Online computation and competitive analysis
Online computation and competitive analysis
Covariance Matrix Adaptation for Multi-objective Optimization
Evolutionary Computation
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
Approximating the volume of unions and intersections of high-dimensional geometric objects
Computational Geometry: Theory and Applications
On set-based multiobjective optimization
IEEE Transactions on Evolutionary Computation
An efficient algorithm for computing hypervolume contributions**
Evolutionary Computation
On sequential online archiving of objective vectors
EMO'11 Proceedings of the 6th international conference on Evolutionary multi-criterion optimization
Convergence of hypervolume-based archiving algorithms I: effectiveness
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Approximating the least hypervolume contributor: NP-hard in general, but fast in practice
Theoretical Computer Science
Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach
IEEE Transactions on Evolutionary Computation
Bounding the effectiveness of hypervolume-based (µ+λ)-archiving algorithms
LION'12 Proceedings of the 6th international conference on Learning and Intelligent Optimization
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We study the convergence behavior of (μ+λ)-archiving algorithms. A (μ+λ)-archiving algorithm defines how to choose in each generation μ children from μ parents and λ offspring together. Archiving algorithms have to choose individuals online without knowing future offspring. Previous studies assumed the offspring generation to be best-case. We assume the initial population and the offspring generation to be worst-case and use the competitive ratio to measure how much smaller hypervolumes an archiving algorithm finds due to not knowing the future in advance. We prove that all archiving algorithms which increase the hypervolume in each step (if they can) are only μ-competitive. We also present a new archiving algorithm which is (4+2/μ)-competitive. This algorithm not only achieves a constant competitive ratio, but is also efficiently computable. Both properties provably do not hold for the commonly used greedy archiving algorithms, for example those used in SIBEA, SMS-EMOA, or the generational MO-CMA-ES.