an:06302283
Zbl 1407.90150
Fages, Jean-Guillaume; Lap??gue, Tanguy
Filtering AtMostNValue with difference constraints: application to the shift minimisation personnel task scheduling problem
EN
Artif. Intell. 212, 116-133 (2014).
00333174
2014
j
90B35 68T20 90C10
constraint-programming; global constraints; AtMostNValue; shift minimisation personnel task scheduling problem
Summary: The problem of minimising the number of distinct values among a set of variables subject to difference constraints occurs in many real-life contexts. This is the case of the Shift Minimisation Personnel Task Scheduling Problem, introduced by Krishnamoorthy et al., which is used as a case study all along this paper. Constraint-Programming enables to formulate this problem easily, through several \texttt{AllDifferent} constraints and a single \texttt{AtMostNValue} constraint. However, the independence of these constraints results in a poor lower bounding, hence a difficulty to prove optimality. This paper introduces a formalism to describe a family of propagators for \texttt{AtMostNValue}. In particular, we provide simple but significant improvement of the state-of-the-art \texttt{AtMostNValue} propagator of Bessi??re et al., to filter the conjunction of an \texttt{AtMostNValue} constraint and disequalities. In addition, we provide an original search strategy which relies on constraint reification. Extensive experiments show that our contribution significantly improves a straightforward model, so that it competes with the best known approaches from Operational Research.