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Skills & Competence

Mathematical solver

LEDAS Math Solver is aimed at solving satisfaction/optimization problems under constraints expressed by

  • Algebraic equations/inequalities (white-boxes)
  • External functions (black-boxes)
  • Design tables
  • Finite domain constraints
  • Geometric and other domain-specific constraints.

To efficiently deal with such problems, LEDAS Math Solver is built as an integration of constraint satisfaction/optimization methods, algorithms of numerical mathematics, efficient system architecture as well as a set of user and programmer tools:

  • Methods
    • CP. Generalized Constraint Propagation over Interval and Finite Domains
    • CPX (CP eXtended). CP-method adjusted for finite-domain problems
    • AC4, AC5. Classical methods for achieving Arc-consistency over Finite Domains
    • Gauss. Solving systems of linear algebraic equations
    • Interior Point. A method of linear programming improved to find sub-optimal solutions
    • Newton. Interval variant of Newton method for solving nonlinear equations
    • Bisection. General method for locating solutions
    • Branch and Bound. Well-known method of solving optimization problems
    • Tabular constraint processing (design tables, data bases, etc.)
    • Gradient method to deal with so-called black-box satisfaction/optimization widely used in mechanical CAD domain
    • Searching sub-optimal solution (with a proof of its sub-optimality)
    • Integer Local Search
    • A set of global constraint satisfaction methods for finite domains ("alldifferent", "global cardinality" and others)
  • Efficient interval library with directed rounding providing verified results
  • Transparent C API
  • Script
    All functionality can be accessed from Python language with the help of PySolver module
  • High Level Language
    Including: sets, strings, structures; operations with arrays; implicit functions, models

For many benchmarks, LEDAS Solver outperforms all known results of our competitors.

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