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Polars-backed LP/MIP eDSL on top of HiGHS — a generic optimization-modelling kernel.

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# polar-high

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A Python library for building and solving large linear and
mixed-integer optimisation programs, i.e. domain specific language
(DSL) for algebraic modelling. Variables and parameters are
[polars](https://pola.rs/) DataFrames, expressions are joined and
grouped lazily, and the matrix is assembled directly through
[HiGHS](https://highs.dev/) — or exported as MPS for any other LP/MIP
solver. The kernel is intentionally domain-free: it has no opinions
about energy systems, supply chains, or any specific application.

## Install

```bash
pip install polar-high
```

Requires Python 3.11+. HiGHS ships in `highspy`, no separate install.

## Quickstart

A tiny dispatch LP — wind + coal over three hours, minimise cost
subject to capacity and per-hour demand.

```python
import polars as pl

from polar_high import Param, Problem, Sum

p = Problem()

# Index sets — declared once, reused below
unit_index = pl.DataFrame({"unit": ["wind", "coal"]})
time_index = pl.DataFrame({"hour": [1, 2, 3]})
composite_index = unit_index.join(time_index, how="cross")

# Decision variable v_production[unit, hour] >= 0
v_production = p.add_var(
    "v_production",
    dims=("unit", "hour"),
    index=composite_index,
    lower=0.0,
)

# Operating cost per unit
cost = Param(
    ("unit",),
    pl.DataFrame({"unit": ["wind", "coal"], "value": [2.0, 8.0]}),
)

# Available capacity per unit per hour — built per-unit, then concatenated
cap_wind = time_index.with_columns(
    pl.lit("wind").alias("unit"),
    pl.Series("value", [3.0, 1.0, 4.0]),
)
cap_coal = time_index.with_columns(
    pl.lit("coal").alias("unit"),
    pl.Series("value", [10.0, 10.0, 10.0]),
)
cap = Param(
    ("unit", "hour"),
    pl.concat([cap_wind, cap_coal]).select("unit", "hour", "value"),
)

# Demand per hour
demand = Param(
    ("hour",),
    time_index.with_columns(pl.Series("value", [5.0, 6.0, 4.0])),
)

# Minimise total cost
p.set_objective(cost * v_production, sense="min")

# v_production[unit, hour] <= cap[unit, hour]
p.add_cstr(
    "capacity",
    over=composite_index,
    lhs_terms={"production": v_production},
    sense="<=",
    rhs_terms={"cap": cap},
)

# Σ_unit v_production[unit, hour] == demand[hour]
p.add_cstr(
    "demand_balance",
    over=time_index,
    lhs_terms={"production": Sum(v_production, over=("unit",))},
    sense="==",
    rhs_terms={"demand": demand},
)

sol = p.solve()
print(f"objective: {sol.obj}")  # 72.0
print(sol.value("v_production"))
```

The same code lives at [`tests/fixtures/quickstart_example.py`](tests/fixtures/quickstart_example.py) and is executed in the test suite, so README and docs stay in sync.

## Documentation

Full docs at **<https://nodal-tools.fi/polar-high/>** — published
with MkDocs + [mike](https://github.com/jimporter/mike) for per-version
reads.

- **[Concepts](https://nodal-tools.fi/polar-high/latest/concepts/)** —
  the indexed-frame mental model (`Var`, `Param`, `Sum`, `Where`,
  `Lag`, broadcasting/join semantics).
- **[Guide](https://nodal-tools.fi/polar-high/latest/guide/warm-starting/)** —
  warm-starting, decomposition building blocks, performance tuning,
  debugging.
- **[API reference](https://nodal-tools.fi/polar-high/latest/reference/api/)** —
  autogenerated from docstrings.
- **[Compare](https://nodal-tools.fi/polar-high/latest/compare/alternatives/)** —
  how polar-high relates to Pyomo, JuMP, gurobipy, linopy, and
  GNU MathProg.

Build locally: `pip install -e ".[docs]" && mkdocs serve`.

## Used by

polar-high is the build engine behind the
[FlexTool](https://github.com/irena-flextool/flextool) energy-system
modelling toolkit (still in dev branch only, 7.5.2026 situation).
FlexTool's fleet of system tests (from earlier
GNU MathProg to HiGHS implementation) has been used to test
polar-high in real modelling use cases. In addition
polar-high kernel has its own set of unit and system tests.

## Created by

polar-high was created by **Juha Kiviluoma** of **Nodal-Tools** using
**Claude Opus**.

## License

Apache-2.0 — see [LICENSE](LICENSE) and [NOTICE](NOTICE).
Changelog: [CHANGELOG.md](CHANGELOG.md).

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