSearchMode is active in your run?
I tested some Julia code I found here:using JuMP, Gurobi
m = Model(optimizer_with_attributes(Gurobi.Optimizer, "PoolSearchMode"=>2, "PoolSolutions" => 1000))
@variables(m,begin
0 <= x <= 5
0 <= y <= 10, Int
z, Bin
zz, Bin
end)
@objective(m, Max, x + 2y + 5*(z+zz))
@constraint(m, x + y + z + zz<= 10)
@constraint(m, x + 2y + z + zz <= 15)
@constraint(m, z + zz <= 1)
optimize!(m)This produces the following output
Set parameter PoolSearchMode to value 2 Set parameter PoolSolutions to value 1000 Gurobi Optimizer version 11.0.3 build v11.0.3rc0 (win64 - Windows 10.0 (19045.2)) CPU model: 11th Gen Intel(R) Core(TM) i7-1165G7 @ 2.80GHz, instruction set [SSE2|AVX|AVX2|AVX512] Thread count: 4 physical cores, 8 logical processors, using up to 8 threads Optimize a model with 3 rows, 4 columns and 10 nonzeros Model fingerprint: 0xea01b6e5 Variable types: 1 continuous, 3 integer (2 binary) Coefficient statistics: Matrix range [1e+00, 2e+00] Objective range [1e+00, 5e+00] Bounds range [5e+00, 1e+01] RHS range [1e+00, 2e+01] Found heuristic solution: objective 15.0000000 Presolve time: 0.01s Presolved: 3 rows, 4 columns, 10 nonzeros Variable types: 1 continuous, 3 integer (2 binary) Found heuristic solution: objective 18.0000000 Root relaxation: objective 1.900000e+01, 3 iterations, 0.00 seconds (0.00 work units) Nodes | Current Node | Objective Bounds | Work Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time * 0 0 0 19.0000000 19.00000 0.00% - 0s Optimal solution found at node 0 - now completing solution pool... Nodes | Current Node | Pool Obj. Bounds | Work | | Worst | Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time 0 0 - 0 - 19.00000 - - 0s 0 0 - 0 - 19.00000 - - 0s 0 2 - 0 - 19.00000 - - 0s Explored 47 nodes (10 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 8 (of 8 available processors) Solution count 24: 19 19 19 ... 5 No other solutions better than 5Here, you can see the line
Optimal solution found at node 0 - now completing solution pool...
Can you verify this also happen in your runs?
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Dear Marika,
Thank you for the suggestion to check if the parameter is correctly activated. Thanks to that I noticed that I set the parameters within an if-statement that did not hold. Adapting this made the parameters active and I now obtain an equal number of solutions!
Thank you for your help!0
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