Section: Application Domains

Combinatorial optimization

The number and economic impact of combinatorial optimization problems found in the industrial world are constantly increasing. They cover:

• resource allocation;

• placement, bin packing;

• scheduling;

• planning;

• transport;

• etc.

The last fifty years have brought many improvements in Operations Research resolution techniques. In this context, Constraint Programming can be seen as providing, on the one hand, constraint propagation algorithms that can be applied to various numerical or symbolic constraints, and on the other hand, declarative languages to model real-life problems and express complex resolution strategies. The latter point is crucial for designing new algorithms that cannot be defined without a sufficiently high-level language to express them. It allowed for better results than traditional methods, for instance in scheduling, and is promised to an even better future when thinking about the cooperation of global resolution, local consistency techniques and search methods.

The European FP6 Strep project Net-WMS that we have coordinated, has shown the benefit of combining discrete geometry constraints with rules to express physical, common sense and packing business constraints to solve packing problems in the context of warehouse management systems for the automotive industry. In this context, we have developed a rule-based modeling language, called Rules2CP , to express requirements in a declarative and flexible manner, and compile them to efficient constraint programs using reified constraints and a global constraint dedicated to geometrical placement problems in high dimension.