Core benchmark: space_shuttle

This page presents benchmark results for the space_shuttle problem across different platforms and configurations.

Note

The linear solver is MUMPS for all experiments.

Ubuntu Latest CPU

This benchmark suite evaluates optimal control problems on a standard CPU platform using GitHub Actions runners.

⚙️ Configuration

Problems: beam, chain, double_oscillator, electric_vehicle, glider, insurance, jackson, robbins, robot, rocket, space_shuttle, steering, vanderpol
Solvers: ipopt, madnlp
Models: adnlp, exa, jump
Grid sizes: 200, 500, 1000, 2000 discretization points
Discretization: trapeze method
Tolerance: 1.0e-8
Ipopt strategy: adaptive barrier parameter
Limits: 1000 iterations max, 500.0s wall time

🖥️ Environment

📅 Timestamp     : 2025-11-17 15:16:44 UTC
🔧 Julia version : 1.11.7
💻 OS            : Linux
🖥️ Machine       : runnervmg1sw1

You can download the exact environment used for this benchmark:

📦 Project.toml - Package dependencies
📋 Manifest.toml - Complete dependency tree with versions
📜 Benchmark script - Julia script to run the benchmark

These files allow you to reproduce the benchmark environment and results exactly.

ℹ️ Version info

Julia Version 1.11.7
Commit f2b3dbda30a (2025-09-08 12:10 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
  JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager

📦 Package status

Project CTBenchmarks v0.2.3
Status `~/work/CTBenchmarks.jl/CTBenchmarks.jl/Project.toml`
  [6e4b80f9] BenchmarkTools v1.6.3
⌃ [54762871] CTBase v0.16.2
  [052768ef] CUDA v5.9.4
  [a93c6f00] DataFrames v1.8.1
  [ffbed154] DocStringExtensions v0.9.5
  [b6b21f68] Ipopt v1.13.0
  [682c06a0] JSON v1.3.0
  [4076af6c] JuMP v1.29.3
  [d72a61cc] MadNLPGPU v0.7.16
  [3b83494e] MadNLPMumps v0.5.1
  [f4238b75] NLPModelsIpopt v0.11.0
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  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [6462fe0b] Sockets v1.11.0
Info Packages marked with ⌃ have new versions available and may be upgradable.

📚 Complete manifest

Project CTBenchmarks v0.2.3
Status `~/work/CTBenchmarks.jl/CTBenchmarks.jl/Manifest.toml`
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Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

📈 Time vs Grid Size (Ubuntu Latest CPU)

🔁 Iterations vs CPU time (Ubuntu Latest CPU)

🧭 Solution: N = 200 (Ubuntu Latest CPU)

🧭 Solution: N = 500 (Ubuntu Latest CPU)

🧭 Solution: N = 1000 (Ubuntu Latest CPU)

🧭 Solution: N = 2000 (Ubuntu Latest CPU)

📊 Table of Results (Ubuntu Latest CPU)

Problem: `space_shuttle`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	1553.635	125	0.385378	max
✓	200	`adnlp`	`madnlp`	2075.636	149	0.385493	max
✓	200	`exa`	`ipopt`	863.838	125	0.385378	max
✓	200	`exa`	`madnlp`	792.255	149	0.385493	max	✓
✓	200	`jump`	`ipopt`	4371.215	145	0.385378	max
✓	200	`jump`	`madnlp`	2983.996	114	0.385379	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✗	500	`adnlp`	`ipopt`	N/A	N/A	N/A	N/A
✓	500	`adnlp`	`madnlp`	10509.533	140	0.595875	max
✓	500	`exa`	`ipopt`	1841.688	109	0.595875	max
✓	500	`exa`	`madnlp`	1764.043	140	0.595875	max	✓
✓	500	`jump`	`ipopt`	8022.964	115	0.595875	max
✓	500	`jump`	`madnlp`	6329.949	77	0.595875	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`adnlp`	`ipopt`	44156.902	230	0.303609	max
✗	1000	`adnlp`	`madnlp`	N/A	N/A	N/A	N/A
✓	1000	`exa`	`ipopt`	13413.330	201	0.303742	max	✓
✓	1000	`exa`	`madnlp`	16842.068	542	0.305020	max
✓	1000	`jump`	`ipopt`	22892.643	140	0.305020	max
✓	1000	`jump`	`madnlp`	222187.136	866	0.305020	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion
✗	2000	`adnlp`	`ipopt`	529354.418	129	-0.016033	max
✗	2000	`adnlp`	`madnlp`	76284.755	201	0.358308	max
✗	2000	`exa`	`ipopt`	654078.452	122	-0.009002	max
✗	2000	`exa`	`madnlp`	13862.377	190	0.380599	max
✗	2000	`jump`	`ipopt`	303876.908	1000	-1.257847	max
✗	2000	`jump`	`madnlp`	171617.493	393	0.582806	max

