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Curated by: [Andrew Rosemberg & Contributors]

Dataset Card for Parametric Optimization Problems

This dataset is a collection of parametrized optimization problems stored in MathOptFormat (.mof.json) files. Each file encodes a mathematical optimization problem—its objective, constraints, and parameters—using a standardized data structure for portability and ease of parsing.

Dataset Details

Dataset Description

Parametric optimization problems arise in scenarios where certain elements (e.g., coefficients, constraints) may vary according to problem parameters. This collection gathers different problem instances across various domains (e.g., power systems, control, resource allocation) in a uniform JSON-based format. Users can load, modify, and solve these problems with specialized libraries—particularly with the LearningToOptimize.jl package in Julia.

A general form of a parameterized convex optimization problem is

$\begin{aligned} &\min_{x} \quad f(x; \theta) \\ &\text{subject to} \quad g_i(x; \theta) \leq 0, \quad i = 1,\dots, m \\ &\quad\quad\quad\quad A(\theta)x = b(\theta) \end{aligned}$

where $\theta$ is the parameter.

Usage

Using the LearningToOptimize.jl package in julia, users can generate problem variants by sampling parameter values follwing defined rules:

using LearningToOptimize

general_sampler(
    "PGLib/Load/ACPPowerModel/pglib_opf_case3_lmbd.m_ACPPowerModel_load.mof.json";
    samplers=[
        (original_parameters) -> scaled_distribution_sampler(original_parameters, 10000),
        (original_parameters) -> line_sampler(original_parameters, 1.01:0.01:1.25), 
        (original_parameters) -> box_sampler(original_parameters, 300),
    ],
)

where scaled_distribution_sampler, line_sampler and box_sampler are some examples of built in samplers.

Outside Dataset Sources

PGLib: power-grid-lib
JuMP JuMP Tutorials

Uses

Direct Use

These problems can be directly used to:

Test solver performance on a variety of instances.
Benchmark machine learning models that learn optimization proxies.
Generate synthetic scenarios by applying parametric samplers for stress-testing or research.

Out-of-Scope Use

The dataset is not intended for training general-purpose NLP or computer vision models.
Direct personal or sensitive information is not included, so any privacy-infringing use does not apply.

Dataset Structure

TBD

File Structure

In a typical .mof.json file, you will find:

Objectives: Specifies the optimization sense (e.g., Min, Max) and the functions to be optimized.
Variables: A list of decision variables, potentially including parameters as special variable entries.
Constraints: Each constraint references a function (made up of one or more variables) and a set specifying bounds, including Parameter sets for parametric variables.

An example snippet for a parameter:

{
  "function": {
    "name": "name_of_parameter",
    "type": "Variable"
  },
  "set": {
    "type": "Parameter",
    "value": 1.0
  }
}