UMOEA/D: A Multiobjective Evolutionary Algorithm for Uniform Pareto
  Objectives based on Decomposition
Xiaoyuan Zhang Xi Lin Yichi Zhang Yifan Chen Qingfu Zhang
Multiobjective optimization (MOO) is prevalent in numerous applications, in
which a Pareto front (PF) is constructed to display optima under various
preferences. Previous methods commonly utilize the set of Pareto objectives
(particles on the PF) to represent the entire PF. However, the empirical
distribution of the Pareto objectives on the PF is rarely studied, which
implicitly impedes the generation of diverse and representative Pareto
objectives in previous methods. To bridge the gap, we suggest in this paper
constructing \emph{uniformly distributed} Pareto objectives on the PF, so as to
alleviate the limited diversity found in previous MOO approaches. We are the
first to formally define the concept of ``uniformity" for an MOO problem. We
optimize the maximal minimal distances on the Pareto front using a neural
network, resulting in both asymptotically and non-asymptotically uniform Pareto
objectives. Our proposed method is validated through experiments on real-world
and synthetic problems, which demonstrates the efficacy in generating
high-quality uniform Pareto objectives and the encouraging performance
exceeding existing state-of-the-art methods.
  The detailed model implementation and the code are scheduled to be
open-sourced upon publication.