Benchmarks¶

Time and memory to build each model and hand it to the solver, in specsolve and four other libraries. Nothing is solved, and CI checks that every library builds the same model (bench/models/).

Solver Show As Axes

Libraries

click to hide

drag on a chart to zoom every chart

Reading the charts¶

One panel per model, one line per library. The x axis counts columns: the variables that reach the solver. Solver picks the solver for every panel and the table.

specsolve is the thick violet line.
The grey line is the matrix floor: a finished matrix handed to the solver in one call, passModel for HiGHS and loadModel for Gurobi. Its gap to specsolve is everything specsolve does before the solver holds the model. Its memory includes its own copy of the arrays.
A point is a median, and its whisker is the middle half of the rounds. Overlapping whiskers are a tie (why the median).
A shaded funnel is a projection past the 30 s or 16 GB budget. A wide funnel is a guess.
÷ specsolve puts specsolve at 1×, so a line at 3× is three times slower or larger. A point outside the window is named at the edge it crosses.
Drag a box on any chart to zoom them all, and the table with them. A drag along one side zooms one axis. Double-click or Reset zoom to see everything.
The table divides by specsolve. Purple is where specsolve is faster, orange where the other library is, and grey within 10%. >30 s and >16 GB are sizes the budget refused.

The models¶

Columns and rows count the variables and the constraints that reach the solver, one per value that exists. Every variable and constraint also runs over snapshot, and a model grows by its snapshots alone.

	dispatch	network	nodal	sector
for	bounds and one balance: the shape an array library suits best	a small PyPSA model: lines, stores, solar and wind, and pooled caps	dispatch at nodes, where a technology exists only where it is installed	each technology delivers one of five carriers, such as heat or hydrogen
variables	p[generator]	p[bus, tech], f[line], charge[store], discharge[store], soc[store]	p[node, tech]	p[node, tech]
constraints	power_balance	balance[bus], soc_balance[store], pool_cap[pool]	balance[node]	balance[node, carrier]
grouped sums	—	line → bus, store → bus, bus × tech → pool	—	—
dimensions	generator 100	bus 50, tech 12, line 100, store 50	node 50, tech 12	node 50, tech 12, carrier 5
density	100%	25%	25%	25%
snapshots	2–100k	2–25k	2–20k	2–20k
columns per snapshot	100	400	150	150
rows per snapshot	1	150	50	125
nonzeros per snapshot	100	800	150	150

From 100k columns up, linopy's peak memory stays within 1.3× of specsolve's on HiGHS, except on network, the one model that sums through a grouping. There it is 2.7× at 1M columns, 1.75 GB against 0.65 GB, and the memory budget stops linopy at that size (#2039).

A script that solves one model¶

The charts leave out what a script pays to start: the interpreter, the import and the first build. This table times a new process from launch to exit, on HiGHS.

launch to exit	dispatch 10k columns	network 10k columns	nodal 3k columns	sector 3k columns
specsolve	0.46 s	0.51 s	0.47 s	0.49 s
specsolve-in-memory	0.46 s · 1.0x	0.50 s · 1.0x	0.46 s · 1.0x	0.47 s · 1.0x
linopy	0.96 s · 2.1x	1.10 s · 2.1x	0.92 s · 2.0x	0.95 s · 1.9x
pyomo	0.69 s · 1.5x	0.89 s · 1.7x	0.68 s · 1.4x	0.74 s · 1.5x

A script that solves one small model with specsolve finishes in about half a second, about half of linopy's time (#2031).

Not measured yet¶

Sparsity other than a quarter. nodal, network and sector are sparse at one density, a quarter of the node and technology pairs. pixi run density sweeps nodal from dense to one pair in twelve, and no published run has taken that sweep.
Solve time. Every number stops when the model reaches the solver.

Method¶

Each measurement runs in its own process, with import excluded and teardown included, on an idle machine. A point is the median of nine rounds, or of five where a round takes over a second. Peak memory is ru_maxrss. A projection's two edges carry the last measured step forward, one at its cost per column and one at its growth rate. uv run --locked bench/reproduce.py runs it again with every version pinned, and the harness has every flag and caveat, such as the allocator cost on polars' peak (#896).