Core benchmark: electric_vehicle

This page presents benchmark results for the electric_vehicle 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
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  [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
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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: `electric_vehicle`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	8.532	4	1228.698880	min
✓	200	`adnlp`	`madnlp`	8.080	4	1228.698880	min
✓	200	`exa`	`ipopt`	4.556	4	1228.698880	min
✓	200	`exa`	`madnlp`	3.897	4	1228.698880	min	✓
✓	200	`jump`	`ipopt`	5.880	4	1228.698880	min
✓	200	`jump`	`madnlp`	6.964	4	1228.698880	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	19.292	4	1228.599284	min
✓	500	`adnlp`	`madnlp`	18.391	4	1228.599284	min
✓	500	`exa`	`ipopt`	9.344	4	1228.599284	min
✓	500	`exa`	`madnlp`	8.332	4	1228.599284	min	✓
✓	500	`jump`	`ipopt`	12.944	4	1228.599284	min
✓	500	`jump`	`madnlp`	16.297	4	1228.599284	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`adnlp`	`ipopt`	41.684	4	1228.585040	min
✓	1000	`adnlp`	`madnlp`	42.744	4	1228.585040	min
✓	1000	`exa`	`ipopt`	17.360	4	1228.585040	min
✓	1000	`exa`	`madnlp`	15.456	4	1228.585040	min	✓
✓	1000	`jump`	`ipopt`	23.806	4	1228.585040	min
✓	1000	`jump`	`madnlp`	32.637	4	1228.585040	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	2000	`adnlp`	`ipopt`	101.431	4	1228.581478	min
✓	2000	`adnlp`	`madnlp`	121.007	4	1228.581478	min
✓	2000	`exa`	`ipopt`	33.532	4	1228.581478	min	✓
✓	2000	`exa`	`madnlp`	54.978	4	1228.581478	min
✓	2000	`jump`	`ipopt`	48.451	4	1228.581478	min
✓	2000	`jump`	`madnlp`	86.680	4	1228.581478	min

ℹ️ Log

Benchmarks results:

