An Efficient Algorithm for a Sharp Approximation of Universally Quantified Inequalities

TL;DR

This paper presents a new branch and prune algorithm tailored for a specific class of quantified constraint satisfaction problems involving universally quantified inequalities, demonstrating improved performance over existing methods.

Contribution

The paper introduces a novel generic branch and prune algorithm specifically designed for continuous QCSPs with universally quantified inequalities, including specialized operators and rules.

Findings

Algorithm outperforms state-of-the-art methods

Effective handling of parameters in constraints

Applicable to engineering and design problems

Abstract

This paper introduces a new algorithm for solving a sub-class of quantified constraint satisfaction problems (QCSP) where existential quantifiers precede universally quantified inequalities on continuous domains. This class of QCSPs has numerous applications in engineering and design. We propose here a new generic branch and prune algorithm for solving such continuous QCSPs. Standard pruning operators and solution identification operators are specialized for universally quantified inequalities. Special rules are also proposed for handling the parameters of the constraints. First experimentation show that our algorithm outperforms the state of the art methods.