an:06842360
Zbl 1387.90148
van Cauwelaert, Sascha; Schaus, Pierre
Efficient filtering for the resource-cost alldifferent constraint
EN
Constraints 22, No. 4, 493-511 (2017).
00369522
2017
j
90C10 90C27
alldifferent; assignment cost; filtering; scalability; scheduling; energy; resource; product matrix travelling salesman problem
Summary: This paper studies a family of optimization problems where a set of items, each requiring a possibly different amount of resource, must be assigned to different slots for which the price of the resource can vary. The objective is then to assign items such that the overall resource cost is minimized. Such problems arise commonly in domains such as production scheduling in the presence of fluctuating renewable energy costs or variants of the Travelling Salesman Problem. In Constraint Programming, this can be naturally modeled in two ways: (a) with a sum of \textsc{element} constraints; (b) with a \textsc{MinimumAssignment} constraint. Unfortunately the sum of \textsc{element} constraints obtains a weak filtering and the \textsc{MinimumAssignment} constraint does not scale well on large instances. This work proposes a third approach by introducing the \textsc{ResourceCostAllDifferent} constraint and an associated incremental and scalable filtering algorithm, running in \(\mathcal{O}(n\cdot m)\), where \(n\) is the number of unbound variables and \(m\) is the maximum domain size of unbound variables. Its goal is to compute the total cost in a scalable manner by dealing with the fact that all assignments must be different. We first evaluate the efficiency of the new filtering on a real industrial problem and then on the Product Matrix Travelling Salesman Problem, a special case of the Asymmetric Travelling Salesman Problem. The study shows experimentally that our approach generally outperforms the decomposition and the \textsc{MinimumAssignment} ones for the problems we considered.