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 criterion vectors (Pareto front) and a clear overview of the different trade-offs of the problem. However, providing many solutions to the decision-maker may also be overwhelming. As an alternative approach, showing a representative set 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 alternatives 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 $ϵ$-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 a representation of it. The uniformity and cardinality algorithms proved to be very efficient both on binary and on 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.

使用生成方法处理多目标问题具有一些有趣的优势，因为它为决策者提供了有关非支配准则向量集（帕累托前沿）的完整信息，以及对不同准则向量权衡的清晰概述问题。然而，为决策者提供许多解决方案也可能会让人不知所措。作为替代方法，显示一组具有代表性的帕累托前沿可能是有利的。选择这样一个代表集本身也是一个多目标问题，必须考虑要呈现的备选方案的数量、代表的均匀性和/或覆盖范围，以保证其质量。本文针对具有两个或多个目标函数的多目标整数线性规划问题的表示问题提出了三种算法，他们每个人都处理问题的每个维度（基数、覆盖率和均匀性）。这些算法都是基于$\epsilon$-约束方法。此外，本文还提出了克服帕累托前沿边界估计不佳的策略。这些算法在有效生成整个帕累托前沿或其表示的能力上进行了测试。均匀性和基数算法被证明在二进制和整数问题上都非常有效，在文献中名列前茅。覆盖率和均匀性算法都在其目标上提供了高质量的表示，而基数算法似乎是最灵活的，优先考虑较低基数表示的均匀性和较高基数的覆盖率。