Linear relaxations and reduced-cost based propagation of continuous variable subscripts

In hybrid solvers for combinatorial optimisation, combining Constraint (Logic) Programming (CLP) and Mixed Integer Programming (MIP), it is important to have tight connections between the two domains. We extend and generalise previous work on automatic linearisations and propagation of symbolic CLP constraints that cross the boundary between CLP and MIP. We also present how reduced costs from the linear programming relaxation can be used for domain reduction on the CLP side. Computational results comparing our hybrid approach with pure CLP and MIP on a configuration problem show significant speed-ups.