The BIN_COUNTS Constraint: Filtering and Applications
This work addresses constraint programming challenges in bin counting and statistical testing, offering incremental improvements for specific domains.
The paper introduces the BIN_COUNTS constraint for counting decision variables in bins and a new χ² test constraint, applying them to problems like the Balanced Academic Curriculum Problem with numerical studies.
We introduce the BIN_COUNTS constraint, which deals with the problem of counting the number of decision variables in a set which are assigned values that lie in given bins. We illustrate a decomposition and a filtering algorithm that achieves generalised arc consistency. We contrast the filtering power of these two approaches and we discuss a number of applications. We show that BIN_COUNTS can be employed to develop a decomposition for the $χ^2$ test constraint, a new statistical constraint that we introduce in this work. We also show how this new constraint can be employed in the context of the Balanced Academic Curriculum Problem and of the Balanced Nursing Workload Problem. For both these problems we carry out numerical studies involving our reformulations. Finally, we present a further application of the $χ^2$ test constraint in the context of confidence interval analysis.