Solving finite-domain linear constraints in presence of the $\texttt{alldifferent}$
This work addresses a specific bottleneck in constraint programming for combinatorial optimization, but it is incremental as it builds on existing filtering algorithms.
The paper tackles the problem of improving filtering for linear constraints in constraint satisfaction problems when combined with alldifferent constraints, resulting in stronger bounds and propagation, with experimental evaluation showing great potential on five test problems.
In this paper, we investigate the possibility of improvement of the widely-used filtering algorithm for the linear constraints in constraint satisfaction problems in the presence of the alldifferent constraints. In many cases, the fact that the variables in a linear constraint are also constrained by some alldifferent constraints may help us to calculate stronger bounds of the variables, leading to a stronger constraint propagation. We propose an improved filtering algorithm that targets such cases. We provide a detailed description of the proposed algorithm and prove its correctness. We evaluate the approach on five different problems that involve combinations of the linear and the alldifferent constraints. We also compare our algorithm to other relevant approaches. The experimental results show a great potential of the proposed improvement.