┌─ Problem: electric_vehicle
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:   5.880 ms | iters: 4     | obj: 1.228699e+03  (min) | CPU:   9.83 KiB
│  │  ✓ | adnlp    | time:   8.532 ms | iters: 4     | obj: 1.228699e+03  (min) | CPU:   2.71 MiB
│  │  ✓ | exa      | time:   4.556 ms | iters: 4     | obj: 1.228699e+03  (min) | CPU:  58.31 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  12.944 ms | iters: 4     | obj: 1.228599e+03  (min) | CPU:  10.09 KiB
│  │  ✓ | adnlp    | time:  19.292 ms | iters: 4     | obj: 1.228599e+03  (min) | CPU:   6.74 MiB
│  │  ✓ | exa      | time:   9.344 ms | iters: 4     | obj: 1.228599e+03  (min) | CPU: 107.38 KiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:  23.806 ms | iters: 4     | obj: 1.228585e+03  (min) | CPU:  10.09 KiB
│  │  ✓ | adnlp    | time:  41.684 ms | iters: 4     | obj: 1.228585e+03  (min) | CPU:  13.44 MiB
│  │  ✓ | exa      | time:  17.360 ms | iters: 4     | obj: 1.228585e+03  (min) | CPU: 189.56 KiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time:  48.451 ms | iters: 4     | obj: 1.228581e+03  (min) | CPU:  10.09 KiB
│  │  ✓ | adnlp    | time: 101.431 ms | iters: 4     | obj: 1.228581e+03  (min) | CPU:  26.84 MiB
│  │  ✓ | exa      | time:  33.532 ms | iters: 4     | obj: 1.228581e+03  (min) | CPU: 353.62 KiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:   6.964 ms | iters: 4     | obj: 1.228699e+03  (min) | CPU:   4.64 MiB
│  │  ✓ | adnlp    | time:   8.080 ms | iters: 4     | obj: 1.228699e+03  (min) | CPU:   3.86 MiB
│  │  ✓ | exa      | time:   3.897 ms | iters: 4     | obj: 1.228699e+03  (min) | CPU:   1.65 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  16.297 ms | iters: 4     | obj: 1.228599e+03  (min) | CPU:  10.71 MiB
│  │  ✓ | adnlp    | time:  18.391 ms | iters: 4     | obj: 1.228599e+03  (min) | CPU:   8.98 MiB
│  │  ✓ | exa      | time:   8.332 ms | iters: 4     | obj: 1.228599e+03  (min) | CPU:   3.46 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:  32.637 ms | iters: 4     | obj: 1.228585e+03  (min) | CPU:  22.21 MiB
│  │  ✓ | adnlp    | time:  42.744 ms | iters: 4     | obj: 1.228585e+03  (min) | CPU:  17.52 MiB
│  │  ✓ | exa      | time:  15.456 ms | iters: 4     | obj: 1.228585e+03  (min) | CPU:   6.47 MiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time:  86.680 ms | iters: 4     | obj: 1.228581e+03  (min) | CPU:  42.46 MiB
│  │  ✓ | adnlp    | time: 121.007 ms | iters: 4     | obj: 1.228581e+03  (min) | CPU:  34.59 MiB
│  │  ✓ | exa      | time:  54.978 ms | iters: 4     | obj: 1.228581e+03  (min) | CPU:  12.50 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
  [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
  [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
  [276daf66] SpecialFunctions v2.6.1
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  [856f044c] MKL_jll v2025.2.0+0
  [d7ed1dd3] MUMPS_seq_jll v500.800.100+0
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⌅ [30392449] Pixman_jll v0.44.2+0
  [c0090381] Qt6Base_jll v6.8.2+2
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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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  [2a0f44e3] Base64 v1.11.0
  [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
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.11.0
  [56ddb016] Logging v1.11.0
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  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
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  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
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  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.11.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [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
  [e37daf67] LibGit2_jll v1.7.2+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
  [14a3606d] MozillaCACerts_jll v2023.12.12
  [4536629a] OpenBLAS_jll v0.3.27+1
  [05823500] OpenLibm_jll v0.8.5+0
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.7.0+0
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.59.0+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 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: `electric_vehicle`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	200	`adnlp`	`ipopt`	10.087	4	1228.698880	min
✓	200	`adnlp`	`madnlp`	9.563	4	1228.698880	min
✓	200	`exa`	`ipopt`	5.073	4	1228.698880	min
✓	200	`exa`	`madnlp`	4.313	4	1228.698880	min	✓
✓	200	`jump`	`ipopt`	6.626	4	1228.698880	min
✓	200	`jump`	`madnlp`	8.454	4	1228.698880	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	500	`adnlp`	`ipopt`	25.369	4	1228.599284	min
✓	500	`adnlp`	`madnlp`	24.511	4	1228.599284	min
✓	500	`exa`	`ipopt`	10.073	4	1228.599284	min
✓	500	`exa`	`madnlp`	9.184	4	1228.599284	min	✓
✓	500	`jump`	`ipopt`	14.879	4	1228.599284	min
✓	500	`jump`	`madnlp`	19.636	4	1228.599284	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`adnlp`	`ipopt`	48.028	4	1228.585040	min
✓	1000	`adnlp`	`madnlp`	62.680	4	1228.585040	min
✓	1000	`exa`	`ipopt`	18.673	4	1228.585040	min
✓	1000	`exa`	`madnlp`	16.809	4	1228.585040	min	✓
✓	1000	`jump`	`ipopt`	27.305	4	1228.585040	min
✓	1000	`jump`	`madnlp`	38.991	4	1228.585040	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	2000	`adnlp`	`ipopt`	146.336	4	1228.581478	min
✓	2000	`adnlp`	`madnlp`	193.542	4	1228.581478	min
✓	2000	`exa`	`ipopt`	35.680	4	1228.581478	min	✓
✓	2000	`exa`	`madnlp`	60.883	4	1228.581478	min
✓	2000	`jump`	`ipopt`	59.167	4	1228.581478	min
✓	2000	`jump`	`madnlp`	105.114	4	1228.581478	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	5000	`adnlp`	`ipopt`	409.911	4	1228.580480	min
✓	5000	`adnlp`	`madnlp`	437.919	4	1228.580480	min
✓	5000	`exa`	`ipopt`	90.130	4	1228.580480	min	✓
✓	5000	`exa`	`madnlp`	158.257	4	1228.580480	min
✓	5000	`jump`	`ipopt`	181.097	4	1228.580480	min
✓	5000	`jump`	`madnlp`	301.655	4	1228.580480	min

