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arXiv · 1709.10377

Simple Problems: The Simplicial Gluing Structure of Pareto Sets and Pareto Fronts

Naoki Hamada
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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.

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Naoki Hamada. 2017-04-18. Simple Problems: The Simplicial Gluing Structure of Pareto Sets and Pareto Fronts. https://doi.org/10.1145/3067695.3076069

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