ℹ️ Log

Benchmarks results:

┌─ Problem: space_shuttle
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:   4.371 s  | iters: 145   | obj: 3.853783e-01  (max) | CPU: 272.27 KiB
│  │  ✓ | adnlp    | time:   1.554 s  | iters: 125   | obj: 3.853783e-01  (max) | CPU: 213.22 MiB
│  │  ✓ | exa      | time: 863.838 ms | iters: 125   | obj: 3.853783e-01  (max) | CPU: 333.86 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:   8.023 s  | iters: 115   | obj: 5.958750e-01  (max) | CPU: 216.48 KiB
│  │  ✗ | adnlp   : ERROR: DomainError(Inf, "sincos(x) is only defined for finite x.")
│  │  ✓ | exa      | time:   1.842 s  | iters: 109   | obj: 5.958750e-01  (max) | CPU: 490.80 KiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:  22.893 s  | iters: 140   | obj: 3.050197e-01  (max) | CPU: 266.09 KiB
│  │  ✓ | adnlp    | time:  44.157 s  | iters: 230   | obj: 3.036092e-01  (max) | CPU:   1.90 GiB
│  │  ✓ | exa      | time:  13.413 s  | iters: 201   | obj: 3.037425e-01  (max) | CPU: 875.75 KiB
│  │
│  │  N = 2000
│  │  ✗ | jump     | time: 303.877 s  | iters: 1000  | obj: -1.257847e+00 (max) | CPU:   2.39 MiB
│  │  ✗ | adnlp    | time: 529.354 s  | iters: 129   | obj: -1.603350e-02 (max) | CPU:   2.28 GiB
│  │  ✗ | exa      | time: 654.078 s  | iters: 122   | obj: -9.001577e-03 (max) | CPU:   1.35 MiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:   2.984 s  | iters: 114   | obj: 3.853794e-01  (max) | CPU: 148.56 MiB
│  │  ✓ | adnlp    | time:   2.076 s  | iters: 149   | obj: 3.854934e-01  (max) | CPU: 302.38 MiB
│  │  ✓ | exa      | time: 792.255 ms | iters: 149   | obj: 3.854934e-01  (max) | CPU:  44.96 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:   6.330 s  | iters: 77    | obj: 5.958750e-01  (max) | CPU: 343.37 MiB
│  │  ✓ | adnlp    | time:  10.510 s  | iters: 140   | obj: 5.958750e-01  (max) | CPU: 692.76 MiB
│  │  ✓ | exa      | time:   1.764 s  | iters: 140   | obj: 5.958750e-01  (max) | CPU: 100.33 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time: 222.187 s  | iters: 866   | obj: 3.050197e-01  (max) | CPU:   2.29 GiB
│  │  ✗ | adnlp   : ERROR: DomainError(Inf, "sincos(x) is only defined for finite x.")
│  │  ✓ | exa      | time:  16.842 s  | iters: 542   | obj: 3.050197e-01  (max) | CPU:   1.00 GiB
│  │
│  │  N = 2000
│  │  ✗ | jump     | time: 171.617 s  | iters: 393   | obj: 5.828060e-01  (max) | CPU:   2.91 GiB
│  │  ✗ | adnlp    | time:  76.285 s  | iters: 201   | obj: 3.583080e-01  (max) | CPU:   4.06 GiB
│  │  ✗ | exa      | time:  13.862 s  | iters: 190   | obj: 3.805993e-01  (max) | CPU: 557.28 MiB
│  └─
└─

Moonshot CPU

Results on self-hosted CPU hardware.

⚙️ Configuration

Problems: beam, chain, double_oscillator, electric_vehicle, glider, insurance, jackson, robbins, robot, rocket, space_shuttle, steering, vanderpol
Solvers: ipopt, madnlp
Models: adnlp, exa, jump
Grid sizes: 200, 500, 1000, 2000, 5000 discretization points
Discretization: trapeze method
Tolerance: 1.0e-8
Ipopt strategy: adaptive barrier parameter
Limits: 1000 iterations max, 400.0s wall time

🖥️ Environment

📅 Timestamp     : 2025-11-17 19:47:37 UTC
🔧 Julia version : 1.11.7
💻 OS            : Linux
🖥️ Machine       : moonshot

You can download the exact environment used for this benchmark:

📦 Project.toml - Package dependencies
📋 Manifest.toml - Complete dependency tree with versions
📜 Benchmark script - Julia script to run the benchmark

These files allow you to reproduce the benchmark environment and results exactly.

