Variable Objective Large Neighborhood Search: A Practical Approach to Solve Over-Constrained Problems

Everyone having used Constraint Programming (CP) to solve hard combinatorial optimization problems with a standard exhaustive Branch & Bound Depth First Search (B&B DFS) has probably experienced scalability issues. In the 2011 Panel of the Future of CP, one of the identified challenges was the need to handle large-scale problems. In this paper, we address the scalability issues of CP when minimizing a sum objective function. We suggest extending the Large Neighborhood Search (LNS) framework enabling it with the possibility of changing dynamically the objective function along the restarts. The motivation for this extended framework - called the Variable Objective Large Neighborhood Search (VO-LNS) - is solving efficiently a real-life over-constrained timetabling application. Our experiments show that this simple approach has two main benefits on solving this problem: 1) a better pruning, boosting the speed of LNS to reach high quality solutions, 2) a better control to balance or weight the terms composing the sum objective function, especially in over-constrained problems.