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MiniZinc Examples

Here we give several MiniZinc examples. For each one, we provide a problem description, a model, one or more data files, and one or more solutions provided by our implementation.

Golomb

A Golomb ruler may be defined as a set of m integers 0 = a₁ < a₂ < … < a_m such that the m(m-1)/2 differences a_j - a_i, 1 ≤ i < j ≤ m are distinct. Such a ruler is said to contain m marks and is of length a_m. The objective is to find optimal (minimum length) or near optimal rulers. 

Job-Shop

Example from the MiniZinc paper: n×n job shop scheduling in MiniZinc.

Langford

Langford's Problem (CSPlib problem 24). Instance L(k,n): Arrange k sets of numbers 1 to n so that each appearance of the number m is m numbers on from the last. For example, the L(3,9) problem is to arrange 3 sets of the numbers 1 to 9 so that the first two 1's and the second two 1's appear one number apart, the first two 2's and the second two 2's appear two numbers apart, etc.

Minimum Cost Flow

Classic OR problem: Find the minimum cost flow in a network, while satisfying the demands in the nodes, and not violating the capacities of the arcs.

Multidimensional Knapsack Problem

The classical 0/1 multidimensional knapsack problem. There is a knapsack with m different capacity constraints. There are n items with profits and weights. The goal is to maximise the total profit of the items in the knapsack while not violating any of the capacity constraints.

Open Shop Scheduling

Rectangular Scheduling Problem. J jobs have to be performed using M machines with the objective of minimising the total makespan.

Perfect Squares

Perfect squares: find a set of integers the sum of whose squares is itself a square.

Photo

A group of N people wants to take a group photo. Each person can give P preferences next to whom he or she wants to be placed in the photo. The problem to be solved is to find a placement that satisfies as many preferences as possible.

Production Planning

Product example from the OPL book.

N-Queens

Place N queens on a N x N chess board such that none of the queens can attack each other.

Hoist Scheduling

MiniZinc model of one-hoist scheduling. Robert Rodosek and Mark Wallace. A Generic Model and Hybrid Algorithm for Hoist Scheduling Problems. In Michael J. Maher and Jean-Francois Puget eds. Principles and Practice of Constraint Programming - CP98, Springer, Lecture Notes in Computer Science, volume 1520, 1998.

Sudoku

Simple sudoku for squares of arbitrary size N = S².

Who owns the zebra?

Also known as "Einstein's puzzle". For details see the comment at the top of the model file. There is no separate data file for this problem because it is formulated in such a way that the model and data cannot be easily separated.