Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Constraint satisfaction in logic programming
Constraint satisfaction in logic programming
An algorithm for solving the job-shop problem
Management Science
Solving large combinatorial problems in logic programming
Journal of Logic Programming - Logic programming applications
An additive bounding procedure for the asymmetric travelling salesman problem
Mathematical Programming: Series A and B
A filtering algorithm for constraints of difference in CSPs
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Solving TSP with time windows with constraints
Proceedings of the 1999 international conference on Logic programming
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part I
Hybrid Benders Decomposition Algorithms in Constraint Logic Programming
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
A global constraint for total weighted completion time for cumulative resources
Engineering Applications of Artificial Intelligence
A Global Constraint for Total Weighted Completion Time
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Hi-index | 0.00 |
Constraint Programming (CP) has been successfully applied to several combinatorial optimization problems. One of its advantages is the availability of complex global constraints performing efficient propagation and interacting with each other through shared variables. However, CP techniques have shown their limitations in dealing with optimization problems since the link between the objective function and problem decision variables is often quite loose and does not produce an effective propagation. We propose to integrate optimization components in global constraints, aimed at optimally solving a relaxation corresponding to the constraint itself. The optimal solution of the relaxation provides pieces of information which can be exploited in order to perform pruning on the basis of cost-based reasoning. In fact, we exploit reduction rules based on lower bound and reduced costs calculation to remove those branches which cannot improve the best solution found so far. The interest of integrating efficient well-known Operations Research (OR) algorithms into CP is mainly due to the smooth interaction between CP domain reduction and information provided by the relaxation acting on variable domains which can be seen as a icommunication channel among different techniques. We have applied this technique to symmetric and asymmetric Traveling Salesman Problem (TSP) instances both because the TSP is an interesting problem arising in many real-life applications, and because pure CP techniques lead to disappointing results for this problem. We have tested the proposed optimization constraints using ILOG solver. Computational results on benchmarks available from literature, and comparison with related approaches are described in the paper. The proposed method on pure TSPs improves the performances of CP solvers, but is still far from the OR state of the art techniques for solving the problem. However, due to the flexibility of the CP framework, we could easily use the same technique on TSP with Time Windows, a time constrained variant of the TSP. For this type of problem, we achieve results that are comparable with state of the art OR results.