OPL is a modeling language for mathematical programming and combinatorial optimization. It is the first language to combine high-level algebraic and set notations from mathematical modeling languages with a rich constraint language and the ability to specify search procedures and strategies that are the essence of constraint programming. This paper describes the facilities available in OPL to specify search procedures. It describes the abstractions of OPL to specify both the search tree (search) and how to explore it (strategies). The paper also illustrates how to use these high-level constructs to implement traditional search procedures in constraint programming and scheduling.

Mathematical modeling and constraint programming languages have orthogonal strengths in stating combinatorial optimization problems. Modeling languages typically feature high-level set and algebraic notations, while constraint programming languages provide a rich constraint language and the ability to specify search procedures. This paper shows that many of the functionalities typically found in modeling languages can be integrated elegantly in constraint programming libraries without dening a specic language or preprocessor. In particular, it presents the design of OPL++, a C++ modeling layer for constraint programming that combines the salient features of both approaches. Of particular interest is the one-to-one correspondance between high-level models and OPL++ statements and the negligible overhead induced by the extensions.