Theory and Algorithms for Finding Knees
Herausgeber: Purshouse, Robin C. and Fleming, Peter J. and Fonseca, Carlos M. and Greco, Salvatore and Shaw, Jane
Buchtitel: Evolutionary Multi-Criterion Optimization
Reihe: Lecture Notes in Computer Science
Verlag: Springer Berlin Heidelberg
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 results on a number of test problems.
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DOI Link: 10.1007/978-3-642-37140-0_15