New <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si22.svg"><mml:mrow><mml:mi>ϵ</mml:mi><mml:mo linebreak="goodbreak">−</mml:mo></mml:mrow></mml:math>constraint methods for multi-objective integer linear programming: A Pareto front representation approach

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