Simple Problems: The Simplicial Gluing Structure of Pareto Sets and Pareto Fronts
Optimization and Control
2017-10-02 v1 Neural and Evolutionary Computing
Abstract
Quite a few studies on real-world applications of multi-objective optimization reported that their Pareto sets and Pareto fronts form a topological simplex. Such a class of problems was recently named the simple problems, and their Pareto set and Pareto front were observed to have a gluing structure similar to the faces of a simplex. This paper gives a theoretical justification for that observation by proving the gluing structure of the Pareto sets/fronts of subproblems of a simple problem. The simplicity of standard benchmark problems is studied.
Keywords
Cite
@article{arxiv.1709.10377,
title = {Simple Problems: The Simplicial Gluing Structure of Pareto Sets and Pareto Fronts},
author = {Naoki Hamada},
journal= {arXiv preprint arXiv:1709.10377},
year = {2017}
}
Comments
10 pages, accepted at GECCO'17 as a poster paper (2 pages)