ℹ️ Version info

Julia Version 1.11.7
Commit f2b3dbda30a (2025-09-08 12:10 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 144 × Intel(R) Xeon(R) Gold 6140 CPU @ 2.30GHz
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, skylake-avx512)
Threads: 16 default, 0 interactive, 8 GC (on 144 virtual cores)
Environment:
  JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager
  JULIA_DEPOT_PATH = /scratch/github-actions/julia_depot
  LD_LIBRARY_PATH = /home/mschanen/local/lib:/home/mschanen/local/lib:
  JULIA_NUM_THREADS = 16

📦 Package status

Project CTBenchmarks v0.2.3
Status `/scratch/github-actions/actions_runner_control_toolbox/_work/CTBenchmarks.jl/CTBenchmarks.jl/Project.toml`
  [6e4b80f9] BenchmarkTools v1.6.3
⌃ [54762871] CTBase v0.16.2
  [052768ef] CUDA v5.9.4
  [a93c6f00] DataFrames v1.8.1
  [ffbed154] DocStringExtensions v0.9.5
  [b6b21f68] Ipopt v1.13.0
  [682c06a0] JSON v1.3.0
  [4076af6c] JuMP v1.29.3
  [d72a61cc] MadNLPGPU v0.7.16
  [3b83494e] MadNLPMumps v0.5.1
  [f4238b75] NLPModelsIpopt v0.11.0
  [5f98b655] OptimalControl v1.1.6
  [59046045] OptimalControlProblems v0.3.2
  [91a5bcdd] Plots v1.41.1
  [bd369af6] Tables v1.12.1
  [ade2ca70] Dates v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [6462fe0b] Sockets v1.11.0
Info Packages marked with ⌃ have new versions available and may be upgradable.

