Introduction to algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Comparison of Multiobjective Evolutionary Algorithms: Empirical Results
Evolutionary Computation
Covariance Matrix Adaptation for Multi-objective Optimization
Evolutionary Computation
Proceedings of the 9th 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
Articulating user preferences in many-objective problems by sampling the weighted hypervolume
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
The measure of Pareto optima applications to multi-objective metaheuristics
EMO'03 Proceedings of the 2nd international conference on Evolutionary multi-criterion optimization
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
Articulating user preferences in many-objective problems by sampling the weighted hypervolume
Proceedings of the 11th 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
Proceedings of the 12th annual conference on Genetic and evolutionary computation
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
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
An efficient algorithm for computing hypervolume contributions**
Evolutionary Computation
SEAL'10 Proceedings of the 8th international conference on Simulated evolution and learning
The logarithmic hypervolume indicator
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Hypervolume-based multiobjective optimization: Theoretical foundations and practical implications
Theoretical Computer Science
Approximation quality of the hypervolume indicator
Artificial Intelligence
Population size matters: rigorous runtime results for maximizing the hypervolume indicator
Proceedings of the 15th annual conference on Genetic and evolutionary computation
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Optimizing the hypervolume indicator within evolutionary multiobjective optimizers has become popular in the last years. Recently, the indicator has been generalized to the weighted case to incorporate various user preferences into hypervolume-based search algorithms. There are two main open questions in this context: (i) how does the specified weight influence the distribution of a fixed number of points that maximize the weighted hypervolume indicator? (ii) how can the user articulate her preferences easily without specifying a certain weight distribution function? In this paper, we tackle both questions. First, we theoretically investigate optimal distributions of μ points that maximize the weighted hypervolume indicator. Second, based on the obtained theoretical results, we propose a new approach to articulate user preferences within biobjective hypervolume-based optimization in terms of specifying a desired density of points on a predefined (imaginary) Pareto front. Within this approach, a new exact algorithm based on dynamic programming is proposed which selects the set of μ points that maximizes the (weighted) hypervolume indicator. Experiments on various test functions show the usefulness of this new preference articulation approach and the agreement between theory and practice.