Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Combining convergence and diversity in evolutionary multiobjective optimization
Evolutionary Computation
Covariance Matrix Adaptation for Multi-objective Optimization
Evolutionary Computation
Approximating the Volume of Unions and Intersections of High-Dimensional Geometric Objects
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
On set-based multiobjective optimization
IEEE Transactions on Evolutionary Computation
Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach
IEEE Transactions on Evolutionary Computation
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
Performance assessment of multiobjective optimizers: an analysis and review
IEEE Transactions on Evolutionary Computation
Convergence of set-based multi-objective optimization, indicators and deteriorative cycles
Theoretical Computer Science
Approximation quality of the hypervolume indicator
Artificial Intelligence
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Evolutionary multi-objective optimization deals with the task of computing a minimal set of search points according to a given set of objective functions. The task has been made explicit in a recent paper by Zitzler et al. [13]. We take an order-theoretic view on this task and examine how the use of indicator functions can help to direct the search towards Pareto optimal sets. Thereby, we point out that evolutionary algorithms for multi-objective optimization working on the dominance relation of search points have to deal with a cyclic behavior that may lead to worsenings with respect to the Pareto-dominance relation defined on sets. Later on, we point out in which situations well-known binary and unary indicators can help to avoid this cyclic behavior.