📚 Complete manifest

Project CTBenchmarks v0.2.3
Status `/scratch/github-actions/actions_runner_control_toolbox/_work/CTBenchmarks.jl/CTBenchmarks.jl/Manifest.toml`
  [54578032] ADNLPModels v0.8.13
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  [14f7f29c] AMD v0.5.3
  [621f4979] AbstractFFTs v1.5.0
  [79e6a3ab] Adapt v4.4.0
  [66dad0bd] AliasTables v1.1.3
  [a9b6321e] Atomix v1.1.2
  [13072b0f] AxisAlgorithms v1.1.0
  [ab4f0b2a] BFloat16s v0.6.0
  [6e4b80f9] BenchmarkTools v1.6.3
  [d1d4a3ce] BitFlags v0.1.9
  [fa961155] CEnum v0.5.0
⌃ [54762871] CTBase v0.16.2
  [790bbbee] CTDirect v0.17.4
  [1c39547c] CTFlows v0.8.9
  [34c4fa32] CTModels v0.6.9
  [32681960] CTParser v0.7.1
  [052768ef] CUDA v5.9.4
  [1af6417a] CUDA_Runtime_Discovery v1.0.0
  [45b445bb] CUDSS v0.6.1
  [d360d2e6] ChainRulesCore v1.26.0
  [523fee87] CodecBzip2 v0.8.5
  [944b1d66] CodecZlib v0.7.8
  [35d6a980] ColorSchemes v3.31.0
  [3da002f7] ColorTypes v0.12.1
  [c3611d14] ColorVectorSpace v0.11.0
  [5ae59095] Colors v0.13.1
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [34da2185] Compat v4.18.1
  [f0e56b4a] ConcurrentUtilities v2.5.0
  [d38c429a] Contour v0.6.3
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [a93c6f00] DataFrames v1.8.1
  [864edb3b] DataStructures v0.19.3
  [e2d170a0] DataValueInterfaces v1.0.0
  [8bb1440f] DelimitedFiles v1.9.1
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [ffbed154] DocStringExtensions v0.9.5
  [1037b233] ExaModels v0.9.2
  [460bff9d] ExceptionUnwrapping v0.1.11
  [e2ba6199] ExprTools v0.1.10
  [c87230d0] FFMPEG v0.4.5
  [9aa1b823] FastClosures v0.3.2
  [1a297f60] FillArrays v1.15.0
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v1.3.0
  [069b7b12] FunctionWrappers v1.1.3
  [0c68f7d7] GPUArrays v11.2.6
  [46192b85] GPUArraysCore v0.2.0
  [61eb1bfa] GPUCompiler v1.7.4
  [096a3bc2] GPUToolbox v1.0.0
  [28b8d3ca] GR v0.73.18
  [42e2da0e] Grisu v1.0.2
  [34c5aeac] HSL v0.5.2
  [cd3eb016] HTTP v1.10.19
  [076d061b] HashArrayMappedTries v0.2.0
  [842dd82b] InlineStrings v1.4.5
  [a98d9a8b] Interpolations v0.16.2
  [41ab1584] InvertedIndices v1.3.1
  [b6b21f68] Ipopt v1.13.0
  [92d709cd] IrrationalConstants v0.2.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.11
  [692b3bcd] JLLWrappers v1.7.1
  [682c06a0] JSON v1.3.0
  [0f8b85d8] JSON3 v1.14.3
  [4076af6c] JuMP v1.29.3
  [63c18a36] KernelAbstractions v0.9.39
  [40e66cde] LDLFactorizations v0.10.1
  [929cbde3] LLVM v9.4.4
  [8b046642] LLVMLoopInfo v1.0.0
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.10
  [5c8ed15e] LinearOperators v2.11.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.2.0
  [33e6dc65] MKL v0.9.0
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.16
  [2621e9c9] MadNLP v0.8.12
  [d72a61cc] MadNLPGPU v0.7.16
  [3b83494e] MadNLPMumps v0.5.1
  [b8f27783] MathOptInterface v1.46.0
  [739be429] MbedTLS v1.1.9
  [442fdcdd] Measures v0.3.3
  [2679e427] Metis v1.5.0
  [e1d29d7a] Missings v1.2.0
  [d8a4904e] MutableArithmetics v1.6.7
  [a4795742] NLPModels v0.21.5
  [f4238b75] NLPModelsIpopt v0.11.0
  [e01155f1] NLPModelsModifiers v0.7.2
  [5da4648a] NVTX v1.0.1
  [77ba4419] NaNMath v1.1.3
  [6fe1bfb0] OffsetArrays v1.17.0
  [4d8831e6] OpenSSL v1.6.0
  [5f98b655] OptimalControl v1.1.6
  [59046045] OptimalControlProblems v0.3.2
  [bac558e1] OrderedCollections v1.8.1
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.3
  [ccf2f8ad] PlotThemes v3.3.0
  [995b91a9] PlotUtils v1.4.4
  [91a5bcdd] Plots v1.41.1
  [2dfb63ee] PooledArrays v1.4.3
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.5.0
  [08abe8d2] PrettyTables v3.1.0
  [43287f4e] PtrArrays v1.3.0
  [be4d8f0f] Quadmath v0.5.13
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  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
  [ff4d7338] SolverCore v0.3.8
  [a2af1166] SortingAlgorithms v1.2.2
  [9f842d2f] SparseConnectivityTracer v1.1.3
  [0a514795] SparseMatrixColorings v0.4.23
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⌅ [30392449] Pixman_jll v0.44.2+0
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⌅ [319450e9] SPRAL_jll v2025.5.20+0
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⌅ [02c8fc9c] XML2_jll v2.13.9+0
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  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
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  [9e88b42a] Serialization v1.11.0
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  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
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  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.6.0+0
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  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
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  [4536629a] OpenBLAS_jll v0.3.27+1
  [05823500] OpenLibm_jll v0.8.5+0
  [efcefdf7] PCRE2_jll v10.42.0+1
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Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

📈 Time vs Grid Size (Moonshot CPU)

🔁 Iterations vs CPU time (Moonshot CPU)

🧭 Solution: N = 200 (Moonshot CPU)

🧭 Solution: N = 500 (Moonshot CPU)

🧭 Solution: N = 1000 (Moonshot CPU)

🧭 Solution: N = 2000 (Moonshot CPU)

🧭 Solution: N = 5000 (Moonshot CPU)

📊 Table of Results (Moonshot CPU)

