# Historical simulation in SDDP.jl
**URL:** https://discourse.julialang.org/t/historical-simulation-in-sddp-jl/109473
**Category:** Optimization (Mathematical)
**Tags:** question, sddp
**Created:** [January 30, 2024, 9:13pm UTC](https://discourse.julialang.org/t/historical-simulation-in-sddp-jl/109473 "2024-01-30T21:13:13Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@Sorooshsa](https://discourse.julialang.org/u/Sorooshsa)
#### Post date: [January 30, 2024, 9:13pm UTC](https://discourse.julialang.org/t/historical-simulation-in-sddp-jl/109473/1 "2024-01-30T21:13:13Z")
Hi,
I did simulation in SDDP.jl using historical data. It works; however, I could not retrieve the optimal solutions anymore by simply putting [:variable] as an argument in SDDP.simulate.
What should we do in historical simulation to obtain the optimal solution?
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [January 30, 2024, 9:14pm UTC](https://discourse.julialang.org/t/historical-simulation-in-sddp-jl/109473/2 "2024-01-30T21:14:21Z")
> I could not retrieve the optimal solutions anymore by simply putting [:variable] as an argument in SDDP.simulate
You should be able to.
Do you have a reproducible example?
---
### Author:  [@Sorooshsa](https://discourse.julialang.org/u/Sorooshsa)
#### Post date: [January 30, 2024, 9:44pm UTC](https://discourse.julialang.org/t/historical-simulation-in-sddp-jl/109473/3 "2024-01-30T21:44:58Z")
```julia
using SDDP, HiGHS
T = Array{Float64,2}[[1.0]', [0.75 0.25], [0.75 0.25; 0.25 0.75]]
Ω = [
(inflow = 0.0, fuel_multiplier = 1.5),
(inflow = 50.0, fuel_multiplier = 1.0),
(inflow = 100.0, fuel_multiplier = 0.75),
]
model = SDDP.MarkovianPolicyGraph(
transition_matrices = Array{Float64,2}[
[1.0]',
[0.75 0.25],
[0.75 0.25; 0.25 0.75],
],
sense = :Min,
lower_bound = 0.0,
optimizer = HiGHS.Optimizer,
) do subproblem, node
# Unpack the stage and Markov index.
t, markov_state = node
# Define the state variable.
@variable(subproblem, 0 <= volume <= 200, SDDP.State, initial_value = 200)
# Define the control variables.
@variables(subproblem, begin
thermal_generation >= 0
hydro_generation >= 0
hydro_spill >= 0
inflow
end)
# Define the constraints
@constraints(
subproblem,
begin
volume.out == volume.in + inflow - hydro_generation - hydro_spill
thermal_generation + hydro_generation == 150.0
end
)
# Note how we can use `markov_state` to dispatch an `if` statement.
probability = if markov_state == 1 # wet climate state
[1 / 6, 1 / 3, 1 / 2]
else # dry climate state
[1 / 2, 1 / 3, 1 / 6]
end
fuel_cost = [50.0, 100.0, 150.0]
SDDP.parameterize(subproblem, Ω, probability) do ω
JuMP.fix(inflow, ω.inflow)
@stageobjective(
subproblem,
ω.fuel_multiplier * fuel_cost[t] * thermal_generation
)
end
end
SDDP.train(model, time_limit = 10)
simulations = SDDP.simulate(
model,
sampling_scheme = SDDP.Historical([
((1, 1), Ω[1]),
((2, 2), Ω[3]),
((3, 1), Ω[2]),
]), [:hydro_spill])
```
I took this code from:
> **[Markovian policy graphs · SDDP.jl](https://sddp.dev/stable/tutorial/markov_uncertainty/#Markovian-policy-graphs)**
>
> Documentation for SDDP.jl.
, and just put [:hydro\_spill] at the end of the code. I just run it and got this error:
```julia
MethodError: no method matching simulate(::SDDP.PolicyGraph{Tuple{Int64, Int64}}, ::Vector{Symbol}; sampling_scheme::SDDP.Historical{Tuple{Int64, Int64}, NamedTuple{(:inflow, :fuel_multiplier), Tuple{Float64, Float64}}})
```
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [January 30, 2024, 10:01pm UTC](https://discourse.julialang.org/t/historical-simulation-in-sddp-jl/109473/4 "2024-01-30T22:01:33Z")
`sampling_scheme` is a keyword argument. You need to pass the required positional arguments first:
```julia
simulations = SDDP.simulate(
model,
1,
[:hydro_spill];
sampling_scheme = SDDP.Historical([
((1, 1), Ω[1]),
((2, 2), Ω[3]),
((3, 1), Ω[2]),
]),
)
```