mathematics

MINTO

MINTO 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 MINTO rather than just read about it. In short: MINTO (Mixed Integer Optimizer) is an integer programming solver which uses branch and bound algorithm. MINTO is a software system that solves mixed integer programming problem by a branch and bound algorithm with linear programming relaxations.

Key takeaways

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

Reference excerpt

MINTO (Mixed Integer Optimizer) is an integer programming solver which uses branch and bound algorithm. MINTO is a software system that solves mixed integer programming problem by a branch and bound algorithm with linear programming relaxations. It also provides automatic constraint classification, preprocessing, primal heuristics and constraint generation. It also has inbuilt cut generation and can create knapsack cuts, GUB cuts, clique cuts, implication cuts, flow cuts, mixed integer rounding and Gomory cuts. Moreover, the user can enrich the basic algorithm by providing a variety of specialized application routines that can customize MINTO to achieve higher efficiency for a problem class. MINTO does not have a linear programming (LP) solver of its own. It can use most of the LP solvers, like CLP, CPLEX, XPRESS through the OSI interface of COIN-OR. MINTO can read files in MPS and can also be called as a solver from AMPL. It can run on both Linux and Windows operating system. MINTO is a non-commercial solver and the executables are available for free download from its home page at COR@L.

See also COIN-OR (Computational Infrastructure for Operations Research)

References J.T. Linderoth and T.K. Ralphs, Noncommercial Software for Mixed-Integer Linear Programming, Integer Programming: Theory and Practice, John Karlof (ed.), CRC Press Operations Research Series, 2005, 253–303. (Working Paper Version PDF)

External links MINTO Homepage

Worked examples

Example 1 — a first encounter with MINTO

Start with the simplest possible case. Write down what MINTO 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 MINTO 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 MINTO 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 MINTO

In research: MINTO 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 MINTO 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: MINTO is common in secondary-school and first-year university syllabi. It links to neighbouring topics Mathematical optimization software, so understanding it makes those chapters shorter.
In everyday life: Look for MINTO 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.

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How to study MINTO in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what MINTO 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 MINTO out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is MINTO in simple terms?

Why does MINTO 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 MINTO?

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 MINTO.