Problem: `space_shuttle`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	1842.807	125	0.385378	max
✓	200	`adnlp`	`madnlp`	2582.047	149	0.385493	max
✓	200	`exa`	`ipopt`	949.593	125	0.385378	max
✓	200	`exa`	`madnlp`	851.353	149	0.385493	max	✓
✓	200	`jump`	`ipopt`	6816.370	192	0.384849	max
✓	200	`jump`	`madnlp`	3286.564	114	0.385379	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	4630.356	109	0.595875	max
✓	500	`adnlp`	`madnlp`	13353.413	140	0.595875	max
✓	500	`exa`	`ipopt`	2034.909	109	0.595875	max
✓	500	`exa`	`madnlp`	1843.700	140	0.595875	max	✓
✓	500	`jump`	`ipopt`	10911.113	115	0.595875	max
✓	500	`jump`	`madnlp`	7752.960	77	0.595875	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`adnlp`	`ipopt`	75345.144	231	0.305020	max
✓	1000	`adnlp`	`madnlp`	58017.470	370	0.305020	max
✓	1000	`exa`	`ipopt`	12988.510	171	0.305020	max	✓
✓	1000	`exa`	`madnlp`	13154.323	291	0.305020	max
✓	1000	`jump`	`ipopt`	35154.890	172	0.303571	max
✗	1000	`jump`	`madnlp`	120899.019	370	0.140900	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion
✗	2000	`adnlp`	`ipopt`	402092.600	649	0.360688	max
✗	2000	`adnlp`	`madnlp`	N/A	N/A	N/A	N/A
✗	2000	`exa`	`ipopt`	406668.243	382	-0.200765	max
✗	2000	`exa`	`madnlp`	17617.003	181	0.331654	max
✗	2000	`jump`	`ipopt`	400242.420	949	-0.119163	max
✗	2000	`jump`	`madnlp`	401549.789	568	0.135605	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion
✗	5000	`adnlp`	`ipopt`	400203.747	282	0.054968	max
✗	5000	`adnlp`	`madnlp`	184081.776	182	0.440704	max
✗	5000	`exa`	`ipopt`	400291.214	167	0.767049	max
✗	5000	`exa`	`madnlp`	33945.876	139	0.052355	max
✗	5000	`jump`	`ipopt`	915766.329	115	0.061424	max
✗	5000	`jump`	`madnlp`	191986.294	177	-0.733694	max

ℹ️ Log

Benchmarks results:

┌─ Problem: space_shuttle
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:   6.816 s  | iters: 192   | obj: 3.848491e-01  (max) | CPU: 363.95 KiB
│  │  ✓ | adnlp    | time:   1.843 s  | iters: 125   | obj: 3.853783e-01  (max) | CPU: 213.22 MiB
│  │  ✓ | exa      | time: 949.593 ms | iters: 125   | obj: 3.853783e-01  (max) | CPU: 333.86 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  10.911 s  | iters: 115   | obj: 5.958750e-01  (max) | CPU: 216.48 KiB
│  │  ✓ | adnlp    | time:   4.630 s  | iters: 109   | obj: 5.958750e-01  (max) | CPU: 463.15 MiB
│  │  ✓ | exa      | time:   2.035 s  | iters: 109   | obj: 5.958750e-01  (max) | CPU: 490.80 KiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:  35.155 s  | iters: 172   | obj: 3.035711e-01  (max) | CPU: 325.89 KiB
│  │  ✓ | adnlp    | time:  75.345 s  | iters: 231   | obj: 3.050197e-01  (max) | CPU:   1.91 GiB
│  │  ✓ | exa      | time:  12.989 s  | iters: 171   | obj: 3.050197e-01  (max) | CPU: 846.48 KiB
│  │
│  │  N = 2000
│  │  ✗ | jump     | time: 400.242 s  | iters: 949   | obj: -1.191634e-01 (max) | CPU:   2.34 MiB
│  │  ✗ | adnlp    | time: 402.093 s  | iters: 649   | obj: 3.606880e-01  (max) | CPU:  11.25 GiB
│  │  ✗ | exa      | time: 406.668 s  | iters: 382   | obj: -2.007651e-01 (max) | CPU:   1.63 MiB
│  │
│  │  N = 5000
│  │  ✗ | jump     | time: 915.766 s  | iters: 115   | obj: 6.142435e-02  (max) | CPU: 221.47 KiB
│  │  ✗ | adnlp    | time: 400.204 s  | iters: 282   | obj: 5.496788e-02  (max) | CPU:  12.32 GiB
│  │  ✗ | exa      | time: 400.291 s  | iters: 167   | obj: 7.670488e-01  (max) | CPU:   3.09 MiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:   3.287 s  | iters: 114   | obj: 3.853794e-01  (max) | CPU: 148.56 MiB
│  │  ✓ | adnlp    | time:   2.582 s  | iters: 149   | obj: 3.854934e-01  (max) | CPU: 302.38 MiB
│  │  ✓ | exa      | time: 851.353 ms | iters: 149   | obj: 3.854934e-01  (max) | CPU:  44.96 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:   7.753 s  | iters: 77    | obj: 5.958750e-01  (max) | CPU: 343.37 MiB
│  │  ✓ | adnlp    | time:  13.353 s  | iters: 140   | obj: 5.958750e-01  (max) | CPU: 692.77 MiB
│  │  ✓ | exa      | time:   1.844 s  | iters: 140   | obj: 5.958750e-01  (max) | CPU: 100.33 MiB
│  │
│  │  N = 1000
│  │  ✗ | jump     | time: 120.899 s  | iters: 370   | obj: 1.409004e-01  (max) | CPU:   1.29 GiB
│  │  ✓ | adnlp    | time:  58.017 s  | iters: 370   | obj: 3.050197e-01  (max) | CPU:   4.21 GiB
│  │  ✓ | exa      | time:  13.154 s  | iters: 291   | obj: 3.050197e-01  (max) | CPU: 518.10 MiB
│  │
│  │  N = 2000
│  │  ✗ | jump     | time: 401.550 s  | iters: 568   | obj: 1.356048e-01  (max) | CPU:   3.42 GiB
│  │  ✗ | adnlp   : ERROR: DomainError(Inf, "sincos(x) is only defined for finite x.")
│  │  ✗ | exa      | time:  17.617 s  | iters: 181   | obj: 3.316539e-01  (max) | CPU: 530.24 MiB
│  │
│  │  N = 5000
│  │  ✗ | jump     | time: 191.986 s  | iters: 177   | obj: -7.336941e-01 (max) | CPU:   4.10 GiB
│  │  ✗ | adnlp    | time: 184.082 s  | iters: 182   | obj: 4.407037e-01  (max) | CPU:   9.49 GiB
│  │  ✗ | exa      | time:  33.946 s  | iters: 139   | obj: 5.235457e-02  (max) | CPU:   1.15 GiB
│  └─
└─

