Three Generalizations of the FOCUS Constraint

TL;DR

This paper introduces three generalized versions of the FOCUS constraint to improve flexibility in modeling solution concentration, along with complete filtering algorithms and decomposition methods for each.

Contribution

It presents three novel generalizations of the FOCUS constraint, enhancing its applicability and providing algorithms and decompositions for efficient constraint solving.

Findings

Developed three new generalized FOCUS constraints.

Provided complete filtering algorithms for each generalization.

Discussed decomposition strategies for implementation.

Abstract

The FOCUS constraint expresses the notion that solutions are concentrated. In practice, this constraint suffers from the rigidity of its semantics. To tackle this issue, we propose three generalizations of the FOCUS constraint. We provide for each one a complete filtering algorithm as well as discussing decompositions.