5bound

5bound is a theoretical framework used in optimization and constraint solving to prune search spaces by maintaining and propagating five distinct types of bounds on decision variables. It extends traditional bound propagation by integrating multiple bounding techniques into a unified scheme, enabling tighter feasibility checks and faster convergence in complex problems.

Five bound types are employed: arithmetic lower bounds that reflect minimum feasible values; arithmetic upper bounds for maximum feasible values; logical bounds derived from propositional constraints and implications; probabilistic bounds that use data-driven confidence intervals; and relational bounds that exploit dependencies among variables to restrict joint ranges. Together, these bounds form a bound set that updates as the solver progresses.

In a typical 5bound workflow, a solver initializes each variable with broad bounds, then iteratively propagates all five types of bounds through constraints. When a bound becomes tighter, it may trigger further propagation or domain pruning. The framework emphasizes maintaining consistency across bound types to prevent oscillations and to exploit complementary information.

5bound is applied in various domains, including constraint programming, mixed-integer linear programming, satisfiability modulo theories, scheduling and planning, and parameter search in machine learning. It aims to improve pruning efficiency on large-scale problems where single-bound methods struggle.

While 5bound originated in theoretical discussions and has appeared in practice-oriented notes and tutorials, its adoption remains experimental. Proponents argue that the approach can yield substantial performance gains when problems exhibit rich inter-variable structure, whereas critics note increased implementation complexity and diminishing returns on poorly constrained problems.

Related topics include bound propagation, constraint programming, and pruning strategies for search.