StructDualDynProg: Problem 5.2, 3 stages
This tutorial was generated using Literate.jl. Download the source as a .jl file. Download the source as a .ipynb file.
This example comes from StochasticDualDynamicProgramming.jl.
using SDDP, HiGHS, Testfunction test_prob52_3stages() model = SDDP.LinearPolicyGraph(; stages = 3, lower_bound = 0.0, optimizer = HiGHS.Optimizer, ) do sp, t n = 4 m = 3 i_c = [16, 5, 32, 2] C = [25, 80, 6.5, 160] T = [8760, 7000, 1500] / 8760 D2 = [diff([0, 3919, 7329, 10315]) diff([0, 7086, 9004, 11169])] p2 = [0.9, 0.1] @variable(sp, x[i = 1:n] >= 0, SDDP.State, initial_value = 0.0) @variables(sp, begin y[1:n, 1:m] >= 0 v[1:n] >= 0 penalty >= 0 ξ[j = 1:m] end) @constraints(sp, begin [i = 1:n], x[i].out == x[i].in + v[i] [i = 1:n], sum(y[i, :]) <= x[i].in [j = 1:m], sum(y[:, j]) + penalty >= ξ[j] end) @stageobjective(sp, i_c'v + C' * y * T + 1e5 * penalty) if t != 1 # no uncertainty in first stage SDDP.parameterize(sp, 1:size(D2, 2), p2) do ω for j in 1:m fix(ξ[j], D2[j, ω]) end end end if t == 3 @constraint(sp, sum(v) == 0) end end det = SDDP.deterministic_equivalent(model, HiGHS.Optimizer) set_silent(det) optimize!(det) @test objective_value(det) ≈ 406712.49 atol = 0.1 SDDP.train(model; log_frequency = 10) @test SDDP.calculate_bound(model) ≈ 406712.49 atol = 0.1 returnendtest_prob52_3stages()-------------------------------------------------------------------
SDDP.jl (c) Oscar Dowson and contributors, 2017-26
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problem
nodes : 3
state variables : 4
scenarios : 4.00000e+00
existing cuts : false
options
solver : serial mode
risk measure : SDDP.Expectation()
sampling scheme : SDDP.InSampleMonteCarlo
subproblem structure
VariableRef : [29, 29]
AffExpr in MOI.EqualTo{Float64} : [4, 5]
AffExpr in MOI.GreaterThan{Float64} : [3, 3]
AffExpr in MOI.LessThan{Float64} : [4, 4]
VariableRef in MOI.EqualTo{Float64} : [3, 3]
VariableRef in MOI.GreaterThan{Float64} : [22, 22]
VariableRef in MOI.LessThan{Float64} : [1, 1]
numerical stability report
matrix range [1e+00, 1e+00]
objective range [1e+00, 1e+05]
bounds range [0e+00, 0e+00]
rhs range [0e+00, 0e+00]
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iteration simulation bound time (s) solves pid
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10 5.099074e+05 3.509666e+05 6.911993e-03 92 1
20 4.055335e+05 4.054833e+05 1.157808e-02 172 1
30 3.959476e+05 4.067125e+05 1.543498e-02 264 1
40 4.497721e+05 4.067125e+05 1.883101e-02 344 1
47 3.959476e+05 4.067125e+05 2.161717e-02 400 1
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status : simulation_stopping
total time (s) : 2.161717e-02
total solves : 400
best bound : 4.067125e+05
numeric issues : 0
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