Local Probing for Resource

This paper investigates a form of algorithm hybridization that combines constraint satisfaction algorithms with local search algorithms. On one hand, constraint satisfaction algorithms are eeective at nding feasible solutions for tightly constrained problems with complex constraints. On the other hand, local search algorithms are usually better at nding solutions that are good with respect to an optimization function when the problem is loosely constrained, or has simple constraints that can be embedded into neighbourhood operators. The tight hybridization of these two algorithm classes may lead to more powerful algorithms for certain classes of large scale combinatorial optimization problems (LSCOs). A new hybrid algorithm, local probing, is introduced for resource constrained scheduling where the aim is to optimize an objective function while satisfying both resource and temporal constraints. The problem is solved in a backtracking branch-and-bound tree. In each node of the tree, a relaxed temporal sub-problem is created by removing resource constraints, and a proberr which, in this paper, consists of a local search algorithm with a dynamic neighbourhood operator generates a partial solution that satisses the remaining constraints and gives a good value to the objective function. Possible resource violations are solved in the backtracking search tree by posting (or removing when backtracking) temporal precedence constraints which are guaranteed to be satissed by the neighbourhood operator. For the local search prober, we introduce dynamic neighbourhood operators that satisfy the constraints of the temporal sub-problem using techniques based on limited discrepancy search and linear programming. Experiments are carried out on a class of resource constrained scheduling problems extended with a generic objective function.