Multiple Objective Optimization with Vector Evaluated Genetic Algorithms
Proceedings of the 1st International Conference on Genetic Algorithms
Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study
PPSN V Proceedings of the 5th International Conference on Parallel Problem Solving from Nature
Completely Derandomized Self-Adaptation in Evolution Strategies
Evolutionary Computation
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
Convergence of hypervolume-based archiving algorithms I: effectiveness
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Hypervolume-based multiobjective optimization: Theoretical foundations and practical implications
Theoretical Computer Science
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Evolutionary multi-objective algorithms (EMOA) using performance indicators for the selection of individuals have turned out to be a successful technique for multi-objective problems. Especially, the selection based on the $\mathcal{S}$-metric, as implemented in the SMS-EMOA, seems to be effective. A special feature of this EMOA is the greedy (μ + 1) selection. Based on a pathological example for a population of size two and a discrete Pareto front it has been proven that a (μ + 1)- (or 1-greedy) EMOA may fail in finding a population maximizing the $\mathcal{S}$-metric. This work investigates the performance of (μ + 1)-EMOA with small fixed-size populations on Pareto fronts of innumerable size. We prove that an optimal distribution of points can always be achieved on linear Pareto fronts. Empirical studies support the conjecture that this also holds for convex and concave Pareto fronts, but not for continuous shapes in general. Furthermore, the pathological example is generalized to a continuous objective space and it is demonstrated that also (μ + k )-EMOA are not able to robustly detect the globally optimal distribution.