Fourteen self-contained optimisation problems, one directory each. Every directory holds a README.md describing the formulation and a runner.py that builds the model, solves it, and verifies the result end to end.

Run one from the repository root:

uv run python examples/maxcut/runner.py --seed 42

Every runner accepts --seed, --interpreter (python or rust), --solver, and -o/--output. Problem size flags vary; each directory's README.md carries the exact table.

Examples that encode graph cuts, colouring, covers, independent sets, and tours.

• Max-Cut -- Find a 2-colour partition of a weighted graph that maximises the cut weight.
• Graph Coloring -- Assign colours to graph nodes so adjacent nodes do not share a colour.
• Maximum Independent Set -- Select the largest subset of graph nodes with no selected edge between them.
• Vertex Cover -- Select the smallest vertex subset that covers every graph edge.
• Travelling Salesman Problem -- Find the shortest Hamiltonian tour through a random symmetric distance matrix.

Examples that select subsets, cover demands, pack bins, and balance integer weights.

• Knapsack -- Select items that maximise value while respecting a capacity constraint.
• Bin Packing -- Pack items into the minimum number of fixed-capacity bins.
• Set Cover -- Select the minimum set collection whose union covers the universe.
• Weighted Set Cover -- Select sets with capacities to cover element demands at minimum cost.
• Number Partition -- Split positive integers into two subsets with nearly equal sums.
• Portfolio Optimization -- Select a fixed-size portfolio while penalising higher-order risk interactions.
• Portfolio Rebalance -- Choose signed integer asset weights against a risk matrix and a budget.

Examples that reduce clauses and higher-order pseudo-Boolean objectives to quadratic models.

• Max-3-SAT -- Find the assignment that satisfies the maximum number of 3-literal clauses.
• Cubic Optimization -- Minimise a cubic pseudo-Boolean objective through HOBO degree reduction.
• Quartic Optimization -- Minimise a degree-4 pseudo-Boolean objective through two-stage REDUCE chaining.

• Using the Examples -- what every directory has in common, how to run one, and how to adapt one into a problem of your own
• Modelling with XQCP -- the DSL these runners are written in
• Cookbook -- the recurring encoding patterns these examples are built from