ℹ️ Log

Benchmarks results:

┌─ Problem: electric_vehicle
│
├──┬ Solver: ipopt, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:   6.626 ms | iters: 4     | obj: 1.228699e+03  (min) | CPU:   9.83 KiB
│  │  ✓ | adnlp    | time:  10.087 ms | iters: 4     | obj: 1.228699e+03  (min) | CPU:   2.71 MiB
│  │  ✓ | exa      | time:   5.073 ms | iters: 4     | obj: 1.228699e+03  (min) | CPU:  58.31 KiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  14.879 ms | iters: 4     | obj: 1.228599e+03  (min) | CPU:  10.09 KiB
│  │  ✓ | adnlp    | time:  25.369 ms | iters: 4     | obj: 1.228599e+03  (min) | CPU:   6.74 MiB
│  │  ✓ | exa      | time:  10.073 ms | iters: 4     | obj: 1.228599e+03  (min) | CPU: 107.38 KiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:  27.305 ms | iters: 4     | obj: 1.228585e+03  (min) | CPU:  10.09 KiB
│  │  ✓ | adnlp    | time:  48.028 ms | iters: 4     | obj: 1.228585e+03  (min) | CPU:  13.44 MiB
│  │  ✓ | exa      | time:  18.673 ms | iters: 4     | obj: 1.228585e+03  (min) | CPU: 189.56 KiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time:  59.167 ms | iters: 4     | obj: 1.228581e+03  (min) | CPU:  10.09 KiB
│  │  ✓ | adnlp    | time: 146.336 ms | iters: 4     | obj: 1.228581e+03  (min) | CPU:  26.84 MiB
│  │  ✓ | exa      | time:  35.680 ms | iters: 4     | obj: 1.228581e+03  (min) | CPU: 353.62 KiB
│  │
│  │  N = 5000
│  │  ✓ | jump     | time: 181.097 ms | iters: 4     | obj: 1.228580e+03  (min) | CPU:  10.09 KiB
│  │  ✓ | adnlp    | time: 409.911 ms | iters: 4     | obj: 1.228580e+03  (min) | CPU:  67.06 MiB
│  │  ✓ | exa      | time:  90.130 ms | iters: 4     | obj: 1.228580e+03  (min) | CPU: 845.81 KiB
│  └─
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 200
│  │  ✓ | jump     | time:   8.454 ms | iters: 4     | obj: 1.228699e+03  (min) | CPU:   4.64 MiB
│  │  ✓ | adnlp    | time:   9.563 ms | iters: 4     | obj: 1.228699e+03  (min) | CPU:   3.86 MiB
│  │  ✓ | exa      | time:   4.313 ms | iters: 4     | obj: 1.228699e+03  (min) | CPU:   1.65 MiB
│  │
│  │  N = 500
│  │  ✓ | jump     | time:  19.636 ms | iters: 4     | obj: 1.228599e+03  (min) | CPU:  10.71 MiB
│  │  ✓ | adnlp    | time:  24.511 ms | iters: 4     | obj: 1.228599e+03  (min) | CPU:   8.98 MiB
│  │  ✓ | exa      | time:   9.184 ms | iters: 4     | obj: 1.228599e+03  (min) | CPU:   3.46 MiB
│  │
│  │  N = 1000
│  │  ✓ | jump     | time:  38.991 ms | iters: 4     | obj: 1.228585e+03  (min) | CPU:  22.21 MiB
│  │  ✓ | adnlp    | time:  62.680 ms | iters: 4     | obj: 1.228585e+03  (min) | CPU:  17.52 MiB
│  │  ✓ | exa      | time:  16.809 ms | iters: 4     | obj: 1.228585e+03  (min) | CPU:   6.47 MiB
│  │
│  │  N = 2000
│  │  ✓ | jump     | time: 105.114 ms | iters: 4     | obj: 1.228581e+03  (min) | CPU:  42.46 MiB
│  │  ✓ | adnlp    | time: 193.542 ms | iters: 4     | obj: 1.228581e+03  (min) | CPU:  34.59 MiB
│  │  ✓ | exa      | time:  60.883 ms | iters: 4     | obj: 1.228581e+03  (min) | CPU:  12.50 MiB
│  │
│  │  N = 5000
│  │  ✓ | jump     | time: 301.655 ms | iters: 4     | obj: 1.228580e+03  (min) | CPU: 108.22 MiB
│  │  ✓ | adnlp    | time: 437.919 ms | iters: 4     | obj: 1.228580e+03  (min) | CPU:  85.82 MiB
│  │  ✓ | exa      | time: 158.257 ms | iters: 4     | obj: 1.228580e+03  (min) | CPU:  30.57 MiB
│  └─
└─

