MIP++¶

MIP++ is a header-only, dependency-free C++23 library for linear, mixed-integer, and quadratic programming — the fastest way to write portable, solver-agnostic optimization models in modern C++. It gives you an algebraic modeling syntax as readable as JuMP or Pyomo, but compiles down to direct calls into the solver's own C API. The same model code targets any of 11 solvers — you choose the backend at compile time, and its shared library is loaded dynamically at runtime, with no link-time solver dependency.

#include <print>

#include "mippp/solvers/highs/all.hpp"

using namespace mippp;
using namespace mippp::operators;

int main() {
    highs_lp model;  // loads HiGHS at runtime, swap for gurobi_*, cbc_*, ...

    auto x1 = model.add_variable();
    auto x2 = model.add_variable({.upper_bound = 3});

    model.set_maximization();
    model.set_objective(4 * x1 + 5 * x2);
    model.add_constraint(x1 <= 4);
    model.add_constraint(2 * x1 + x2 <= 9);

    model.solve();
    auto sol = model.get_solution();

    std::println("objective = {}", model.get_solution_value());
    std::println("x1 = {}, x2 = {}", sol[x1], sol[x2]);
    return 0;
}

Where to start¶

The documentation follows the path of a modeling study: build a model, solve it, read the results, then wrap an algorithm around it.

1. Getting started — read in order, about half an hour.

• Why MIP++ — the design choices behind the library, why they matter for operations-research work, and who the library is (and is not) for. Start here.
• Installation — requirements, Conan or CMake setup, and making solver libraries discoverable.
• A first model — a guided tour of the program above.
• Coming from gurobipy, JuMP or PuLP — a translation table, and the six things that differ.

2. Modeling — variables and index sets, expressions and constraint families, objectives (including quadratic), special constraints.

3. Solving — status, limits and tolerances, diagnosing infeasibility, solutions, duals and reduced costs, re-solving and model updates.

4. Algorithms — branch-and-cut with lazy constraints, column generation, the deletion filter.

5. Solvers — choosing a solver among the 11 backends, and writing solver-generic code for cross-solver experiments.

Complete runnable programs — N-Queens, Sudoku, TSP with lazy constraints, cutting stock by column generation, an infeasible transportation plan diagnosed through its IIS — are indexed in Worked examples.

Supported solvers¶

_{Per-feature support (duals, callbacks, MIP starts, IIS, …) varies by backend — see the feature matrices in Choosing a solver.}

Performance¶

Time to build the N-Queens model (N² binary variables, 6N−6 constraints) — MIP++ in milliseconds, the other interfaces as a multiple of it on the same backend:

A million binary variables in 152 ms through HiGHS, 67 ms through Cbc — and within 2–8% (102–108%) of what the Gurobi C API itself costs. The Python layers land one to two orders of magnitude above that. Build time is noise when a single solve runs for hours — it matters on very large models and in loops that touch the model constantly, and the Performance page is explicit about that scope. Full tables across eight backends, the case where MIP++ loses (SCIP), the limitations and the methodology are there too — benchmark code and raw per-solver timings in mippp_nqueens.

Acknowledgements¶

MIP++ is grounded in the PhD thesis and postdoctoral positions of François Hamonic, funded by Région Sud - Provence-Alpes-Côte d'Azur, Natural Solutions, the European Research Council grant SCALED to Cécile ALBERT (ERC-STG no. 949812), the ANR project RESILIENCE (no. ANR-24-PEVD-0002) and the project OASIS of ITEM, an A*Midex Initiative d'Excellence institute funded under France 2030 (AMX-19-IET-012).

Documentation, citing, license¶

• 📖 Documentation: fhamonic.github.io/mippp — sources live under docs/.
• 📄 If you use MIP++ in academic work, please cite it — see CITATION.cff.
• ⚖️ Licensed under the Boost Software License 1.0.