Genetic algorithm operators restricted to precedent constraint sets: genetic algorithm designs with or without branch and bound approach for solving scheduling problems with disjunctive constraints

We consider any scheduling problem in which the decisions to be made consist in choosing the direction of a set of disjunctive edges. To represent either any set of feasible solutions where some choices are already done on a sub-set of disjunctive edges or any feasible solution, we designed a ternary direct coding. This ternary coding may be integrated both into branch and bound approaches (BaB) and into genetic algorithm approaches (GA). We describe the genetic operators associated with this ternary direct coding. We then show how GA may be strongly integrated into a BaB algorithm using a single machine example 1//ΣT_i, where Emmons dominant properties may be incorporated using again the same ternary direct coding. The paper ends with some numerical examples