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
  [f6369f11] ForwardDiff v1.3.0
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  [46192b85] GPUArraysCore v0.2.0
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  [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
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  [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
  [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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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: `electric_vehicle`

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	1000	`exa`	`madnlp`	14.110	3	1228.585115	min	✓
✓	1000	`exa_gpu`	`madnlp`	85.244	11	1227.994075	min

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	5000	`exa`	`madnlp`	134.786	3	1228.580555	min
✓	5000	`exa_gpu`	`madnlp`	100.971	12	1225.635036	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	10000	`exa`	`madnlp`	291.415	3	1228.580412	min
✓	10000	`exa_gpu`	`madnlp`	122.904	12	1222.694929	min	✓

Success	N	Model	Solver	Time (ms)	Iters	Objective	Criterion	Best
✓	20000	`exa`	`madnlp`	620.227	3	1228.580376	min
✓	20000	`exa_gpu`	`madnlp`	147.379	12	1216.825416	min	✓

ℹ️ Log

Benchmarks results:

┌─ Problem: electric_vehicle
│
├──┬ Solver: madnlp, Discretization: trapeze
│  │
│  │  N = 1000
│  │  ✓ | exa      | time:  14.110 ms | iters: 3     | obj: 1.228585e+03  (min) | CPU:   6.35 MiB
│  │  ✓ | exa_gpu  | time:  85.244 ms | iters: 11    | obj: 1.227994e+03  (min) | CPU:  5.932 MiB | GPU: 17.560 MiB
│  │
│  │  N = 5000
│  │  ✓ | exa      | time: 134.786 ms | iters: 3     | obj: 1.228581e+03  (min) | CPU:  29.99 MiB
│  │  ✓ | exa_gpu  | time: 100.971 ms | iters: 12    | obj: 1.225635e+03  (min) | CPU: 10.411 MiB | GPU: 88.029 MiB
│  │
│  │  N = 10000
│  │  ✓ | exa      | time: 291.415 ms | iters: 3     | obj: 1.228580e+03  (min) | CPU:  59.53 MiB
│  │  ✓ | exa_gpu  | time: 122.904 ms | iters: 12    | obj: 1.222695e+03  (min) | CPU: 15.529 MiB | GPU: 176.041 MiB
│  │
│  │  N = 20000
│  │  ✓ | exa      | time: 620.227 ms | iters: 3     | obj: 1.228580e+03  (min) | CPU: 118.61 MiB
│  │  ✓ | exa_gpu  | time: 147.379 ms | iters: 12    | obj: 1.216825e+03  (min) | CPU: 25.722 MiB | GPU: 352.017 MiB
│  └─
└─