Multiobjective query optimization
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Bicriterion Single Machine Scheduling with Resource Dependent Processing Times
SIAM Journal on Optimization
Combining convergence and diversity in evolutionary multiobjective optimization
Evolutionary Computation
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Multicriteria Optimization
Efficiently computing succinct trade-off curves
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Covariance Matrix Adaptation for Multi-objective Optimization
Evolutionary Computation
G-Metric: an M-ary quality indicator for the evaluation of non-dominated sets
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Theory of the hypervolume indicator: optimal μ-distributions and the choice of the reference point
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
Investigating and exploiting the bias of the weighted hypervolume to articulate user preferences
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Multiplicative approximations and the hypervolume indicator
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
On set-based multiobjective optimization
IEEE Transactions on Evolutionary Computation
Set-based multi-objective optimization, indicators, and deteriorative cycles
Proceedings of the 12th annual conference on Genetic and evolutionary computation
The maximum hypervolume set yields near-optimal approximation
Proceedings of the 12th annual conference on Genetic and evolutionary computation
How good is the Chord algorithm?
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Tight bounds for the approximation ratio of the hypervolume indicator
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
Small Approximate Pareto Sets for Biobjective Shortest Paths and Other Problems
SIAM Journal on Computing
An efficient algorithm for computing hypervolume contributions**
Evolutionary Computation
The logarithmic hypervolume indicator
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
An EMO algorithm using the hypervolume measure as selection criterion
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
Running time analysis of a multiobjective evolutionary algorithm on simple and hard problems
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
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
Properties of an adaptive archiving algorithm for storing nondominated vectors
IEEE Transactions on Evolutionary Computation
Performance assessment of multiobjective optimizers: an analysis and review
IEEE Transactions on Evolutionary Computation
Parameterized average-case complexity of the hypervolume indicator
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Population size matters: rigorous runtime results for maximizing the hypervolume indicator
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Speeding up many-objective optimization by Monte Carlo approximations
Artificial Intelligence
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In order to allow a comparison of (otherwise incomparable) sets, many evolutionary multi-objective optimizers use indicator functions to guide the search and to evaluate the performance of search algorithms. The most widely used indicator is the hypervolume indicator. It measures the volume of the dominated portion of the objective space bounded from below by a reference point. Though the hypervolume indicator is very popular, it has not been shown that maximizing the hypervolume indicator of sets of bounded size is indeed equivalent to the overall objective of finding a good approximation of the Pareto front. To address this question, we compare the optimal approximation ratio with the approximation ratio achieved by two-dimensional sets maximizing the hypervolume indicator. We bound the optimal multiplicative approximation ratio of n points by 1+@Q(1/n) for arbitrary Pareto fronts. Furthermore, we prove that the same asymptotic approximation ratio is achieved by sets of n points that maximize the hypervolume indicator. However, there is a provable gap between the two approximation ratios which is even exponential in the ratio between the largest and the smallest value of the front. We also examine the additive approximation ratio of the hypervolume indicator in two dimensions and prove that it achieves the optimal additive approximation ratio apart from a small ratio =