jump-dev / jump-dev/MathOptInterface.jl

Performance problem with deeply nested nonlinear expressions

Offen
#3,065 11 Kommentare 0 Reaktionen 0 zugewiesene Personen Auf GitHub ansehen
Vorherrschende Sprache
Julia
Sterne
504
Forks
101
Ø Merge
6 Std. 26 Min.
Gemergte PRs (30 T.)
22

Beschreibung

Hello, I am interested in switching from CasADi tu JuMP for optimal control (the system is quaternion kinematics, so not a lot of variables). My MATLAB CasADi model does multistep RK4 integration for multiple shooting (4 steps/interval, 10 intervals) and builds and solves the problem in < 2s. The equivalent JuMP code builds the model for many minutes, using up to 10GB of RAM, and is basically unusable. This is the JuMP code I wrote:
```julia
using ReferenceFrameRotations, DifferentialEquations, Plots
##
function qdot(X, u)
collect(dquat(Quaternion(X), u))
end

function RK4(f, X, u, dt)
k1 = dt*f(X , u)
k2 = dt*f(X+k1/2, u)
k3 = dt*f(X+k2/2, u)
k4 = dt*f(X+k3 , u)
X + (k1+2k2+2k3+k4)/6
end

model = Model(Ipopt.Optimizer)

DCMf = [
-1 0 0
0 0 1
0 1 0
]

# two quaternions represent the same orientation
qf = -convert(Quaternion, DCM(DCMf)) |> collect

N = 2

T = 1
dt = T / (N-1)

tabq = @variable(model, [1:4, 1:N], base_name="q")

tabu = @variable(model, [1:3, 1:N-1], base_name="ω_b")

cost = 0

for i = 1:N-1
F = [tabq[:, i]; cost]
for M = 1:4
F = RK4((X, u) -> [qdot(X[1:4], u); 1/2 * u' * u], F, tabu[:, i], dt)
end
@constraint(model, tabq[:, i+1] == F[1:4])
cost = F[end]
end

#traj constraints
@constraint(model, tabq[:, 1] == q0)
@constraint(model, tabq[:, N] == qf)

# @constraint(model, c[i=1:N], tabq[:, i]' * tabq[:, i] == 1)

@objective(model, Min, cost)

#start values
set_start_value.(tabq, q0)
```
I set N = 2 to prove it's slow even for a single step (similar problems happen with single-step high order RK schemes, such as RK8, which leads me to believe JuMP can't handle big expressions really well). For comparison, if I build a single-step model with 50 steps (approx. 4steps/interval x 10 intervals for the working CasADi model) like this:
```julia
model = Model(Ipopt.Optimizer)

DCMf = [
-1 0 0
0 0 1
0 1 0
]

# two quaternions represent the same orientation
qf = -convert(Quaternion, DCM(DCMf)) |> collect

N = 50

T = 1
dt = T / (N-1)

tabq = @variable(model, [1:4, 1:N], base_name="q")

tabu = @variable(model, [1:3, 1:N-1], base_name="ω_b")

cost = 0

for i = 1:N-1
#can't do multistep integration
F = RK4((X, u) -> [qdot(X[1:4], u); 1/2 * u' * u], [tabq[:, i]; cost], tabu[:, i], dt)
@constraint(model, tabq[:, i+1] == F[1:4])
cost = F[end]
end

#traj constraints
@constraint(model, tabq[:, 1] == q0)
@constraint(model, tabq[:, N] == qf)

# @constraint(model, c[i=1:N], tabq[:, i]' * tabq[:, i] == 1)

@objective(model, Min, cost)

#start values
set_start_value.(tabq, q0)
model
##
optimize!(model)
```
It then works reasonably fast. I don't understand why JuMP can't handle the first code; in my view, this is a big limitation. Is there a particular way of coding in JuMP I'm missing, or is this truly JuMP's fault?

Beitragsleitfaden

Für dieses Repository ist kein Beitragsleitfaden indexiert

Bewertung

Dieses Issue wurde noch nicht bewertet.

Neue Issues direkt in Ihr Postfach

Eine kurze Übersicht über anfängerfreundliche GitHub-Issues.