Selective Constraint Generation for the MS-CFLP-CI

The problem of enabling localization of facilities with incompatibilities between clients (MS-CFLP-CI) adds to the classic problem the requirement that incompatible pairs are not served by the same facility. Recent work has advanced with Simulated Annealing and Large Neighborhood Search, especially in large instances. We review the role of exact methods by selectively generating incompatibility constraints. The approach combines effective flow-based lazy separation, initial cuts, and clicks. We certified optimality for 8 instances out of a set of 30, 3 of which are new optimals that improve the incumbents previously reported in the literature. In the time limit, the fast solver improves the values reported by the 2025 LNS. For the other instances evaluated, the method did not prove to be as efficient as the state of the art. The structural analysis shows that less than 1% of the incompatibility constraints are active in the optimums of the largest instance analyzed, explaining the effectiveness of the selective strategy.