Moonshot GPU

Results on self-hosted GPU hardware.

⚙️ Configuration

Problems: beam, chain, double_oscillator, electric_vehicle, glider, insurance, jackson, robbins, robot, rocket, space_shuttle, steering, vanderpol
Solvers: madnlp
Models: exa, exa_gpu
Grid sizes: 1000, 5000, 10000, 20000 discretization points
Discretization: trapeze method
Tolerance: 1.0e-6
Ipopt strategy: adaptive barrier parameter
Limits: 1000 iterations max, 1000.0s wall time

🖥️ Environment

📅 Timestamp     : 2025-11-17 22:08:51 UTC
🔧 Julia version : 1.11.7
💻 OS            : Linux
🖥️ Machine       : moonshot

You can download the exact environment used for this benchmark:

📦 Project.toml - Package dependencies
📋 Manifest.toml - Complete dependency tree with versions
📜 Benchmark script - Julia script to run the benchmark

These files allow you to reproduce the benchmark environment and results exactly.

ℹ️ Version info

Julia Version 1.11.7
Commit f2b3dbda30a (2025-09-08 12:10 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 144 × Intel(R) Xeon(R) Gold 6140 CPU @ 2.30GHz
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, skylake-avx512)
Threads: 16 default, 0 interactive, 8 GC (on 144 virtual cores)
Environment:
  JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager
  JULIA_DEPOT_PATH = /scratch/github-actions/julia_depot
  LD_LIBRARY_PATH = /home/mschanen/local/lib:/home/mschanen/local/lib:
  JULIA_NUM_THREADS = 16

📦 Package status

Project CTBenchmarks v0.2.3
Status `/scratch/github-actions/actions_runner_control_toolbox/_work/CTBenchmarks.jl/CTBenchmarks.jl/Project.toml`
  [6e4b80f9] BenchmarkTools v1.6.3
⌃ [54762871] CTBase v0.16.2
  [052768ef] CUDA v5.9.4
  [a93c6f00] DataFrames v1.8.1
  [ffbed154] DocStringExtensions v0.9.5
  [b6b21f68] Ipopt v1.13.0
  [682c06a0] JSON v1.3.0
  [4076af6c] JuMP v1.29.3
  [d72a61cc] MadNLPGPU v0.7.16
  [3b83494e] MadNLPMumps v0.5.1
  [f4238b75] NLPModelsIpopt v0.11.0
  [5f98b655] OptimalControl v1.1.6
  [59046045] OptimalControlProblems v0.3.2
  [91a5bcdd] Plots v1.41.1
  [bd369af6] Tables v1.12.1
  [ade2ca70] Dates v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [6462fe0b] Sockets v1.11.0
Info Packages marked with ⌃ have new versions available and may be upgradable.

