Utilitarian and Egalitarian Solutions for Multi-objective Constraint Optimization

We address the problem of multi-objective constraint optimization problems (MO-COPs). Solving a MO-COP traditionally consists in computing the set of all Pareto optimal solutions, which is an exponentially large set in the general case. So this causes two main problems: first is the time complexity concern, second is a lack of decisiveness. In this paper, we formalize the notion of a MO-COP operator which associates every MO-COP with a subset of Pareto optimal solutions satisfying some desirable additional properties. Then, we present two specific classes of MO-COP operators that give preference to some subsets of Pareto optimal solutions. These operators correspond to two classical doctrines in Decision Theory: utilitarianism and egalitarianism. They compute solutions much more efficiently than standard operators computing all Pareto optimal solutions. In practice, they return a very few number of solutions even for problems involving a high number of objectives.