mathematics

MiniZinc

MiniZinc is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand MiniZinc rather than just read about it. In short: MiniZinc is a constraint modelling language (or algebraic modeling language) to describe and solve high-complexity problems using a variety of well-known solving paradigms for combinatorial problems including constraint programming, integer programming, SAT, and SMT. Following the constraint programming paradigm, in MiniZinc a problem is specified in terms of known values (parameters), unknown values (decision varia…

Key takeaways

MiniZinc belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect MiniZinc to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of MiniZinc from memory before moving on to harder problems.

Reference excerpt

MiniZinc is a constraint modelling language (or algebraic modeling language) to describe and solve high-complexity problems using a variety of well-known solving paradigms for combinatorial problems including constraint programming, integer programming, SAT, and SMT. Following the constraint programming paradigm, in MiniZinc a problem is specified in terms of known values (parameters), unknown values (decision variables), and the relationship (constraints) between these values. MiniZinc promotes the use of global constraints to model well-known structures in problems. These global constraints improve the clarity of the model and allow solvers to use the most effective method to exploit the structure. A MiniZinc problem instance is translated (or flattened) to a level at which it only supports constraints that are supported by the target solver and then given to the solver using its preferred format. Currently MiniZinc can communicate with solvers using its own format "FlatZinc" or .nl files. A big advantage of MiniZinc is the possibility to use different solvers from the same MiniZinc instance. MiniZinc supports many solvers, both open source and commercial software, including CBC, Choco, Chuffed, HiGHS, Gurobi, IPOPT, and OR-Tools. MiniZinc is interoperable with other languages such as R and Python.

Language The following MiniZinc model can be used to solve the famous n-queens puzzle:

References

External links Official website MiniZinc on GitHub

Illustrations

Worked examples

Example 1 — a first encounter with MiniZinc

Start with the simplest possible case. Write down what MiniZinc claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to MiniZinc before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about MiniZinc ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of MiniZinc

In research: MiniZinc appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses MiniZinc in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: MiniZinc is common in secondary-school and first-year university syllabi. It links to neighbouring topics Algebraic modeling languages, Computer algebra systems, Mathematical modeling, so understanding it makes those chapters shorter.
In everyday life: Look for MiniZinc outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study MiniZinc in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what MiniZinc means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain MiniZinc out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is MiniZinc in simple terms?

Why does MiniZinc matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study MiniZinc?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on MiniZinc.