Encodings of the Sequence Constraint
نویسندگان
چکیده
The SEQUENCE constraint is useful in modelling car sequencing, rostering, scheduling and related problems. We introduce half a dozen new encodings of the SEQUENCE constraint, some of which do not hinder propagation. We prove that, down a branch of a search tree, domain consistency can be enforced on the SEQUENCE constraint in just O(n log n) time. This improves upon the previous bound of O(n) for each call down the tree. We also consider a generalization of the SEQUENCE constraint – the Multiple SEQUENCE constraint. Our experiments suggest that, on very large and tight problems, domain consistency algorithms are best. However, on smaller or looser problems, much simpler encodings are better, even though these encodings hinder propagation. When there are multiple SEQUENCE constraints, a more expensive propagator shows promise.
منابع مشابه
An Efficient Bi-objective Genetic Algorithm for the Single Batch-Processing Machine Scheduling Problem with Sequence Dependent Family Setup Time and Non-identical Job Sizes
This paper considers the problem of minimizing make-span and maximum tardiness simultaneously for scheduling jobs under non-identical job sizes, dynamic job arrivals, incompatible job families,and sequence-dependentfamily setup time on the single batch- processor, where split size of jobs is allowed between batches. At first, a new Mixed Integer Linear Programming (MILP) model is proposed for t...
متن کاملA Lower Bound on CNF Encodings of the At-Most-One Constraint
Constraint “at most one” is a basic cardinality constraint which requires that at most one of its n boolean inputs is set to 1. This constraint is widely used when translating a problem into a conjunctive normal form (CNF) and we investigate its CNF encodings suitable for this purpose. An encoding differs from a CNF representation of a function in that it can use auxiliary variables. We are esp...
متن کاملLocal Search on SAT-encoded Colouring Problems
Constraint satisfaction problems can be SAT-encoded in more than one way, and the choice of encoding can be as important as the choice of search algorithm. Theoretical results are few but experimental comparisons have been made between encodings, using both local and backtrack search algorithms. This paper compares local search performance on seven encodings of graph colouring benchmarks. Two o...
متن کاملLocal Search on SAT-Encoded CSPs
Constraint satisfaction problems can be SAT-encoded in more than one way, and the choice of encoding can be as important as the choice of search algorithm. Theoretical results are few but experimental comparisons have been made between encodings, using both local and backtrack search algorithms. This paper compares local search performance on seven encodings of graph colouring benchmarks. Two o...
متن کاملLocal Consistencies in SAT
We introduce some new mappings of constraint satisfaction problems into propositional satisfiability. These encodings generalize most of the existing encodings. Unit propagation on those encodings is the same as establishing relational k-arc consistency on the original problem. They can also be used to establish (i,j)-consistency on binary constraints. Experiments show that these encodings are ...
متن کامل