Basic Introductory Tutorial on Interval Constraints

Table Of Contents

 

  1. History of Interval Constraints
  2. What are Interval Constraints?
  3. Interval Constraint Processing
  4. General Applications
  5. Advantages of Interval Constraints

History

Interval constraints were first introduced by J.G. Cleary in paper "Logical Arithmetic".

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What are Interval Constraints?

Interval Constraint is a generic term used to denote a constraint in which variables are linked with intervals.

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Interval Constraint Processing

Interval constraint processing is a method used to process sets of continuous or mixed constraints over the real numbers. It relates techniques in CP and IC, propagation and search methods in constraint programming and the processes from interval computations

The Interval Constraint approach combines :

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Applications

  • Game Theory
  • Mechanical Design
  • Chemistry
  • Aeronautics
  • Medical Diagnosis
  • Image Synthesis
  • Computer-aided design
  • Computer graphics
  • Hybrid integer/non-linear continuous problems
  • Biocomputing (3D geometry)
  • Engineering, etc.

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Advantages of Interval Constraints

  • It shows in some cases superior efficiency to classical mathematical programming methods.
  • It can deal with a large class of constraints(possibly non polynomial ones)
  • Due to the clever use of outward-rounding, it gives correct results(no solution is lost) despite of the finiteness of number representation in floating point arithmetic.

 

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