📚 Complete manifest

Project CTBenchmarks v0.2.3
Status `/scratch/github-actions/actions_runner_control_toolbox/_work/CTBenchmarks.jl/CTBenchmarks.jl/Manifest.toml`
  [54578032] ADNLPModels v0.8.13
  [47edcb42] ADTypes v1.19.0
  [14f7f29c] AMD v0.5.3
  [621f4979] AbstractFFTs v1.5.0
  [79e6a3ab] Adapt v4.4.0
  [66dad0bd] AliasTables v1.1.3
  [a9b6321e] Atomix v1.1.2
  [13072b0f] AxisAlgorithms v1.1.0
  [ab4f0b2a] BFloat16s v0.6.0
  [6e4b80f9] BenchmarkTools v1.6.3
  [d1d4a3ce] BitFlags v0.1.9
  [fa961155] CEnum v0.5.0
⌃ [54762871] CTBase v0.16.2
  [790bbbee] CTDirect v0.17.4
  [1c39547c] CTFlows v0.8.9
  [34c4fa32] CTModels v0.6.9
  [32681960] CTParser v0.7.1
  [052768ef] CUDA v5.9.4
  [1af6417a] CUDA_Runtime_Discovery v1.0.0
  [45b445bb] CUDSS v0.6.1
  [d360d2e6] ChainRulesCore v1.26.0
  [523fee87] CodecBzip2 v0.8.5
  [944b1d66] CodecZlib v0.7.8
  [35d6a980] ColorSchemes v3.31.0
  [3da002f7] ColorTypes v0.12.1
  [c3611d14] ColorVectorSpace v0.11.0
  [5ae59095] Colors v0.13.1
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [34da2185] Compat v4.18.1
  [f0e56b4a] ConcurrentUtilities v2.5.0
  [d38c429a] Contour v0.6.3
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [a93c6f00] DataFrames v1.8.1
  [864edb3b] DataStructures v0.19.3
  [e2d170a0] DataValueInterfaces v1.0.0
  [8bb1440f] DelimitedFiles v1.9.1
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [ffbed154] DocStringExtensions v0.9.5
  [1037b233] ExaModels v0.9.2
  [460bff9d] ExceptionUnwrapping v0.1.11
  [e2ba6199] ExprTools v0.1.10
  [c87230d0] FFMPEG v0.4.5
  [9aa1b823] FastClosures v0.3.2
  [1a297f60] FillArrays v1.15.0
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
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  [46192b85] GPUArraysCore v0.2.0
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  [34c5aeac] HSL v0.5.2
  [cd3eb016] HTTP v1.10.19
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  [842dd82b] InlineStrings v1.4.5
  [a98d9a8b] Interpolations v0.16.2
  [41ab1584] InvertedIndices v1.3.1
  [b6b21f68] Ipopt v1.13.0
  [92d709cd] IrrationalConstants v0.2.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.11
  [692b3bcd] JLLWrappers v1.7.1
  [682c06a0] JSON v1.3.0
  [0f8b85d8] JSON3 v1.14.3
  [4076af6c] JuMP v1.29.3
  [63c18a36] KernelAbstractions v0.9.39
  [40e66cde] LDLFactorizations v0.10.1
  [929cbde3] LLVM v9.4.4
  [8b046642] LLVMLoopInfo v1.0.0
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.10
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  [33e6dc65] MKL v0.9.0
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  [1914dd2f] MacroTools v0.5.16
  [2621e9c9] MadNLP v0.8.12
  [d72a61cc] MadNLPGPU v0.7.16
  [3b83494e] MadNLPMumps v0.5.1
  [b8f27783] MathOptInterface v1.46.0
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  [442fdcdd] Measures v0.3.3
  [2679e427] Metis v1.5.0
  [e1d29d7a] Missings v1.2.0
  [d8a4904e] MutableArithmetics v1.6.7
  [a4795742] NLPModels v0.21.5
  [f4238b75] NLPModelsIpopt v0.11.0
  [e01155f1] NLPModelsModifiers v0.7.2
  [5da4648a] NVTX v1.0.1
  [77ba4419] NaNMath v1.1.3
  [6fe1bfb0] OffsetArrays v1.17.0
  [4d8831e6] OpenSSL v1.6.0
  [5f98b655] OptimalControl v1.1.6
  [59046045] OptimalControlProblems v0.3.2
  [bac558e1] OrderedCollections v1.8.1
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.3
  [ccf2f8ad] PlotThemes v3.3.0
  [995b91a9] PlotUtils v1.4.4
  [91a5bcdd] Plots v1.41.1
  [2dfb63ee] PooledArrays v1.4.3
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.5.0
  [08abe8d2] PrettyTables v3.1.0
  [43287f4e] PtrArrays v1.3.0
  [be4d8f0f] Quadmath v0.5.13
  [74087812] Random123 v1.7.1
  [e6cf234a] RandomNumbers v1.6.0
  [c84ed2f1] Ratios v0.4.5
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.1
  [37e2e3b7] ReverseDiff v1.16.1
  [7e506255] ScopedValues v1.5.0
  [6c6a2e73] Scratch v1.3.0
  [91c51154] SentinelArrays v1.4.8
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
  [ff4d7338] SolverCore v0.3.8
  [a2af1166] SortingAlgorithms v1.2.2
  [9f842d2f] SparseConnectivityTracer v1.1.3
  [0a514795] SparseMatrixColorings v0.4.23
  [276daf66] SpecialFunctions v2.6.1
  [860ef19b] StableRNGs v1.0.4
  [90137ffa] StaticArrays v1.9.15
  [1e83bf80] StaticArraysCore v1.4.4
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.1
  [2913bbd2] StatsBase v0.34.8
  [892a3eda] StringManipulation v0.4.1
  [856f2bd8] StructTypes v1.11.0
  [ec057cc2] StructUtils v2.6.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.1
  [62fd8b95] TensorCore v0.1.1
  [a759f4b9] TimerOutputs v0.5.29
  [e689c965] Tracy v0.1.6
  [3bb67fe8] TranscodingStreams v0.11.3
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  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [013be700] UnsafeAtomics v0.3.0
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Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

