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Performance problem with deeply nested nonlinear expressions

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@blegat 已經在處理了。

開始於 2025年7月22日。

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難度
4/5
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3-5 天
新手友好度
45/100
Issue 類型
缺陷
描述清晰度
基本清楚
活躍度
冷清
技術堆疊
julia
領域
performance, tooling

研究方向

從提供的 Julia 重現開始，尤其是 N = 2 的 multistep RK4 模型和 N = 50 的 single-step 比較。將模型建構與最佳化分開進行基準測試，並檢查在重複展開 RK4 的過程中巢狀運算式如何增長。完成的標準是確定速度變慢究竟出在 JuMP/MathOptInterface 還是建模模式上，並提供一個最小基準測試和一份記錄在案的編碼方向。

由索引模型根據 Issue 內容生成。

描述

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:

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:

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?

主要語言
Julia
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506
分支
103
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1 天 1 小時
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9

環境準備

這個專案沒有提供開發容器、Dockerfile 或貢獻指南，環境需要你自己搭建：先看它的 README，通用步驟見我們的新手貢獻指南。

從這裡開始

  1. 先讀完整個 Issue，再讀專案的貢獻指南。
  2. 在 Issue 下留言說明你要接手 —— 這能避免兩個人做同樣的事。
  3. Fork 儲存庫，在一個分支上完成修改。
  4. 送出 Pull Request，並在描述裡引用這個 Issue 編號。

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