Authors
Pradyumn Kumar Shukla, Marlon Alexander Braun, Hartmut Schmeck
Publication date
2013
Conference
Evolutionary Multi-Criterion Optimization: 7th International Conference, EMO 2013, Sheffield, UK, March 19-22, 2013. Proceedings 7
Pages
156-170
Publisher
Springer Berlin Heidelberg
Description
A multi-objective optimization problem involves multiple and conflicting objectives. These conflicting objectives give rise to a set of Pareto-optimal solutions. However, not all the members of the Pareto-optimal set have equally nice properties. The classical concept of proper Pareto-optimality is a way of characterizing good Pareto-optimal solutions. In this paper, we metrize this concept to induce an ordering on the Pareto-optimal set. The use of this metric allows us to define a proper knee region, which contains solutions below a user-specified threshold metric. We theoretically analyze past definitions of knee points, and in particular, reformulate a commonly used nonlinear program, to achieve convergence results. Additionally, mathematical properties of the proper knee region are investigated. We also develop two multi-objective evolutionary algorithms towards finding proper knees and present simulation …
Total citations
20132014201520162017201820192020202120222023202432373315121
Scholar articles
PK Shukla, MA Braun, H Schmeck - … Optimization: 7th International Conference, EMO 2013 …, 2013