📈 Time vs Grid Size (Moonshot GPU)

🔁 Iterations vs CPU time (Moonshot GPU)

🧭 Solution: N = 1000 (Moonshot GPU)

🧭 Solution: N = 5000 (Moonshot GPU)

🧭 Solution: N = 10000 (Moonshot GPU)

🧭 Solution: N = 20000 (Moonshot GPU)

📊 Table of Results (Moonshot GPU)

Problem: `space_shuttle`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`exa`	`madnlp`	13092.426	340	0.305020	max
✓	1000	`exa_gpu`	`madnlp`	9046.010	357	-0.056848	max	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✗	5000	`exa`	`madnlp`	66139.728	301	-0.920265	max
✗	5000	`exa_gpu`	`madnlp`	18225.106	227	-0.032411	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✗	10000	`exa`	`madnlp`	89671.464	185	0.231016	max
✗	10000	`exa_gpu`	`madnlp`	23550.223	173	0.621127	max

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✗	20000	`exa`	`madnlp`	150486.992	147	0.618521	max
✗	20000	`exa_gpu`	`madnlp`	59245.531	237	-0.026268	max

ℹ️ Log

Benchmarks results:

┌─ Problem: space_shuttle
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  13.092 s  | iters: 340   | obj: 3.050195e-01  (max) | CPU: 599.43 MiB
│  │  ✓ | exa_gpu  | time:   9.046 s  | iters: 357   | obj: -5.684795e-02 (max) | CPU: 275.328 MiB | GPU: 287.866 MiB
│  │
│  │  N = 5000
│  │  ✗ | exa      | time:  66.140 s  | iters: 301   | obj: -9.202651e-01 (max) | CPU:   1.95 GiB
│  │  ✗ | exa_gpu  | time:  18.225 s  | iters: 227   | obj: -3.241132e-02 (max) | CPU: 267.598 MiB | GPU:  1.209 GiB
│  │
│  │  N = 10000
│  │  ✗ | exa      | time:  89.671 s  | iters: 185   | obj: 2.310158e-01  (max) | CPU:   2.92 GiB
│  │  ✗ | exa_gpu  | time:  23.550 s  | iters: 173   | obj: 6.211275e-01  (max) | CPU: 255.220 MiB | GPU:  2.208 GiB
│  │
│  │  N = 20000
│  │  ✗ | exa      | time: 150.487 s  | iters: 147   | obj: 6.185205e-01  (max) | CPU:   4.85 GiB
│  │  ✗ | exa_gpu  | time:  59.246 s  | iters: 237   | obj: -2.626773e-02 (max) | CPU: 434.485 MiB | GPU:  4.781 GiB
│  └─
└─