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using CoolPDLP
using HiGHS: HiGHS
using JLArrays
using JuMP: JuMP, MOI
using MathOptBenchmarkInstances: Netlib, list_instances, read_instance

Creating a MILP

You can use QPSReader.jl to read a MILP from a local MPS file, or MathOptBenchmarkInstances.jl to automatically download standard benchmark sets (which we do here).

dataset = Netlib
list = list_instances(dataset)
name = list[4]
qps, path = read_instance(dataset, name);

A MILP object can be constructed from there:

milp = MILP(qps; dataset, name, path)
MILP instance afiro from dataset Netlib:
- types:
  - values Float64
  - vectors Vector{Float64}
  - matrices SparseArrays.SparseMatrixCSC{Float64, Int64}
- variables: 32
  - 32 continuous
  - 0 integer
- constraints: 27
  - 19 inequalities
  - 8 equalities
- nonzeros: 83

Its attributes can be queried:

nbvar(milp)
32
nbcons(milp)
27

Note that manual construction is also an option if you provide the constraints, variable bounds and objectives as arrays.

Solving a MILP

You can use the PDLP algortithm to solve the continuous relaxation of a MILP. The first thing to do is define parameters inside a PDLP struct.

algo = PDLP(;
    termination_reltol = 1.0e-6,
    time_limit = 10.0,
)
PDLP algorithm:
- ConversionParameters: types=(Float64, Int64, SparseArrays.SparseMatrixCSC), backend=KernelAbstractions.CPU(false)
- PreconditioningParameters: chambolle_pock_alpha=1.0, ruiz_iter=10
- StepSizeParameters: invnorm_scaling=0.9, primal_weight_damping=0.5, zero_tol=1.0e-8
- RestartParameters: sufficient_decay=0.2, necessary_decay=0.8, artificial_decay=0.36
- GenericParameters: show_progress=false, check_every=100, record_error_history=true
- TerminationParameters: termination_reltol=1.0e-6, max_kkt_passes=100000, time_limit=10.0

Then all it takes is to call solve.

sol, stats = solve(milp, algo);

The solution is available as a PrimalDualSolution:

sol.x
32-element Vector{Float64}:
  79.99998483892944
  25.499948968432776
  54.50001175963277
  84.79998144856992
  59.021542483628394
   0.0
   0.0
   0.0
   0.0
   0.0
   ⋮
   0.0
   0.0
   0.0
   0.0
   0.0
 339.94294699076795
 236.51443477946376
  63.394278500975204
   0.0

The stats contain information about the convergence of the algorithm:

stats
Convergence stats with termination status OPTIMAL:
- KKT relative errors: primal 9.909e-08, dual 3.936e-08, gap 3.756e-07
- time elapsed: 1.041 seconds 
- KKT passes: 900

You can check the feasibility and objective value:

is_feasible(sol.x, milp; cons_tol = 1.0e-4)
true
objective_value(sol.x, milp)
-464.75321283671656

Running on the GPU

To run the same algorithm on the GPU, all it takes is to define a different set of parameters and thus force conversion of the instance:

algo_gpu = PDLP(
    Float32,  # desired float type
    Int32,  # desired int type
    GPUSparseMatrixCSR;  # GPU sparse matrix type, replace with e.g. CuSparseMatrixCSR
    backend = JLBackend(),  # replace with e.g. CUDABackend()
    termination_reltol = 1.0f-6,
    time_limit = 10.0,
)
PDLP algorithm:
- ConversionParameters: types=(Float32, Int32, GPUSparseMatrixCSR), backend=JLArrays.JLBackend(false)
- PreconditioningParameters: chambolle_pock_alpha=1.0, ruiz_iter=10
- StepSizeParameters: invnorm_scaling=0.9, primal_weight_damping=0.5, zero_tol=1.0e-8
- RestartParameters: sufficient_decay=0.2, necessary_decay=0.8, artificial_decay=0.36
- GenericParameters: show_progress=false, check_every=100, record_error_history=true
- TerminationParameters: termination_reltol=1.0e-6, max_kkt_passes=100000, time_limit=10.0

The result of the algorithm will live on the GPU:

sol_gpu, stats_gpu = solve(milp, algo_gpu)
sol_gpu.x
32-element JLArrays.JLArray{Float32, 1}:
  80.00002
  25.500057
  54.499992
  84.800026
  59.021748
   0.0
   0.0
   0.0
   0.0
   0.0
   ⋮
   0.0
   0.0
   0.0
   0.0
   0.0
 339.94275
 236.51427
  63.394226
   0.0

To bring in back to the CPU, just call the Array converter.

objective_value(Array(sol_gpu.x), milp)
-464.7530648803711

Using the JuMP interface

If you have a model available in JuMP.jl, you can simply choose CoolPDLP.Optimizer as your solver, and pass it the same options as before.

model = JuMP.read_from_file(path; format = MOI.FileFormats.FORMAT_MPS)
JuMP.set_optimizer(model, CoolPDLP.Optimizer)
JuMP.set_silent(model)
JuMP.set_attribute(model, "termination_reltol", 1.0e-6)
JuMP.set_attribute(model, "matrix_type", GPUSparseMatrixCSR)
JuMP.set_attribute(model, "backend", JLBackend())
JuMP.optimize!(model)
x_jump = JuMP.value.(JuMP.all_variables(model))
32-element Vector{Float64}:
  79.99998483892942
  25.49994896843277
  54.50001175963277
  84.79998144856994
  59.02154248362832
   0.0
   0.0
   0.0
   0.0
   0.0
   ⋮
   0.0
   0.0
   0.0
   0.0
   0.0
 339.94294699076806
 236.51443477946384
  63.39427850097521
   0.0
objective_value(x_jump, milp)
-464.75321283671667

Comparing with HiGHS

To check our solution, let's compare it with the output from the HiGHS solver:

model_highs = JuMP.read_from_file(path; format = MOI.FileFormats.FORMAT_MPS)
JuMP.set_optimizer(model_highs, HiGHS.Optimizer)
JuMP.set_silent(model_highs)
JuMP.optimize!(model_highs)
x_ref = JuMP.value.(JuMP.all_variables(model_highs))
32-element Vector{Float64}:
  80.0
  25.5
  54.5
  84.80000000000001
  18.214285714285715
   0.0
   0.0
   0.0
   0.0
  -0.0
   ⋮
   0.0
   0.0
   0.0
   0.0
   0.0
 339.9428571428572
 383.9428571428572
  -0.0
   0.0

Of course, the solution given by HiGHS is feasible too, and we can compare objective values:

is_feasible(x_ref, milp; cons_tol = 1.0e-4)
true
objective_value(x_ref, milp)
-464.7531428571429

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