Dominance rules in combinatorial optimization problems

Antoine Jouglet (1) , Jacques Carlier (1)

1 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]

The aim of this paper is to study the concept of a "dominance rule" in the context of combinatorial optimization. A dominance rule is established in order to reduce the solution space of a problemby adding new constraints to it, either in a procedure that aims to reduce the domains of variables, or directly in building interesting solutions. Dominance rules have been extensively used over the last fifty years. Surprisingly, to our knowledge, no detailed description of them can be found in the literature other than a few short formal descriptions in the context of enumerativemethods. We are therefore proposing an investigation into what dominance rules are. We first provide a definition of a dominance rule with its different nuances. Next, we analyze how dominance rules are generally formulated and what are the consequences of such formulations. Finally, we enumerate the common characteristics of dominance rules encountered in the literature and in the usual process of solving combinatorial optimization problems.

Mots clés: combinatorial optimization; dominance rules; constraints; modeling

Domaines: Recherche opérationnelle [math.OC]

Antoine Jouglet, Jacques Carlier. Dominance rules in combinatorial optimization problems. European Journal of Operational Research, 2011, 212, pp.433-444. ⟨10.1016/j.ejor.2010.11.008⟩. ⟨hal-00625751⟩