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Convergence of Set-Based Multi-Objective Optimization, Indicators, and Deteriorative Cycles
| Citations: | 2 - 2 self |
BibTeX
@MISC{Berghammer_convergenceof,
author = {Rudolf Berghammer and Tobias Friedrich and Frank Neumann},
title = {Convergence of Set-Based Multi-Objective Optimization, Indicators, and Deteriorative Cycles },
year = {}
}
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Abstract
Multi-objective optimization deals with the task of computing a set of solutions that represents possible trade-offs with respect to a given set of objective functions. Set-based approaches such as evolutionary algorithms are very popular for solving multi-objective optimization problems. Convergence of set-based approaches for multi-objective optimization is essential for their success. We take an order-theoretic view on the convergence of set-based multi-objective optimization and examine how the use of indicator functions can help to direct the search towards Pareto optimal sets. In doing so, we point out that set-based multi-objective optimization working on the dominance relation of search points has to deal with a cyclic behavior that may lead to worsening with respect to the Pareto-dominance relation defined on sets. Later on, we show in which situations well-known binary and unary indicators can help to avoid this cyclic behavior and therefore guarantee convergence of the algorithm. We also study the impact of deteriorative cycles on the runtime behavior and give an example in which they provably slow down the optimization process.
Keyphrases
set-based multi-objective optimization deteriorative cycle set-based approach cyclic behavior possible trade-off search towards pareto optimal set multi-objective optimization deal guarantee convergence order-theoretic view search point unary indicator dominance relation indicator function pareto-dominance relation optimization process multi-objective optimization problem runtime behavior evolutionary algorithm multi-objective optimization objective function
