Constraintbased

Constraintbased, often written as constraint-based or constraint programming, refers to an approach to modeling and solving problems by specifying constraints that must be satisfied by the variables representing decision elements. In constraint programming, problems are formulated as constraint satisfaction problems (CSPs). A problem is described by variables, their finite or enumerated domains, and a set of constraints that restrict combinations of variable values. Solutions are assignments to variables that satisfy all constraints; some formulations also include an objective to optimize.

Solving typically involves constraint propagation to prune domains and detect inconsistencies, combined with search when multiple alternatives remain. Propagation narrows variable domains; heuristics guide branching; common consistency notions include arc-consistency. Constraint-based models can use declarative languages or libraries, such as MiniZinc, ESSENCE, or constraint programming features in Prolog, or libraries in Python or Java. Solvers such as Gecode, Choco, or OR-Tools CP-SAT implement these techniques and can handle problems like scheduling, timetabling, resource allocation, configuration, and puzzle solving.

In operations research and computer science, constraintbased methods are often used for problems where the feasible region is complex or combinatorial. They can be standalone or combined with optimization objectives, producing constraint-based optimization. A related area in systems biology is constraint-based reconstruction and analysis (COBRA), which models metabolic networks using stoichiometric and mass-balance constraints.

Limitations include potential computational hardness and the need for careful modeling to capture real-world constraints without introducing infeasible or overly restrictive formulations.