An integer formulation based on common supersequences to solve the Permutation Problem using a Unit-Capacity Robot
Résumé
Given a finite sequence S over an alphabet, a sequence S’ is a supersequence of S if we can delete some characters in S’ such that the remaining sequence is equal to S. Given a finite set R of sequences, a common supersequence of R is a sequence which is a supersequence of every sequences of R. In this article, using a graph model introduced in [Bendotti et al 2013], we give a necessary and sufficient condition for the PPCR to be feasible (i.e. to posses a solution). We then show that solving a special case of PPCR instances directly reduces to find a shortest common supersequence in a particular sequence set. We propose an integer formulation based on this reduction to solve general case instances. Using this formulation we present some experimental results where large instances coming from the nuclear fuel renewal problem are solved to optimality. In order to produce a solution for non-feasible PPCR instances, we introduce some locations for PPCR instances where a piece can be temporarily hold if required. We show that these locations correspond to Steiner nodes in the graph model and we then extend the integer formulation for the resulting Steiner PPCR.