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Filtering AtMostNValue with difference constraints: application to the shift minimisation personnel task scheduling problem. (English) Zbl 1407.90150
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 AllDifferent constraints and a single 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 AtMostNValue. In particular, we provide simple but significant improvement of the state-of-the-art AtMostNValue propagator of Bessière et al., to filter the conjunction of an 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.

90B35 Deterministic scheduling theory in operations research
68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)
90C10 Integer programming
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