Download Complete Characterization of Near-Optimal Sequences for the Two

Complete Characterization of Near-Optimal
Sequences for the Two-Machine Flow Shop
Scheduling Problem
Jean-Charles Billaut 1 , Emmanuel Hebrard 2, and Pierre Lopez
2
1
Université François-Rabelais Tours
Laboratoire d’Informatique
64 avenue Jean Portalis, 37200 Tours, France
[email protected]
2
CNRS, LAAS, 7 avenue du colonel Roche, 31077 Toulouse, France
Université de Toulouse, UPS, INSA, INP, ISAE, UT1, UTM, LAAS, 31077 Toulouse,
France
{ hebrard,lopez } @laas.fr
Abstract.
In a two-machine flow shop scheduling problem, the set of approximate sequences ( i.e. , solutions within a factor 1+ of the optimal)
can be mapped to the vertices of a permutation lattice.
We introduce two approaches, based on properties derived from the
analysis of permutation lattices, for characterizing large sets of
near-optimal solutions. In the first approach, we look for a sequence of
minimum level in the lattice, since this solution is likely to cover many
optimal or near-optimal solutions. In the second approach, we look for
all sequences of minimal level, thus covering all -approximate sequences.
Integer linear programming and constraint programming models are
first proposed to solve the former problem. For the latter problem, a
direct exploration of the lattice, traversing it by a simple tree search
procedure, is proposed. Computational experiments are given to evaluate these methods and to illustrate the interest and the limits of such
approaches.