StochDynamicProgramming: the stock problem
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 StochDynamicProgramming.jl.
using SDDP, HiGHS, Test
function stock_example()
model = SDDP.PolicyGraph(
SDDP.LinearGraph(5);
lower_bound = -2,
optimizer = HiGHS.Optimizer,
) do sp, stage
@variable(sp, 0 <= state <= 1, SDDP.State, initial_value = 0.5)
@variable(sp, 0 <= control <= 0.5)
@variable(sp, ξ)
@constraint(sp, state.out == state.in - control + ξ)
SDDP.parameterize(sp, 0.0:1/30:0.3) do ω
return JuMP.fix(ξ, ω)
end
@stageobjective(sp, (sin(3 * stage) - 1) * control)
end
SDDP.train(model; log_frequency = 10)
@test SDDP.calculate_bound(model) ≈ -1.471 atol = 0.001
simulation_results = SDDP.simulate(model, 1_000)
@test length(simulation_results) == 1_000
μ = SDDP.Statistics.mean(
sum(data[:stage_objective] for data in simulation) for
simulation in simulation_results
)
@test μ ≈ -1.471 atol = 0.05
return
end
stock_example()-------------------------------------------------------------------
SDDP.jl (c) Oscar Dowson and contributors, 2017-24
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problem
nodes : 5
state variables : 1
scenarios : 1.00000e+05
existing cuts : false
options
solver : serial mode
risk measure : SDDP.Expectation()
sampling scheme : SDDP.InSampleMonteCarlo
subproblem structure
VariableRef : [5, 5]
AffExpr in MOI.EqualTo{Float64} : [1, 1]
VariableRef in MOI.EqualTo{Float64} : [1, 1]
VariableRef in MOI.GreaterThan{Float64} : [3, 3]
VariableRef in MOI.LessThan{Float64} : [2, 3]
numerical stability report
matrix range [1e+00, 1e+00]
objective range [3e-01, 2e+00]
bounds range [5e-01, 2e+00]
rhs range [0e+00, 0e+00]
-------------------------------------------------------------------
iteration simulation bound time (s) solves pid
-------------------------------------------------------------------
10 -1.442965e+00 -1.475770e+00 6.435084e-02 1050 1
20 -1.559536e+00 -1.471842e+00 1.003690e-01 1600 1
30 -1.633260e+00 -1.471526e+00 1.785779e-01 2650 1
40 -1.512908e+00 -1.471277e+00 2.178040e-01 3200 1
50 -1.504160e+00 -1.471172e+00 3.005619e-01 4250 1
60 -1.352909e+00 -1.471159e+00 3.433371e-01 4800 1
70 -1.520847e+00 -1.471079e+00 4.289780e-01 5850 1
80 -1.340949e+00 -1.471075e+00 4.746630e-01 6400 1
90 -1.260376e+00 -1.471075e+00 5.632350e-01 7450 1
100 -1.573293e+00 -1.471075e+00 6.120729e-01 8000 1
110 -1.364263e+00 -1.471075e+00 6.621048e-01 8550 1
120 -1.572199e+00 -1.471075e+00 7.135398e-01 9100 1
130 -1.548012e+00 -1.471075e+00 7.654879e-01 9650 1
140 -1.462561e+00 -1.471075e+00 8.176889e-01 10200 1
150 -1.154072e+00 -1.471075e+00 8.725500e-01 10750 1
160 -1.512908e+00 -1.471075e+00 9.286950e-01 11300 1
170 -1.486600e+00 -1.471075e+00 9.857719e-01 11850 1
180 -1.405274e+00 -1.471075e+00 1.040097e+00 12400 1
187 -1.281632e+00 -1.471075e+00 1.121772e+00 12785 1
-------------------------------------------------------------------
status : simulation_stopping
total time (s) : 1.121772e+00
total solves : 12785
best bound : -1.471075e+00
simulation ci : -1.474018e+00 ± 2.599111e-02
numeric issues : 0
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