In this paper, we are interested in producing discrete and tractable representations of the set of non-dominated points for multi-objective optimization problems, both in the continuous and discrete cases. These representations must satisfy some conditions of coverage, i.e. providing a good approximation of the non-dominated set, spacing, i.e. without redundancies, and cardinality, i.e. with the smallest possible number of points. This leads us to introduce the new concept of (e, e′)-kernels, or e-kernels when ɛ′=ɛ is possible, which correspond to e-Pareto sets satisfying an additional condition of e′-stability. Among these, the kernels of small, or possibly optimal, cardinality are claimed to be good representations of the non-dominated set.
['Cristina Bazgan', 'Florian Jamain', 'Daniel Vanderpooten']
Discrete representation of the non-dominated set for multi-objective optimization problems using kernels