*flip++: a Partial Constraint Satisfaction System for Steelmaking Scheduling

Real world problems are often overconstrained, ill-deened, or tolerate good though suboptimal solutions as long as those are found before a deadline. Such problems are often called partial constraint satisfaction problems (PCSPs). The model for PCSPs was initially inspired by classic constraint satisfaction methods. Another path leading to comparable notions and originating from fuzzy decision making is introduced in the present paper, adding the following features to increase modeling capability: gradual satisfaction, priority, and compromises. Because of these additional degrees of freedom, fuzzy constraints must be ne-tuned for a certain task. However, such ne-tuning cannot be done for all possible instantiations of a problem, and thus is generally done on prototypical constraints. These templates are applied during run-time to a certain actual situation, i.e., dynamically adapted and applied only where necessary. This paper describes issues arising from the existence of such dynamic constraints and how they are handled in the *FLIP++ optimization libraries. Examples from a steelmaking scheduling application are given. Theoretical analysis and some initial experiments indicate that our method makes PCS ready to confront real world problems.