Tech Report CS-95-33

Helios: A Modeling Language for Nonlinear Constraint Solv ing and Global Optimization using Interval Analysis

Pascal VanHentenryck and Laurent Michel

November 1995


This paper introduces Helios, a mathematical modeling language to solve nonlinear constraint systems and global optimization problems using interval analysis. Helios makes it possible to state nonlinear applications almost as in scientific publications by offering computer-readable equivalents of many mathematical notations. As a consequence, Helios significantly simplifies the solving of these applications by letting users focus on modeling aspects instead of on low-level details. Helios statements are used as inputs to state-of-the-art interval analysis algorithms, which combine techniques from numerical analysis and artificial intelligence. Helios has been evaluated on a variety of benchmarks. On traditional constraint-solving benchmarks, it outperforms the interval methods we are aware of and is competitive with state-of-the-art continuation methods. On global optimization problems, Helios outperforms the interval algorithms we are aware of.

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