computer science

MPS (format)

MPS (format) is a computer science 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 MPS (format) rather than just read about it. In short: MPS (Mathematical Programming System) is a file format for presenting and archiving linear programming (LP) and mixed integer programming problems. Overview The format was named after an early IBM LP product and has emerged as a de facto standard ASCII medium among most of the commercial LP solvers.

Key takeaways

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

Reference excerpt

MPS (Mathematical Programming System) is a file format for presenting and archiving linear programming (LP) and mixed integer programming problems.

Overview

The format was named after an early IBM LP product and has emerged as a de facto standard ASCII medium among most of the commercial LP solvers. Essentially all commercial LP solvers accept this format, and it is also accepted by the open-source COIN-OR system. Other software may require a customized reader routine in order to read MPS files. However, with the acceptance of algebraic modeling languages MPS usage has declined. For example, according to the NEOS server statistics in January 2011 less than 1% of submissions were in MPS form compared to 59.4% of AMPL and 29.7% of GAMS submissions. MPS is column-oriented (as opposed to entering the model as equations), and all model components (variables, rows, etc.) receive names. MPS is an old format, so it is set up for punch cards: Fields start in column 2, 5, 15, 25, 40 and 50. Sections of an MPS file are marked by so-called header cards, which are distinguished by their starting in column 1. Although it is typical to use upper-case throughout the file for historical reasons, many MPS-readers will accept mixed-case for anything except the header cards, and some allow mixed-case anywhere. The names that you choose for the individual entities (constraints or variables) are not important to the solver; one should pick meaningful names, or easy names for a post-processing code to read.

MPS format Here is a little sample model written in MPS format (explained in more detail below):

NAME TESTPROB ROWS N COST L LIM1 G LIM2 E MYEQN COLUMNS XONE COST 1 LIM1 1 XONE LIM2 1 YTWO COST 4 LIM1 1 YTWO MYEQN -1 ZTHREE COST 9 LIM2 1 ZTHREE MYEQN 1 RHS RHS1 LIM1 5 LIM2 10 RHS1 MYEQN 7 BOUNDS UP BND1 XONE 4 LO BND1 YTWO -1 UP BND1 YTWO 1 ENDATA

For comparison, here is the same model written out in an equation-oriented format:

Optimize COST: XONE + 4*YTWO + 9*ZTHREE Subject To LIM1: XONE + YTWO <= 5 LIM2: XONE + ZTHREE >= 10 MYEQN: - YTWO + ZTHREE = 7 Bounds XONE <= 4 -1 <= YTWO <= 1 End

As mentioned below, the lower bound on XONE is either zero or -infinity, depending upon implementation, because it is not specified. Strangely, nothing in MPS format specifies the direction of optimization, and there is no standard "default" direction; some LP solvers will maximize if not instructed otherwise, others will minimize, and still others put safety first and have no default and require a selection somewhere in a control program or by a calling parameter. If the model is formulated for minimization and the solver requires maximization (or vice versa), it is easy to convert between the two by negating all coefficients of the objective function. The optimal value of the objective function will then be the negative of the original optimal value, but the values of the variables themselves will be correct. Some programs support specifying minimization/maximization within the MPS file.

OBJSENSE MAX

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with MPS (format)

Start with the simplest possible case. Write down what MPS (format) claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, 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 MPS (format) 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 MPS (format) 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 MPS (format)

In research: MPS (format) appears in computer science 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 MPS (format) 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: MPS (format) is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computer file formats, Linear programming, Mathematical optimization software, so understanding it makes those chapters shorter.
In everyday life: Look for MPS (format) 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 MPS (format) in 20 minutes

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

Frequently asked questions

What is MPS (format) in simple terms?

MPS (Mathematical Programming System) is a file format for presenting and archiving linear programming (LP) and mixed integer programming problems. Overview The format was named after an early IBM LP product and has emerged as a de facto standard ASCII medium among most of the commercial LP solvers.

Why does MPS (format) matter?

Because it connects several computer science 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 MPS (format)?

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 MPS (format).