A hybrid method for modeling and solving constrained search problems

The paper presents a concept and the outline of the implementation of a hybrid approach to modeling and solving constrained problems. Two environments of mathematical programming (MP) and logic programming (LP) were integrated. The strengths of integer programming (IP) and constraint logic programming (CLP), in which constraints are treated in a different way and different methods are implemented, were combined to use the strengths of both. The proposed approach is particularly important for the decision models with an objective function and many discrete decision variables added up in multiple constraints. To validate the proposed approach, two illustrative examples are presented and solved. The first example is the authors' original model of cost optimization in the supply chain with multimodal transportation. The second one is the two-echelon variant of the well-known Capacitated Vehicle Routing Problem, 2E-CVRP.