SLDP: example 1
This tutorial was generated using Literate.jl. Download the source as a .jl file. Download the source as a .ipynb file.
This example is derived from Section 4.2 of the paper: Ahmed, S., Cabral, F. G., & da Costa, B. F. P. (2019). Stochastic Lipschitz Dynamic Programming. Optimization Online. PDF
using SDDP, HiGHS, Testfunction sldp_example_one() model = SDDP.LinearPolicyGraph(; stages = 8, lower_bound = 0.0, optimizer = HiGHS.Optimizer, ) do sp, t @variable(sp, x, SDDP.State, initial_value = 2.0) @variables(sp, begin x⁺ >= 0 x⁻ >= 0 0 <= u <= 1, Bin ω end) @stageobjective(sp, 0.9^(t - 1) * (x⁺ + x⁻)) @constraints(sp, begin x.out == x.in + 2 * u - 1 + ω x⁺ >= x.out x⁻ >= -x.out end) points = [ -0.3089653673606697, -0.2718277412744214, -0.09611178608243474, 0.24645863921577763, 0.5204224537256875, ] SDDP.parameterize(φ -> fix(ω, φ), sp, [points; -points]) return end SDDP.train(model; log_frequency = 10) @test SDDP.calculate_bound(model) <= 1.1675 returnendsldp_example_one()-------------------------------------------------------------------
SDDP.jl (c) Oscar Dowson and contributors, 2017-26
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problem
nodes : 8
state variables : 1
scenarios : 1.00000e+08
existing cuts : false
options
solver : serial mode
risk measure : SDDP.Expectation()
sampling scheme : SDDP.InSampleMonteCarlo
subproblem structure
VariableRef : [7, 7]
AffExpr in MOI.EqualTo{Float64} : [1, 1]
AffExpr in MOI.GreaterThan{Float64} : [2, 2]
VariableRef in MOI.GreaterThan{Float64} : [4, 4]
VariableRef in MOI.LessThan{Float64} : [1, 2]
VariableRef in MOI.ZeroOne : [1, 1]
numerical stability report
matrix range [1e+00, 2e+00]
objective range [5e-01, 1e+00]
bounds range [1e+00, 1e+00]
rhs range [1e+00, 1e+00]
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iteration simulation bound time (s) solves pid
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10 3.272983e+00 1.166965e+00 5.366366e+00 1680 1
20 4.412603e+00 1.166965e+00 5.890186e+00 2560 1
30 3.086857e+00 1.167299e+00 1.076269e+01 4240 1
40 3.816808e+00 1.167299e+00 1.125803e+01 5120 1
50 3.793849e+00 1.167299e+00 1.616854e+01 6800 1
60 3.172515e+00 1.167299e+00 1.671442e+01 7680 1
70 2.935820e+00 1.167410e+00 2.158035e+01 9360 1
80 3.287600e+00 1.167410e+00 2.211692e+01 10240 1
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status : simulation_stopping
total time (s) : 2.211692e+01
total solves : 10240
best bound : 1.167410e+00
numeric issues : 0
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