Použití programování s omezujícími podmínkami při řešení diskrétních úloh

Application of constraint programming (CP) is one of the possible ways of solving discrete problems. It can be used for both search for feasible solution and optimization. CP offers a whole range of approaches for either a solution search or for acceleration of the process of its search -- from search algorithms or consistency techniques to propagation algorithms, which are basically only a combination of the two preceding methods. For optimization we most often use branch and bound approach, which differs in some aspects from a method of the same name used in mathematical programming (MP). Comparison of CP and MP is interesting in many other aspects. With CP the formulation of problems is more flexible, which allows for creation of often simpler and smaller models. On the other hand, its disadvantage is a limited use: Constraint satisfaction (optimisation) problem, as we call the constraint programming problem, cannot contain any discrete variables. CP is suitable especially for problems with a lot of constraints and only few variables, ideally only two. In the beginning, the paper introduces the basic terms of constraint programming, then it describes algorithms and techniques used for solving discrete problems and compares CP with mathematical programming.