  Dealing with multi-objective problems by using generation methods has some
interesting advantages since it provides the decision-maker with the complete
information about the set of non-dominated points (Pareto front) and a clear
overview of the problem. However, providing many solutions to the
decision-maker might also be overwhelming. As an alternative approach,
presenting a representative set of solutions of the Pareto front may be
advantageous. Choosing such a representative set is by itself also a
multi-objective problem that must consider the number of solutions to present,
the uniformity, and/or the coverage of the representation, to guarantee its
quality. This paper proposes three algorithms for the representation problem
for multi-objective integer linear programming problems with two or more
objective functions, each one of them dealing with each dimension of the
problem (cardinality, coverage, and uniformity). Such algorithms are all based
on the $\epsilon$-constraint approach. In addition, the paper also presents
strategies to overcome poor estimations of the Pareto front bounds. The
algorithms were tested on the ability to efficiently generate the whole Pareto
front or its representation. The uniformity and cardinality algorithms proved
to be very efficient both in binary and integer problems, being amongst the
best in the literature. Both coverage and uniformity algorithms provide good
quality representations on their targeted objective, while the cardinality
algorithm appears to be the most flexible, privileging uniformity for lower
cardinality representations and coverage on higher cardinality.
