Journal
JOURNAL OF GLOBAL OPTIMIZATION
Volume 80, Issue 1, Pages 63-86Publisher
SPRINGER
DOI: 10.1007/s10898-020-00971-3
Keywords
Multiobjective optimization; KKT approximation; Proximity measure
Funding
- Projekt DEAL
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The paper presents a proximity measure for KKT conditions violation, which can be used as an indicator for measuring the proximity of a point to the set of efficient solutions. It is well suited for algorithmic use within evolutionary algorithms.
An important aspect of optimization algorithms, for instance evolutionary algorithms, are termination criteria that measure the proximity of the found solution to the optimal solution set. A frequently used approach is the numerical verification of necessary optimality conditions such as the Karush-Kuhn-Tucker (KKT) conditions. In this paper, we present a proximity measure which characterizes the violation of the KKT conditions. It can be computed easily and is continuous in every efficient solution. Hence, it can be used as an indicator for the proximity of a certain point to the set of efficient (Edgeworth-Pareto-minimal) solutions and is well suited for algorithmic use due to its continuity properties. This is especially useful within evolutionary algorithms for candidate selection and termination, which we also illustrate numerically for some test problems.
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