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Simple Problems: The Simplicial Gluing Structure of Pareto Sets and Pareto Fronts
April 18, 2017 Β· Declared Dead Β· π Annual Conference on Genetic and Evolutionary Computation
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Authors
Naoki Hamada
arXiv ID
1709.10377
Category
math.OC: Optimization & Control
Cross-listed
cs.NE
Citations
3
Venue
Annual Conference on Genetic and Evolutionary Computation
Last Checked
3 months ago
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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